A bicycle odometer (w/z eg mk kul2bx:mc67c23f x8mhich measures distance traveled) is attached near the wheel hub and is designed gkzx72m6/ce :klm38 fx mcub 2for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does.eph5 ad )-o,op 6dgvq a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of )pdd5eopvg .h,a-q6o either component of linear acceleration change?

Could a nonrigid body be described by a single 1( :flszrjtf b9j:tr12oxl (l1ril4 3 wtyn6qvalue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger foauw b;n7 .vy3ya7n+qh rce? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do o dvi(uw irva6k;76;5( mijdpa sit-up with your hands behind your head than when your arms are stretched out in front of ;di;5w (6 p(u7i6jdio a rvmvkyou? A diagram may help you to answer this.

A 21-speed bicycle hasiqtd v4f9d) b,d -:chh seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear isidbf-:c ) d,tqhhd9v4 it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to si/yl 7l 7et*/6;.bdatih zgkrun fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, expi/t /d 7*6tl7s elhg.zi;bya klain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry vtbltdnly: f ix/ s:g36s4h54a long, narrow beam?

If the net force on a system is zero, is the net torq85vbi.v 8zeo-4v bsyd g91xfzue also zero? If the net torque on a system is zero, is the neo evv - sf5byx gz4i89.vdb1z8t force zero?

Two inclines have the same height but make different angles withxec ww sbuph-et*q 0sl3g5;qc,/ 8 ;ar the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Expsq*-l0w8ts;rcwq; /gap ,x5b uchee3 lain.

Two solid spheres simultaneously start rolling (from rest) down an tdbbe;q n ; up+4pqoxwh0 ;(e8incline. One sphere haseh uqn0;pxb; 8d ebw(t+qo;p 4 twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same r emius-o9j*b- adius and the same mass. They start from rest at the top of an inij-ums eb 9-o*cline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum aru/v4i4y*kerf *1 ikr kis ;iwii 01j9ie conserved. Yet most moving or rotating obyiiii0ui j/ 1rs;kkk1r e wi*v4*94ifjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how n5xd8m5bz*5vlnu/mfu hh5q1 would this affzlund5hq nu1 855m x*b/v5h fmect the length of the day?

Can the diver of Fig. 8–29 do a somersault eq. m6.17f9usv+h zd5 o wkjncwithout having any initial rotation when she leaves the 6n71f 9m.kce+ d zhojsv .5quwboard?

The moment of inertia of a rotating solid disk about an axis thilc)fbir* 8l:v*c x,hrough its center ofbl*c* f :8liri hx)v,c mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting 9(* jgtyby/ y w1y*k1a.agoygr z mu--on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenj1y g b ow*z*k1atyy (9 g--ruyyga/.mly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the saw/vkjq7 m;:fm me mass. However, one is hollow and the other is solid. Describe an experiment wm:qkm; j v7f/to determine which is which.

The angular velocity of a wheel rotating/:jll.a gl s*o on a horizontal axle points west. In what direction is the :ajo*/llls. glinear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of,x:ce3u 9zzp h a large freely rotating turntable. What happens if you walk towa,z3p x 9cuzh:erd the center?

A shortstop may leap insqp(e- r97wtw to the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direc7st (9qrp-ewwtion (Fig. 8–36). Explain.

On the basis of the law of conservations :/do/. bmvhh of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the h: /dh./bvshmoelicopter stable.

  Express the following angles in radi 3m 3t9merpp*iw4mi+pans: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazi emdv)s7wt0vipx + ss6a+w3s*ng coincidence. Calculate, using the information3vs+a p wes7dismvs 60)x +w*t inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam +6f sl3 1j 4mw7vo *ggcc3schzdiverges at an anglewso 3g*fhz1glcc sv 4jm3c 7+6 $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned o p lh/2 e88blhc0d0jpwff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bladesw0 cje0l2d8lh/b8p ph slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bah7 niodaox 6 y:oh((0sy7 jd,mll makes 1d7:7amox 0yo 6 jiys,o(h(dhn5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter c o+l0,;wp9p gw(puy w5m y:entravels 8.0 km. How many revolutions do the whlwy+ cpy90e ,wo5 :wmu (ngp;peels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. j xe0.k/:d .j9vk,fx e t+lidxCalculate its angular velocity ilji e.9jxxv.,def x+:ktd0k/ n $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. xym24z5 suky29;n tka 8–38). (a) What is the linear speed ofk tu;y5n 2zxy49 a2msk a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angularvsnj*2or )1rs velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po pdh eymiz063 s) z3tiy0p:.mp)ulb h9int
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) mus, ) xp cknt -qti,-fhzw 0pjxr:bq2q,7t a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 1p2 ix0cnj)hq,ft, - qzbqr x7-tw p:k,00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about+ drlc3b6bi m/ its center from 130 rpm to 280 rpm in 4.0 s. Deterl/ridbc3 6+ mbmine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiul32: h hsbr2kfpl*.wjs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts w71 x (ka edn d+ufewj12m8i4raboard the Apollo spacecraft put themselves into a slow rotm(u 41dndrejx 2e1w k8+i afw7ation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to* 69+v9 f lkl:tmutdsm 15,000 rpm in 220 s. Through how many revolutions di mv9t+u*tkfs6:l9 d mld it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in dvz.v x bp:9z8 /gw:koj d(+jw2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stp8jua(-k,aq2xq ia l 9bpr5v8;k ojb;resses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revol;jp5l9aqj2 oqkviru k b;8x8p ba,a -(utions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly froeaj/ vj;57 gd-ntf* dym 240 rpm to 360 rpm in 6.5 s. How far will aa-jgv dty*ef/; n5d j7 point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 859 o jawx-4,kcn1d7hov0rev/min It turns 1500 revolutions before it comes to a stop c,do 1wvhx7o9-akjn 4.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car red5mo4 vfxfplbq j ;e6a8) (n*fhuces its speed uniformly from 95km/h to 45km/h Tfhxvm*lp ofneq8f )b6;j5a(4he tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces ic,gy a3(8lp/tts-on r f9wi)t ts speed uniformly from 95km/h to 45km/h The tires ) lp-8tr/yt3w 9,nicts(faog have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person ridinge +,v,6jvxylkszm3 corc 2ev: f/qs2 / a bike puts all her weight on each pedal when climbing a hill. The pedals rotate i:s,lkjyx2evomz c/6rf+ ,c3e q/ vs2 vn a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force o +5xqqjme+sx +f 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force+x+eqms5xj +q is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheell 7 jd3e.kngo, shown in Fig. 8–39. Assume that a fj3 ed, .7nogklriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m,lja(,f 7ehkfpou 3 .n7 are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and j7aou.n l37,fefp(k hthen released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requiy.ijgrwm 8,xg3 m c8+lpo2e5fre tightening to a torque of 38m5 8 +moj,pyerw32gx.fcl8 ig $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the ar+4, ;,/3el ug;st sgt3xeaopw l4rsixis of roe3ilsw tt;4r ,p;usgal/oe3+ x,s r4gtation is through its center.    $kg \cdot m^2$

  Calculate the moment of inejpu7 5cdtt1( wrtia of a bicycle wheel 66.7 cm in diameter. The rim a (djt7uwp15t cnd tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end ofy0kogvt z7c z:07oxea t zi,(( a thin, light rod is rotated in a horizontal circle of attezo(go( yi,z0z x70k: v7c radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping xcnoy8+,u:di72pe u fa bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between he2y:,u8ep7 o+dfxc niu r hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of 8snj+tn2t0u5,wex/3b 3 aw k1aexvg v the array of point objects shown in Fig. 8–43 abov ee2xa3n b 1ws kt /uva3,5+8jntwgx0ut
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists 6qvqb-cv(n ni /2pr:eof two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning axs mual 2bhdqi2x6e1( * zn0r2t the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each ro eui 2drhl02nx(q1m2bs x6 a*zcket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unife zyuzkq bmal14j13(1 orm cylinder with a radius of 8.50 cm and a mass of 0.580 l1zy k1e(bz1 maqju43kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from r zzqss u3.) tu5+c)-(sxuwbvlest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is ableyqpf8r6 7ome(aq(8,5 itjeo h to accelera(q (oo pmiehje6,yf875qt8 rate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evenvoxb ./ wrw,9stually brought uniformly to rest by a frivw/w . sx9or,bctional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7 3m3pcg xou6/d h y.lp4vhor33$m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the fdsd/k00q hjfbx n0x/9orearm, which rotates about the elbow joint under the action of the triceps musbq khx/jf0d d9/x n00scle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be consideref15makq5i* (d wg8wjav mgix*j8 l+a*d a long thin rod, as shown in Fig. 8–46. l mgq vxaki1jw+w5g * dja*fi8m*(8a5
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of twqwu+emct;6t bcrl. l+w; 50zn o masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest withind9pwppr cohfv+fdkw;:h)) mu/b 702y2 i)gvz four full turns (revolutions) and releases it at a speed o2)m uv7dfh + w:)pohikg/; wy 0 rbc2z9d)vppff 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor haso,+a89hd xkeh 12rppm a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine de7uo s6rch;p7kw n,gg -velops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm roz ayo 0n zhk; o*l-o1:j0r.lwplls without slipping down a lane:y*prl noloh-1 00awz;o kj.z at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respectjezzqz04 (ey7:up aa 9/e s+ nt2ya8yn to the Sun as the sum of two terms,2ye94/nynp :z y+zae87zq u(s ae0at j
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a2621/sl c h/cuwj)al zyx b;hc*eh4 n29gngkv radius of 7.50 m. How much net work is required to accelercy1ngzb 4k/gl wxnh6*hvs9 ;22uh2lc/c jea)ate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from re wa nb3)zn3*1muzi.qest and rolls without slipping dn3ba1um zqzw. *i) ne3own a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is zwji99 dtt+g0 balanced vertically on its tip. It starts to fall and its lower end does not slipgd wjt90+t zi9. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum 2bt h6ur3x (uwgoa-pss6t4 c6pf(mt 6 of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an a bto64 c6-x6sa3(mtsp2 rpfuwug6(htngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform tw72t:4 zg ajigtf) 3scylindrical grinding wheel oft a4j:t w tg732ifgz)s radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is2fis5sw46/; omyx l-oxa d y 9ce/-hkp rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fl-6do oiy; x s-wk5e 4m 2//fpsh9cyxaig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce h+ , dr4lpvh)zter moment of inertia by a factor of about 3.5 when changing from the straight positih p t,+)zvdrl4on to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from q( .pf iwiw ul;,4kz/fan initial rate of 1.0 rev every 2.0 s to auzfwlp,ki i4/ q .;wf( final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around t dkk,0nn)2isrvidj,lb , b*; a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the whe kbn ,02 *rl vtdjnid,,ki);bsel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skatersszm r v.e2q o+ao0;o7 o4jjc: spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the simtocm6v,p;q tklv 5vh 2/ 3 n,z(t+wEarth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertiax2f 2w trelg4q/d/kb bt(p-a, I is dropped onto an identical disk rotating at angular spertegb2k lb qa, 4d2tx/f-p(/wed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.j:jc+7f me 8ob n x+v(yhnw5*c4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the cent xyp2wvck, *2her of a rotating merry-go-round platform22x,kvw hy*pc of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is row p, dk rf.-cxlow 3d89*oyjgv+gz5 /dtating freely with an angular velocity of 0.8 3vgcfd.kj zd5o rx,9g8 p ydolw* /+-w$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapsj atc*u5;m);yk air7d es into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius.57y irud; ;atcj *k)am Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve win 6:p8)lcs nczxds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass +nga8vf0,2ht kb ss0 c$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platfoqum.4oei3jlet0n8+ fe l8 9tmrm, initially at rest, that can rotate freely without friction. The moment of in 3+8fumi lt e e8e04q.jntl9moertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the ed35); .hn fwr shmkb58yiis ry1ge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionly 5;hwybrifhsk n8.53i)m s 1ress bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rots gum,46.qd i+sgm/zlls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds.4q zt,+ /sugimgm s6d from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth suct/. h8 k3pvbzd.6ty h uf74)meo k/rlhh that the same side always faces the Earth. Determine the ratio of the Moon’s spin an ld h6)mh3hy fu8kp vk/.z. teo7/4btrgular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ovh6uhe551 ,hg kvwt: 10x xarvf 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the cy41c4 mzq8 sishape of a uniform cylinder of radius 0.20 m acquires a rotational rate 4 qmi81s y4zccof from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eachvvn0 lqk20eo nryl24: of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diamet2:nek ylrn0q4v o2v0ler 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the4 gi6bueoz nk/*( mr)i rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 timesb;s;n ,ydnvyp v2 2,;/3hyy/jl j qlqu as great, were rotating at a spee sny;bd2/2y nll q/;jyv3hqujyv; p,,d of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution g)q2z, drq.s8jrx1bvl 3x 76 lady1exautomobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diamr1 sa x23ljz,vb8 lxdyxqe 6)r1q.d7geter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustra,lzxmeify6g;jriu 9 1 1op*/ytes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rollingh c6 or)8/ct 11hseoer on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely j 2c ocz3lui3o :xsr,bt82 x7u(i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as showl:ob,x8233oc uxu7sjtr2i cz n. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we g0huwv9jykdeldgt w( 1 j8s.-z.85fmwant to exert a horizontal force F at its axle so that itj(kdw5lhj- 19gz8 vty.swug edf0m8. will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with s;1j*do3t;j ) oaoquge*)g9pstp gt.kpeed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are godepg9gpu3q; )a.k*oojjt;*) t ts1the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.(8g qdp(31 yaf5t,/yhjyz o vi50-kg rock into a sling of length 1.5 m and begins whirling the rock in a near5vgyiyp1(f( za/,dh jq38yotly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as ii+a i yfdkq3r 2-3(ifthin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body. 3 fiq+aidk r(2iiy-f3   

  You are designing a clutch assembly which consists of two cylins maj:7 (lczndlo/mu 3. c:nf2drical plates, of mass2dcmjl 3fu mon n: a:.c(s7z/l $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r r9 6 5)4bj*4z gjzgleurtrk3 prolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must pj4r3ebrl ur ztgjk59z4 6)g*drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dojquy+p+0k 8 pz not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 relaspd/j r x+-z,)fle; volutions as the car reduces its speed uniformly from 90kadl/ re;)-p,fxs+j lzm/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s