A bicycle odometer (which measures distanc ;g- n6agql)msr 6bp2ue traveled) is attached near the wheel hub and is designed for 27)las q b6- ;6npm2ggur-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular vj;gc )2an hipzal)412 3gz bidelocity. Does 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 either component of linear acceleration chang jh adz;nbil3 4g c)ip)2g2za1e?

Could a nonrigid body be d hgi djds2;.og( o -mub/r q-9v-qfwt-escribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a gr 2).ezk* e sc,yiiixcyfuh90 5eater torque than a larger force? 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 a sit-up with your hands behind your heavhfj1 f z,h)c,c2slys2 wdi/ -d than when your arms are stretched out in fro ,vy1-fj2 s,c/hs2 zhfclidw)nt of you? A diagram may help you to answer this.

A 21-speed bicycle has seven g)rsla5u77aw dp ,v1a sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to perp17wa suva )l7ad g5,dal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run favxkvkp9/6 ipwyv7 q5g5k (l/lst have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatv7/ kkyl5wv5ip/ k 9(6pgvxqlional dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long,(l s2tf7t0coj narrow beam?

If the net force on a system is zero, is the net torque als0 +, tjnx6r7ubgxah 8ol3l2c e5hxx/oo zero? If the net torque on a syst72 lt35x6hb+uo j necxgx,8h lorxa0/em is zero, is the net force zero?

Two inclines have the same height but make different angles with the ho )ysxiavzj,tj +:gv7/rizontal. The same steel ball is rolled down each incline. On which inclinj:/ ,ag+ y7v tx)zvisje will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) psjkbm 7:p-1l down an incline. One sphere has 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 energlsbk:7pmj1- py at the bottom?

A sphere and a cylinder have the same radius and the same mass. Th clbjwasmg- , qmwvji0n- 789:ey start from rest at the top of an incline. Which reaches the bot9a-vbw -ml i0w 7sjgm qc8n,:jtom 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 are conseen/) wi.aq8uvmp-h/ orved. Yet most moving or rotating objects eventually slow down and o/hm -a nquvp8./ie)w stop. Explain.

If there were a great migration of pufyqi c vs (0fv6l;6nce) +on-eople toward the Earth’s equator, how would this affect the lenglus(cvv) 6n0f-iqe n6 o y+c;fth of the day?

Can the diver of Fig. 8–d koj7 a4i9w:e cg6e. cn75y/mrquo36w 0pfsb29 do a somersault without having any initial rotation when she leaj 6rdm5wi.sq 74: go9ofa6nyuepkw0/ e bc73 cves the board?

The moment of inertia of a rotating solid disk about an axis through iw+b2s.+n gfyntjt weku / 9:h-ts center of mawy9 u:-s+en.k+ t/fj2 tngb whss 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 on a rotating stool holding a 2-kg mass in each outstr tm15 e hmwr(xsr2ezlo3,t3.)h t5tj vetched hand. If you suddenly drop the masses,z2w rt.,h5totl3ev1s rh) j5 mt3(mxe will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical ablnv-wn/icp+ ll3w - ;nd have the same mass. However, one is hollow and the othe;c -n+in3lllwb w/-vpr is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel r/4meu m9 k:ky4m 7*tq3vsc cwyotating on a horizontal axle points west. In what direction is the linear vel97 v3y*yq emmkccut/ w4:s4mkocity 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 a large freely rotating turnt)+s4t pdnqr m9w5* hngable. What happens if you walk toward the cetwnr *9 p54h dgn)+mqsnter?

A shortstop may leap into the air to catch a ball and throw it quickly. As he t*dz9u.m*+a)hmtzp 8 xhl 6zkf1-pm jjhrows the ball, the upper part ofu*p19k-.zfm+mza)jdlx8h 6z jp *mht his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of q -b/dbm4q+ hfangular momentum, discuss why a helicopter must have more than one rotor (om4/f+q-b dhb qr propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following ang: gan7laf69f kles in radians: (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 amazing cto( .hp:qfzzaq ivlny .(536moincidence. Calculate, using the in: o3 nmyh t65lfia v.p.qq((zzformation 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 diverge -kbyl4k,)1c2b me 7*g c-7vmd bbeiwes at gbc* -4d 7eelb1mmwi ,e ck 72bk-)vyban angle $\theta$ (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. :c/qo8f opanum4x0 lvg ,i 2g8cb7*hv When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the :vbiuqfv n 4oal/, c0h2xcg* gmp8o87blades slow down?    $rad/s^2$

  A child rolls a ball on 4*laxt.k vw:i a level floor 3.5 m to another child. If the ball makes 15.0 revolution xa:l.ki*vtw4s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0in nesez*2g 4/ km. How many revolutions do the wh s2*enzin4e/g eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate itvr-(2v1 lcoi cl0icw*s angular velocity in -co2v(vic 1 rlil0 *cw$rad/s$ $\omega$ =    $rad/sec$
(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.wp8i0.lx9vii 8–38). (a) What is the linear speed of a child seatedx0i89 w vlpi.i 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 angular v 9tf,b(ob;kt2 *zple zelocity 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 spee e:8wnk ogfgulv*bn70;9j 2awd of a point
(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) must a centrif0bd6 qr* cw9iduge rotate if a particle 7.0 cm from the axis of rotation is to experience6dwi9qcrd b0* an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rp(n7gmx3p2zpd+zicxr6 i7c 4e m to 280 rpm in 4.0 s. De n7(czix7pcg e63rdizmp42+x termine
(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 radiusuf8jhfz3a/ 5h $R_1$ 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 aboard the Apollo spacecraft put themsex+ )qr q y(n*hn 5 7edruk21mmswm5ii4lves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute d4 57nk1ur*x m)iisw +eqqyd5hr m m2(nuring 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 unifor wod *t 0541 bgjm0r0nthds.kwmly from rest to 15,000 rpm in 220 s. Through how many revogwo*10 th jwd bnd0kms4.0tr5lutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm s49bbaxlq 4.9ty:c umto 1200 rpm in 2.5 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 fmsf0kmu ,b6 5lor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachinsf50m , buk6mlg 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 from 24.x qsek(/1x, iu8 trtr0 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in e8i /q1ur tk(.txx,srthis time?    m

  A cooling fan is turned off when ai h*k+fl2 ,zbwb +es3it is running at 850rev/min It turns 1500 revolutions bk+lw 3fa+ib s ,*eh2zbefore it comes to a stop.
(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 /axe 7n22c r1nb9mqegthe car reduces its speed uniformly from 95km/h to 45km/h reg7xmc n91qan/b2e2 The 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 revolutionsilc+mu7g , )3u)gc lms as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter ofsmim l 3gcu+l)uc g)7, 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 riding a bike puts all her weight on each pedal when climbin9ww+jv16h onoo 2rv*bg a hill. Thej*wo+16oohvnvb92 w r pedals rotate in 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 of 55 N 7it ve 6; ox-71k;rrawhv /qkqon the end of a door 74 cm wide. What is the magnituk r 1k7v hvw/q6x ;;7qrtaoe-ide of the torque if the force 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 wheel showg;5djjr,jdlmiv,0 t g )qx+i;n in Fig. 8–39. Assume that a friction torque of 0.4 ;+)v i m,;j grgi0 td5,qdjljx$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod, cadn0qoh,c *4 ad6mq which pivots as shown in Fig. 8–40. Initially qnc ha,qd0 4a*,oc 6dmthe rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engir46mo ufkhr)k+ky+2 sne require tightening to a torque of 38 y kroks+r)f 4h2+u6km$m \cdot N$ 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 ti 4wcg.trys* bt 8 +eiqp0t) 4dh5/zuthe axis of rotation is throug)c08* 4ugh+sttwie p ./bd5tirtqyz4 h its center.    $kg \cdot m^2$

  Calculate the moment of iner7 wms5z8 c-10um anf7jloi1jgtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kgm08 51n7wjsfcgl-i m1 uja zo7. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on t+eul z rugo0ez05zv/q1 (;:zx 3: lwam y3kbishe end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculatq; 3x/wgrom(uv:ezky +z3 1: 0biz e l0l5suaze
(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 a bowl on a potter’s whezar2ug b +k ;cw(6ku h6:en4xtel rotating at constant angular speed (Fig. 8–42). The friction force between her hande 2rwna6 +gz:4xbtkk 6(c ;uuhs 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 the array of n9v :b2e, nk26b:+d otskx x6pype6vu point objects shown in Fig. 8–43 a bnx6,yd692uxt:been kpvk :+po2sv6bout
(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 of two oxygen atoms whohfbaw t -63*jdcr 2nt4se 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 at the correctl3f+ f:b9bcls rate, engineers fire ffb9bf cs 3l+l:our 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 rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is : 5bjpkhe5rb6a uniform cylinder with a radius of 8.50 cm and a mass of 0.58ph bebjkr5:650 kg. 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 rest to dqk9p z8fm:g(6 hci: qjvz, .z3 $rev/s$ 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 bb hoido) ..7nmerry-go-round and is able to accelerate 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 torquhbodb7).no.i e 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 eventually bro jj+ynpk .0n 5inchz7w4gjz l1/0 pu7uught uniformzuzg4 7pijc 7kpl nw0 h1 0yn/.j5n+ujly to rest by a frictional 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.t- o5q)ki yx3h6-kg ball at 7 $m/s^2$ 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 tn7dm9gtim2 e q(k 0tr p3:4hsphrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is a2 4 misptt rn70p(:3dhgq9 mekccelerated 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 considered a long thin rod, as m xxfb)s )(1wcyv7raqh 6k8,l shown in Fig. 8–4frv) 7k(b8 6l )wyahxxqm1cs,6.
(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 clpst*bl ,izs 5z2,l b9onsists of two 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 within foub7r ebz*gh+lx,+ ydj7 r full turns (revolutions) and releases it at xz h7ydjeg7+b *b,r+la speed of 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 has a moment of j ;,o h)n7;k,i n)(i/.iyzwq ya ohmvginertia 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 develops a torque of 28u286xzny0tm9 bvp qv40 $m \cdot N$ 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 rolls without slipping down a l*(wj,8po c0d8lq t -k7bjcbb oane at o-t opb07b(j k8l8*bjq,c wc d3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tho:2 l. *nvhvzwo termso2hv *z v.:hnl,
(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 rd;7iig;qke) b7e:hvmass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylin g7b k re7ei;h)q:dv;ider.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and ro4, g6kp5qxkbiuh m/9e lls without slipping down a p/9,kx ebghu6q4 5kmi30.0 $^{\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 balanced vertically on its van; fjwo+w,. tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the +vf.n ;, aowwjground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball roy4,1m(zvc d wtn12poetating on the end of a thin string in a circle opnov 1 w 2zycdm4(,e1tf radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifouao +2q7 kvr2sz,,nc 1u87d2xvwug ukrm cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? +a2uu2s7x d uvr,2o87 ,nuwk1vkgzcq   $kg \cdot m^2$
(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 is rotating atuhz ase*08nj r.2k bw4 a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, .sea*bh4 0k8zrnj u w2the 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 redu(: qtrm 82rr*su*p2x l9 n6mnxj6q tosce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, w26snmlts( q8 u r9jt6rxxm** o2prn:qhat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an ini qk)s7/h-qualz9s l+w tial rate of 1.0 rev q - s zk)97lhl+qas/uwevery 2.0 s to a 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 a vert xyy ljd90pa 05j5gi1jnby*,tical 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 disky b,y5501j yai*xj9nlp 0gdtj of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular mon2;w4: cbn vk24wptve mentum of a figure skater 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 cdfk ip*wve jhm2:k)vp 6gb (g0329njthe Earth
(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 inertia I is dropped onto an ide8vc*etz t9/xo irh+2+ +nfpysntical disk r9fo x vc znest8+t*/hi+2y p+rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 26 wv 6s5k wb)c tj4lgy/dz+kaus378 wfsy.-gv.4 $rev/s$ 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 center of a rotating mg++f j (/atsmherry-go-round platform of radius 3/ gath(jfs++ m.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 rokb. i;*y ze(g j5himwskjo)jr)bv)+0 tating freely with an angular velocity of 0.wz; yebkmgi( oi rj)0js5.vb* )+h j)k8 $rad/s$ 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 eventuagr f ,lta,f9w4lly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its exist a,4tlfg9r f,wing radius. 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 winds in excesje /zz kx7q:.is 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 )sjfto+t5 7 zxz8xmv5$ 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 platform, initially at rest, that can rotate fr9)x3x m* bwizceely without friction. The moment of )3bxiz9 *cwm xinertia 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 edge of a 6.5-m diameter rw 79uxt8; b4 e5o4ijotgo:jkmerry-go-round turntabj ;w8 r94574bo ougoijt :texkle that is mounted on frictionless 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 rolls on the ground with the end of the rope lyingx ykc7a95 z6ux on the top ecxa 765uz yk9xdge 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 from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth d5mka kao )dzybc89)s 8p2l-m such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the la9 p)damalbd-85o8y)z m2 cskktter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a1y+y-*s3 n vajiq03dwmfmk d- rate of 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 shape of a uniform cylinder of)m 8ze/ mpo3vs,me 5ta radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelerationz5/3 8mmveom,p s)eat . Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eo- dv5, l-tkrybr *b(fj q,e5sach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindri5t j,vk-qbos ,( yrdb-5er*flcal hub of mass 0.0050 kg and diameter 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 the rear wheel bk qn 3:.xyvv6x1ct -c($\omega_R$) 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 ou+m +aq;c1ppymr Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 da +y+q;mpmpc1ays. 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 lofrfj5t )sze2 ,w-pollution automobile 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 diameter 1.50 m and mass 240 kg, z,ejs52fft) rand 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 illustragmhq+,n .skc) tes 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 rolling on a horizontal surface at sdz wc j c-t,o)duj;4o;peed 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 pi ),k1 uexwcon8vot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontalnox1e u, )wk8cly 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 shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the fla :uqychg*g ):oor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The steh cg)u *q::aygp has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a foec fx s+p)qjbln.) ayxb 51:0lat road is making a turn with a radius The forces acting on the cxno+a):j5fxbe1 cs0 lqpb y).yclist and cycle are the 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 0.50-kg rock iapsje0b:q r x0j8og;yv.b76 lnto a sling of length 1.5 m and begins whirling the rock in a near7j0bql j6;ex 0sprgay:o b8v.ly 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 bymy: y-j - sn)7vcivd:ody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculay) vsnv idmcj:-7y:-yte the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly whichd1. p0mpnzz .q. f2pkzjl a9g: consists of two cylindrical plates, of mas1n kpgp..d:p0j . 9fazqzm2lzs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolls along the loopedl/n ynei4mt.2 rough track of Fig. 8–58. What is the minim 2.nynem4/ tilum value of the vertical height h that the marble must 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 do pici ln:8ow+ 2o(ju04dgn0+l x-ac qonot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fp8-n:yesij v56fzl m- rom 90km/h to 60km/h The tires 6mjp z-: ls vnef8-5yihave 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