A bicycle odometer (which measures distance traveled) is attached 5d/p0o nl(xd0uv3 q-f;st*s4 ing aep near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 20sf lvsp0d 4-3xgtpeon;/ a* (dnq 5iu4-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on+qwwx :m hm; kcqud2( 2yx 4ti7x(gz8l the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential accelerationxmq4(idwx8xy2 ;:kt uhl 7m z(cq+g 2w? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular ve0nm i2+jjew7 mfara/gl 1+ *ialocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expq+01-2jtpg- avuzfc hh-7*g)b wwmahlain.

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 yow2ccxbn )*h d 4wb/t*hur hands behind your head than when your arms are stretched out in front of you? A diagram may help you t b h /w)chbn*dxtw*4c2o answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pe (gs6 yqxro8+tdal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a largeox6y+ r(q tg8s front sprocket? Why?

Mammals that depend on being able e(uh: 8ofuwfki+u bw:c(r mo 5b* 0j-cto run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics cwkhj f*5ufmcor:- ((8io:0+buuwbe, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–3 k;gi4 a2 zepo 5c;crsrfza8)*5) carry a long, narrow beam?

If the net force on a system is zero, is the net torque ; izvb)bfa6f 0zznmae5b 8xck623d 5jalso zero? If the net torque on a system in ;60jab vfbe28f65kb 3cax m5dzzzi)s zero, is the net force zero?

Two inclines have the same hkj5-257cf,oaud e-pngs4ftseight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the nj 2o-kgffu5t,7c4ap-dss5 espeed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dow :khtby km-+;in 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 thytk: -mi;bh k+e greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sta dyzben d(/5: ru:22tzlpf+y krt from rest at the top of an incline. 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 tyyp(:u2: n el rzzfddk5 t+b/2he greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most sg +: kclhu11pbnemm) n/ pl8.moving or rotating objects eventualln/el1pgb:m sml) n+p. hk cu18y slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wo;zig+ x4j9x6w; fe mmbuld this+4 ;xmwg9b zfx ej;6mi affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initia :c-vhxq b2ub7l rotation when she leaves t u2:-vcbxhqb 7he board?

The moment of inertia of a rotating solid disk about an axis through7wk:qnq/f .eir5r 6 buaw q,f (tzq(p( its center of mf ( .z:bqa,7f(qrwq e/qntkru wi6(p5ass 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 rotatingwr c2qxgg k9g4wl7 hk5o6/t/s eohn 38 stool holding a 2-kg mass in each outstretched hand. el3 8 hkk/q cr 9wghost57ogn26 gwx/4If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have th98(iy0n7bg.h 1dp u)g n* bfoqam;fmoe same mass. However, one is hollow and the other is 1o;7niq*)fy 8bgm mod(nfaubh9 g0p. solid. Describe an experiment to determine which is which.

The angular velocity of r 0l1ra8cvzodq5,0j. fve9y zy1f 4 hva wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the taf0l8z,ory9 fvvyqrvhc0aj 1ze 5d 4.1ngential 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 a/85y f,m3ynp4c n 8u2itkrlofreely rotating turntable. What ha5 8,yilcry atnp/u3f8 mkno4 2ppens if you walk toward the center?

A shortstop may leap into the air to catch a b a( r:szqcw.1fall 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 dir f:1csqzrwa(. ection (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum 3d d-x-vt5thw, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operatex35td dvth --w to keep the helicopter stable.

  Express the following angles in radians: (a)9xeo,ks dil, 2ql, 9yp 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 coincidence. Calcu7/i: 7q,c.d a.ufz q sfguxve/late, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth./7fu sd z:gcx .qaqi/7 v.efu,
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divjxjxcp)25 cdnnymizu -34n58 twi,,s erges at an angnjtmcsz4 iyn8, jdxp5w) 2i, 5-c nx3ule $\theta$ (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 rhq )u ywd39sgf8 t8*ckpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular t 8*sh9gdywc )k ufq83acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level e4o44w j-osioy mp:5 cxv0s1l floor 3.5 m to another child. If the ball makes 15.0 revoluti4o ms0pl44j15cox -ivo y sew:ons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How+md,g.hj+t24t mb vgwj fy kk4aw-o( 6 many revolutions do the wheels make24+h.ow km4wk-d jgjavt+,bym6f gt( ?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cal0ivji8h; 8a2fq/zf zhculate its angular velocity in q0 vjaz zffh882/h;ii $rad/s$ $\omega$ =    $rad/sec$
(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-round7.* bnfjtla *l makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from*7 llntf .bj*a the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angularp*p4hgde +r+-x t7ebz 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 aqqo1bl s :b:s8 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 centrifuge rotate if a particle 4;eiz( zsks7og l vx:f 0-mk/m7.0 cm from the axis of rotation is to sm /v-x0e(o7;zzgl:i 4sf kk mexperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly: x uu1yi-j;sh,rq(,dcj-esk about its center from 130 rpm to 280 rpm in 4.0 -jsu1ek shcu:d(;xj ,yi ,rq- s. Determine
(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 radius wa-d c0nfe9w0u,najf vk1c / 9$R_1$ 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 themscng8tmzz * wci(.a8*k,8k b teelves 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 during a 12-min time interv*ati(k 8m.tcgz8benc,zk w*8 al. 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 15,000 rpm in 220 s. Through udzfv6m)e6;m how many revolutions did itfem)v; z d6m6u turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcu:2w-y/ip7(hqp w4 a mv1e uxyblate
(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 stresses of flying highspeed jets in a whi w2mv;wclvdvwgnbi;+ 27a4,jrling “human centrifuge,” which takes 2jdwwbwac;vv ;mlg +v n7i,4 21.0 min to turn through 20 complete revolutions 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 from 240 rpm to 360 rpm i ,t l1uoogp /y29:agynn 6.5 s. How far 92, /op gyog:ny uat1lwill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mk 5-hr;a rw sotoqm5 ,yf.l5-zin It turns 1500 revolutions befoml zrorhq,sk55wa5 t; y-fo- .re 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 vn6 t0rz),bxlrevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The ti0xzr, bnv6tl)res 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 revc j):1d3h8gf7km z x+pw9ibsvolutions as the car reduces its speed uniformly from 95km/h to 4:+ 17d )3miv9z x8bk scgjfpwh5km/h 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

  A 55-kg person riding a bi- vlbcnzq.sv 2:r mw.(ke puts all her weight on each pedal when climbing a hil srq(cvlz.w n2vm:b-. l. The 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 on the q 3o+j.pyv8/do vadch:wbu uwn;) 5b:end of a door 74 cm wide. What is the magncwyn o +upjq3v:d;:wv8o)u h5.db/ baitude 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 shown in Fig. 8–39. Assubyez )z +9pot ou)i/bp5ala3 /me that a fra /by z)et +)9li/5zpaou3op biction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m ,bu0 y(wx)icl, 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 then released.)y( w0blu x,ic Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engint269evhlz72f1jg oyke require tightening to a torque of 38 g t12o2fjve k9hlz y67$m \cdot N$ 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 ofhuh kl0:xy3l,(g vjm 0 5zc2fd a 10.8-kg sphere of radius 0.648 m when the axis of rotat,0dvl jhx05mz cykg u(hf2 :l3ion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheef8ytzdqd;tn a) 94ns.pg i2c:l 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg.fz;2gtdaq.) snp y8td 4n 9:ci The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, liv q;n 3g 1lhu1r98) xwrkaq)tzght rod is rotated in a horizontal cinqx1q1 k8g);t wrvlhza3)u r9rcle of 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 a bowl on a pottern+jjlx3gr.- lb eq3 .u’s wheel rotating at constant angular speed (Fig. 8–42). The frxr 3g .ub-j3qje n+.lliction force between her 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 the array of poiy(m4mptwto(m,7 m, r f(p mcl5nt objects shown in Fig. 8–43wm5,o(t,(tmmmy4 c(ml7 f p pr about
(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 whose total mass is6z 1ifl( h5 ozwd/avs4v6vto* $5.3 \times10^{ -26}$ 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 correct rate,5 6( tdj /qrkjhuo761f,oh; znncifw9 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 sz91 i n,;r6jk fc5wuo( od6hq/jtfn 7hteady 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 a uniform cylinder with a radius of 8.50 cm (vl(g- 44lgr .jnsihmand a mass of 0.580g(-m g4ivrnl.sj4(h l 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 sw3i * q7keuh9yfga5iz 7xm/b 4xings a bat, accelerating it from rest 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 smdb( 6zvc1ly ,eall hand-driven merry-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 (eachy6 vl1cdze,b( 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 anxd/ vx:tyoewj*2dcn5 g) j5 e2d is eventually brought uniformly to rest by a frictional todeejv x *g / tjd5)wn:5x22cyorque 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 0+d2uz +xf8e1tiyynhdx f 5,vaccelerates a 3.6-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 thrown solely by the action of t;s ,w 5g8qufg+qcnxg 9he forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Tsf8qgq;9n+x w, gcug5he 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 considered a long thin rod, 1b b4dopeec9,0 i*ocuas shown in Fig. 8–46.4c9o be o*dc 0,i1pebu
(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 two ji mb-).zsqk +b6hwv4 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 hx qu87.0muqpz w2m2c 0-pkym within four full turns (revolutiw h2cmmuux k .8mqzp0p-0yq7 2ons) and releases it at a 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 hao jkftk ;q(-)ws 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 develops a torque of 2863qjsh- p*u akdt t,)d0 $m \cdot N$ 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 wi0l)ogoe ,pjnqp59n(bthout slipping down a lane ,p ne(q)b9pog5olj n0at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the h )+fw/du63 m1oo4/gvchbtd lEarth with respect to the Sun as the sum of two4d ovh/+co6 3whgu t f/1md)bl terms,
(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 x4le1wpz4m q7 a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelq pw4zl 1me4x7erate 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 macz0 g,c lr;e(ess 1.80 kg starts from rest and rolls without slipping down a el,;crg ce(0z 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 balanced vertically on its tip. It wu7j v/hbodvgrny 5p+7x5i(. starts to fall and its lower end does not slip. What will be the speed of the uppyv+j7d.p o/uhb nix(5wv 7g5rer end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating pt(s)nq-3kwe on the end of a thin string in a circ)w3-tep( nqk sle of 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 uniform cylindrical grindinb4bu08 ju)u 9 mdm o uo2n0pk,0tjxwg0g wheel of radius 18 cm when rotatintob0ouwx 2du8 0 ug90 k njb4m,0p)jmug 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 hi /z;p ipc(7ij8 :0v7nlb ziyqms side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of i:bvji/q8yp7( inl mpcz z0; 7rotation 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 5jcn+f2nwu nf+3x-d yher 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, wha d- jnff+x2y5n3cnuw+t is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increas ep fqac*qx76+e her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofcqx q*6f7ap +e 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 radsd6 uj4w ai:p*fo v vde* 72y9gt82lotating around 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 frequencyu8 syelv*aja4f :d7o6 9dw*g itvp2d2 of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a sy-xcq,aceqe(zw 007 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 angula;te uf)x6 ex/ur momentum of the 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 mom )nhx/ vu*g/hment of inertia I is dropped onto an identical disk rotating at angular speed *v)gxm/un/ hh $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a)h. 7 1fa-nxnsxn1,p .xdpvdot 2.4 $rev/s$ 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 l2tcpnifqeq y )b yc4;h8s0*i2 r4pd0of a rotating merry-go-round platform of r8n qce;id)p f2s0 *clyq2ty04 rp 4ihbadius 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 mer8)(celdxcrsw 1n; ss2ry-go-round is rotating freely with an angular velocity of 0.8 s n(cls8sdre2)xc;1w $rad/s$ 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 collapses into a white dwarf, losing abo3l6ibi9y x1vq ut half its mass in the process, and win9y6bv3qi lix 1ding up with a radius 1.0% of its existing 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 excess of 120 x(rgwp 7oet3p / 8 4g(gh*be(mf am rzbqba,35$km/h$ 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 7kcdjv8f)z s3 . f3l;bsf, enw$ 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 freel 3bzvec78guy(,a f8 n; qtbb6ty without friction. Tbt883qea, ut(y6;c gbv zn7fb he moment of inertia 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 q/m+n5nds .(ds,i vqkthe edge of a 6.5-m diameter merry-go-round turntable that is mounted v +nd(m5sqkiq.sn, /d 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 lying on the d(8(l jm1b;- igpysc ptop 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 from the spool? How far does thed(syb(-g p8 l;c ijmp1 spool’s center of mass move?

  The Moon orbits the E4 -ngv/fcc z* 5lty,eharth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular yc5/lz4-chvtg,f n* e 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 of ej1t d* 4 f ;/dlmi*jffopc,i;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 o;zzpow;(blja c3v nk3, )x nltnwh,4)f radius 0.20 m acquires a rotational rate3l n h ,;);wn v)c(tolzj,zkpnx34w ab of 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, each of mass 0.050 kee+wlfdafaf1 *8xe1+8.nx b ng and diameter 0.075 m, joined by a (concentric) thin solid cylindrical 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 d. +e1 febffw+a ln8*xn1e8ax 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 theed,u,m4rh8b n angular speed of the 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 8:i3ot ik* la u6dtp8fSun, but with mass 8.0 times as great, were rotating at a speed 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 momeoituaft8:i 3dl *p8 k6ntum.    $\times10^{9 }$ $rev/day$

  One possibility for (6 fa3hk22wk pab;mhqz*lnz+ a low-pollution automobile is for it to use energy stored in a heavy rotpz+ k3 aqh(2n m6;f2*wazl bkhating 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, 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 e/67p6c:fc/ afg 2vakttld.ttes 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 speed v=1-hlxuj jc toqjdfrb08a +a-/9o7vf+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 e; k4dxw-gr)scan pivot freely (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 reled4 -;segwr) xkase, 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 o, d: ah((r )tn*nyyvh1 mma7ain the floor, and we want to exert a horizontal force F at its axle so that it will climb a stepam nn(a,(yh 1 id*tvh:am)7yr against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wi9qz.rrd0-jt tth a radius The forces acting on the cyclist and cyc .-zrt qd0tjr9le 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 into a sling of length 1.5 m and begn*t7n)f7:saj)bkthf/ g 7tn 0r qybp/ ins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 7)r b)/gnakb7n*hp/7t fj0 ystn:ftqs. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s b7;gclwbd68 u sody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinni sul7wgb;dc 86ng skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists o3w2l evw++gp lf two cylindrical plates, of mass ew2vl lpg++3w$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 and6 f gjw1z fmm4o3 pxse8w)4lw, radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop withp1s m6) fwjlwom 3fzx,8e4 g4wout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, busnxf7m, s.)rd .payao.urz.+ole1 ,u t do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speere yw7 7 y8mu jiy,6+5bq-szhpd uniformly fromiqyymh5 spj ,yrzu we-b6+778 90km/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