A bicycle odometer (which measures diry:h0s-fflt be,j;g/ik c o3/stance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle kb/eg y-f 3sio/tl ,crhf;:0jwith 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does 2a80quv9q jvp k6eg1y s1.ueqa point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radia uq1g6u2kyqv 09epqj.8s ev1al and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by atut1 0ttk0gt;gn 40rdr wdn w8h-m))u single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.:0v ;hoicov0*iqeri:

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 head than w+o, iv/rtsgi:hen your arms are stretched out in front of you? A diagram may help you to ans,sii:+/g trvo wer this.

A 21-speed bicycle has seven sprockets at the rear wheel an( si,tjpjh3oj69g1yse g co3 2d three at the pedal cranks. In whsy16ojgs, oetj (jg3ch23 i9pich 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 large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowz0gp-8:mv7*o zsj2.r nq ov oqer legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this dist8o7qo mpv s0z:o-g*nrv qj.z 2ribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry al rzt 2)*ow:x le;ony; long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If theui5 o nwhwg lthbx2 -8l83q5.t net torque on a system is zero, is the bgql8 tnu 3o52 8xwt.5hlw-hinet force zero?

Two inclines have the sam:dv7n x7wkzplqz )b ho2* ;n:se height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the; nl)7dbnwhszz q7v:k*o:px2 bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from b ck2kt-li1.6v lh(yh rest) 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 l( bk6khty i .v2-lc1hhas the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylindezv74lag 1iq is65t u8mr have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the iv 1zlas6 u8q5tg74mibottom 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 conserved. Yet most moving or r 0vgb7:bylp0t;oymn(h1q2es otatiny17v0; ospb2b:0 h(nt gqleymg objects eventually slow down and stop. Explain.

If there were a greatxmw4,n ./iq86 r,qswiz x(x-y bwi*bq migration of people toward the Earth’s equator, how would this affect the iqsq (mibx6q 4/8x z.y -w,*n wxbw,rilength of the day?

Can the diver of Fig. 8–29 do a somersau*6;fclh;*ff efq/smq lt without having any initial rotation whffsc 6f*;em/fqqh ;l* en she leaves the board?

The moment of inertia of a rotating srvdz4 1as,*o yolid disk about an axis through its center of masszdy r14ova ,*s 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 massh9jwip z* (y:7 s )x1uf-ehfoh in each outstretched hand. If(sw*hz:o)1eh9uxfp- h7i jfy you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical ig ab;h(6 fko5and have the same mass. However, one is hollow and the other is solid. Describe o(6akh bgf 5;ian experiment to determine which is which.

The angular velocity of a wheel rotating x:c p14fhe.m eon a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If thee1 xhcep:f.4 m 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 tur x+sci8 )m18waf yc wspj)hd.*ntable. What happens if you walk toward the ce.s+hw msx c)j df8ic81*wa)y pnter?

A shortstop may leap into thb*f7ehlca,0a e 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 h*f0,ab 7cael that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the lapak;uttp4 1, nw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more waap1,4t u; tknpys the second propeller can operate to keep the helicopter stable.

  Express the following -g ylv4-9ozge angles 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 coincidence. Ca/zi .ef)3txkk, m5qg clculate, using the information inside the Front Cover, the angular diamtf,x imq.z/3ekg5 )kc eters (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 beamog-d (5 qb)ttu diverges at an ad -oq(bttu )5gngle $\theta$ (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. rx73p w)mb vn.k tq)8gWhen the motor is turned off during operation, the blades slow to rest in 3p7 qt x83gb)) kwn.rmv.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chidirs+aee k+g s q)fgq +x ixx9-;xr-;3ld. If the ball makes 15.0a++ x)-gd +xskq;egeqs;rxfri 3x9 i- revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter m :5i(s/ it3epz,eey n-z)zxaqq)(rl travels 8.0 km. How many revolutions do the whtsm(er-zx3qiz a) ieey:, ln/ zq )5(peels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcuiyztna8w0ny / ;9 wij+late its angulja / w8ty;nyn0 wi9+izar velocity in $rad/s$ $\omega$ =    $rad/sec$
(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. 8–3e,x9zq -f ez j759pldv8). (a) What is the linear speed of a child seated 1.2 m from9xf9vd l,pz5eje7 z- q the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its or 2qiw4*3qfl. vw,gvvo bit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of b6:x ev fw,rp6a 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 7 kawkv 5ie nja w.q35w9lwo)56.0 cm from the axis of rotation is to experience an acceleratioviw5a9wow .3)65enwl 5k kja qn of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accxku7 u xfp9.0a 8-s7a3jstukxelerates uniformly about its center from 130 rpm to 280 rpm in 4. jxaa.s8k 0-fuu3us 9xpkxt 770 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 radiusmzffvsc-ja( y: 19ou) $R_1$ 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 themsel ml u80sm6hi8jh *utf.ves 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 interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Deteri*sj8hf6uul8 .mhm t0mine
(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 r54q3c ay p6 1rrgiaj*eest to 15,000 rpm in 220 s. Through how mrq35 yc6g jrei4*ap1aany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500w6.s (cxi-sn u rpm to 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 for the stresses of flying highspeed jets in a whirli 1btqg/-(sw u:bdmgggy,5 *ggng “human centrifuge,” which takes 1.0 min to turn through y-/g wgt mq (g*b,du1sg:5b gg20 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 uniformlyza:7e8 l 3koq flez9y( from 240 rpm to 360 rpm in 6.5 s. How far will a point on the leo7ak3 9zfq 8ly(:ez edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 8z.tz8 - gu6vbwwkz( +e50rev/min It turns 1500 revolutions before it comes to aeg6wuktb-.zzz 8+wv( 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 revoyf,u*hv 6i (g2jn,yktco +m-knaki 1)lutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.h1,i* k),y+g2nvk n-itj6(o uakcmfy
(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 astb 4vt+ /;-yi wnyjn*s the car reduces its speed uniformly from 95km/h to 4;-t iybwnnvj /s +t4y*5km/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 bikx -pa;t lcz50fe puts all her weight on each pedal when climbing a hill. The pedals ftca;0x l-5pzrotate 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 end of agq m q;f ;ck4+6 u--htsx.jpddac x88v door 74 cm wide. What is the magnitude of the torqmg acxvk;.xp 846f8d-;htuqd- j+s cque 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 sex;3tldsa 3d/hown in Fig. 8–39. Assume that a frictidx 3 tasd;/3leon torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mas4-, ntu + kggmcz3tzp6sless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontatz6m +,4 tzkcn-uggp 3l position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighten+b; bq(zvgduo e. co*4ing to a torque of 38 ged(v o+b b.qo4u*zc;$m \cdot N$ 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 sph p upidv*2j /r0nk:l3qere of radius 0.648 m when the axis of rotation is thr2lnujp/ pr*3: v0iqkd ough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The r 2-. 2xy(5wprankujjtim and tire have a combined mass of rx5wa(ku- n2tpjj.2 y1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light r7swcy (-rmgrc (:mfu7 od is rotated in a horizontal circle of radius 1.2 m. Csw(cm(-:gcr7yr f7u malculate
(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 wheel rotating at con 4kdtx kbw ).-nydb*x*stant angular speed (Fig. 8–42). The friction force between her hanby k.)*xx-dnw*t kb4d ds 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 point objects shown tqhf ns88 p/b9in Fig. 8–43 aboutfhbqp9/n8s 8t
(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 co9 ulw,ib,.c4kqgaw0s cht e). nsists of 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 at th7 .vqb:.3g zuce85xt-q.hwr glng;ux e correct rate, engineers fire four tangential roc qh; xu:-5 3.e 7x.tvb.nrcglzgqw8gu kets 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 a uniform cy ypr n8*7+y:pbwm9aapbv46hg j8+vnwlinder with a radius of 8.50 cm and a mass of 0.5 h8 jyv+apnw8np b *vba+gy:m697rw4p80 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, app.b2m v(bg,v ccelerating 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 tangentiallaf4 rz997a. gmwdael 8y on a small 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 (ealmzra94eaw7ag.f9 d8ch 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, ;lb9 4mbaj /l obb1m:9t- ia8*xnovsb300 rpm is shut off and is eventually brought unibvo 1nbm4ab-9a/8bxiomj:9b lts * l;formly 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 3.6-kg ball atzc2f59lubm4ub eb ,y-q:f) la 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 6-27ysrn 7wb omvjonb1g 39frthrown solely by the action of the forearm, which rotates about the elbow joint under thb7-o3y m g rbwjns1nvr6 97o2fe action of the triceps muscle, 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 considered a long thin rod, aselv7mu1n+ (o:s ,jjmqi0f x; h shown in Fig. 8–4vmxsi ofh jq(1, m7+ jn:0;ule6.
(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 masses,jxhoowmpuu. m i7(5a 4: wk/*n $m_1$ 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 four full turn1 fsn-,deoyrqlj4g ,)s (revolutions) 1q4fe,n-g, ls )yo rdjand 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 hasp9)v3( raebyd 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 op8t(y;b . k lx5vv n;fjfr1nl.f 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 anl3xwv8et9xfrlx 7* k1d radius 9.0 cm rolls without slipping down a lane at 3.3 lk3x8 t* 1fv7 lxerw9x$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wik7hh7a*8 btbyth respect to the Sun as the sum of twoa8bbh*7k 7hyt 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 a mass of 1640 kg and a radius of 7.50 m.x h538) xarfk.)h4ndk xymuk ; How much net work is required to accelerate it from r.huha )dk3)xf8rkm 5xx; 4yk nest 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 mxm.p ,i6xr d hzu3ix: ki0c0)kg starts from rest and rolls without slipping down a 30.0 ,hr.0m3 :d xcz0u)i xikm6 ixp$^{\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 balancedb;t wjncr *;0n vertically on its 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 ground? [Hint: Use conservation of energyjc ;*nt0b;wnr.]    $m/s$

  What is the angular momentum of a 0.210-kg ball* 5i1 ixoqhuw-9p co/eo9tbs9 rotating on the end of a thin string in a circleh/bo9qio9t osuwe 9*p -ixc51 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 grinsi/: c g6rspxyt:3 ufs)ov6 ,w7s sz+mding wheel of radius 18 cm when rotating at 150 y tic/ r mgswsvof6::)3s +x,suzs6p70 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 platfab,pg. 8im wx9orm 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 rotation decreases to 0. g8aw,.9bpmix8 $rev/s$ (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:erou26j x+uc her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. I62e+u:ux r cjof 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 inck23 f poj-vvngflz9r) hj a7/.rease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate oj)2.jlv ffvapk 9r-oh3nz 7g /f 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 arouno* x4noy)j5 kkd 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 k5) 4nooxjk*y 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 wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figur;h1tbgqd )hkx w5r .ny9swhy936;cmbe 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 thejp10j z9(1xshgele, l 2wcp zz6dl 1:3o9msc d 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 droppeuh,e35-nsylm on +o .4fxpsj; d onto an identical m, -j3ssho 4nypex.n uf5ol;+disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atigxnt pp/- u5; 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 j3-6bavwdk q53)9 e esqwsy m/stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 9206w3 /qmsv3ed5q)k y9b -wsa ej $kg \cdot m^2$ 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 rotatinm wu-61qgke bqow(1 txi93ql1g freely with an angular velocity of 0.xk6 1eitwbq9umoqgw3-11 lq (8 $rad/s$ 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 about half iti25c 21fa3c tf8tnt2g(yx hho s mass in the process, and winding up with a rc52tc8 ohx fnhf12ti( gtya 32adius 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 8c,ip(4lvxowzup njvx3gtzb 94 2 2ve +la ;y)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 v6mf ag u2ir*.$ 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 2-/tt7 srdoeb rotate freely without friction. The moment of inertia of the per/-2e ordstbt 7son 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 - -rk,wgk bq5oj(8 mizdiameter merry-go-round turntable that is mounted on fricti -bo8,kqirw(-km gz5jonless 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 emm kqfylb)/*t+5k*c6jxx;o gnd 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+bmf x6 txj m/l5cy ko;)*gk*q 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 such that thel7* kfs ptv g0k)lpt tm7kms9,gd 51o01gki-h 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 latter case, treat the Moon as a particle orbiting the Earth.7gptt pi0tf*od79k1svgk hl-5lmk )g, ms1k0)    $\times10^{ -6}$

  A cyclist accelerates from rest 3q)h(vm v2rt;prrm 35ione6hat a 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 cy2tu w 0f). gm/c*ioopm vzks/.linder of radius 0.20 m acquires a rotational rate of from rest overfms 2o/o/g 0 pzc)*mkwv .ut.i 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 kg andhtg nvjv qc41o s/,14u diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.4 1vv oc /4hqjut,gns1010 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, howa3dm uy 72mm2w is the 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 ou;q 85o7b wivs(j:sgho r Sun, 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 momentbos :(vqs5 g8wjio h;7um.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use ener z5ule -/of 4yii2)xy jlqm1,agjs6)b gy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter ga6jo yf z21m)/xbyeqs i) l4 -,ljui51.50 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 illustrates+ml i+z l d zdr5 2f ecuuib2d-o5i1dff3p46m2 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 av; y1(hl jmet3t 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 (i.e.,cblt 6w6b8ejr 9:w8u u z rwh:za.ku(zx2(. nv we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held((k. 6z ctrwh eu6 j.wax:vu 9288: urblbnwzz 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 shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has nrz *n1q4 tz;q7nf;gkradius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it willq1tk 74 gnz*nn;rq f;z climb a step 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 yj2irrl-m 74x:)j9m0wy e dne turn with a radius Thej 0rmn :x42m -w79dieyyrl j)e forces acting on the cyclist 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 0.50-25ei i;hg ,tf-m qcgv :x+k0glkg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to aq2il - g5 igt,ef0h+; vkxgcm: 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- xwrm*cskkjsydfuzl,c -86rb ),q1 ; and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretchemw c1 zk-;yb 6*fjq,) lc-ru rs8ksd,xd arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists q)rpe jp9 / *i04waggrof two cylindrical plates, of m)pe r9wir0g* a /qg4jpass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 t0dfri cvkbxy 1vd ,74(he 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 withoub0vid x(,ky 1dc7v4 frt leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but doq7easoz+/ u/2ta h 9rk not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces ietbly d uqfzz58*z*2 *) aep8ets speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular ac 2eypz85)qfdeelbt**8z a*uzceleration 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