A bicycle odometer (which measures distance traveled) va83j;wzn mw- is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bi3va-m;nwzw 8 jcycle with 24-inch wheels?

Suppose a disk rotates at constant angular velf76sp f*md (vxocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases unxd*ff p76m sv(iformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bodyb.xpiq n1h;p lz 1bt 3n8:ol5n be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater tor7 4 xl0lx*dlo7jj ag9kque 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 wgo86 daa z10cbehind your head than when your arms are stretched out in front of you? A diagram may h 0oda8c6zwa1gelp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three almmo-fh/o , 1bhvts6qmfg 69/ t the pedal 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 sprockg/s/tm9 f,h moohf-vqml61b 6 et or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower w.. j jxex 8lk(d5o*lclegs with flesh and muscle concentrated high, . ojke(x5dl l*8 jcwx.close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fi wqcg7d(7+er9nhyx8a g. 8–35) carry a long, narrow beam?

If the net force on a system is zer x 2sx43mxjsk//-mvbrybv 8 . ;zepc-go, is the net torque also zero? If the net torque on a system is zero, is thbzvx-x;/s p. r-382cyekm4 /v gsmbjxe net force zero?

Two inclines have the same height but make different angles with t8iq.eed6u 9i qhe horizontal. The same steel ball is rolled down each incline. On which in6i.98qeueiqd cline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) cqqrefo;.n5 7 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? Whi efo; q5.rc7nqch has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fac;kyhn;c2 x 5rom res;;cx2 k yn5acht 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 the greater rotational KE?

We claim that momentum and angular momckuaje5)t*a 94nb pj,aj(fyq (/05c w0upsgcentum are conserved. Yet most moving or rotating objects eventually slow down and stoea*q jwp0jc0ua5 (4cy 5na9( j,/fkpgb st)uc p. Explain.

If there were a great migrq 0obhz6vmu/( ation of people toward the Earth’s equator, how would this affect the length of tbvo qzm /u0(h6he day?

Can the diver of Fig. 8–29 do a somersault 4tao q d,-r.b hbwfs9)without having any initial rotation when htb)oqw9ar -.,sf 4 bdshe leaves the board?

The moment of inertia:pa2zxd 7o u+gd g:.su of a rotating solid disk about an axis through its center of masupd.gas+oz :2:x7udgs 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 ma egnjokf53bh+f g bw*00dn;s 0ss in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sa nb000h fsoe;jg dkbwg3*n 5f+me? Explain.

Two spheres look identical and have the same mass. However, one is holqq+ew -vr2 1w3tl m)qulow and the o2vrw t e3l+-wm1 qq)quther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating qbf p w*-,x4yzon 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, describb- y4 wqp*xzf,e 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 e3nqzlj (x( .hi +-rcxsdge of a large freely rotating turntable. What happens if you walk toward the centlz x( snxhij +3cq-.r(er?

A shortstop may leap into fg lifhv 5pror(3,98i the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rofii5,83g f ( lprho9rvtates. 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 o 7frtfl2jnn7wq3snei9 n7s zjy--*n1 f conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operatefnj7n *n7 n7isq12f 3t--rn 9 zjewsly to keep the helicopter stable.

  Express the following ag)ty dz; mw3d3 (q7dgjngles 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. Calculate, using t dt) w1(:wf oso:kr+dfhe information inside the wkdd trof +:swf)(o:1Front 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 Moonoq8+iz *ovjn x-6mah8) jk-0 neg6fm e, 380,000 km from Earth. The beam diverges at an angl6* zoj+ioemnkgj80n am8h-fe 6 vq)x-e $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is t+psx gg55/k toi 9c;auurned off during operation, the blades slow to rest in 3t /g9a+;gu5cx5oips k.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 child. If thth0 8dd1 ej 4o-ci:rd*nq6tjse ball makes 15.0 revolutions, what is its diamet*d -h nt r18qjesd it:d4jo0c6er?    m

  A bicycle with tires 68 cm in z)kj. 5dl3pwr diameter travels 8.0 km. How many revolutions do thew)kdr53pzj . l wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates ajb7/;.s avbsm t 2500 rpm. Calculate its angular veloci /. ssb7;mvjabty 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. gd,4py)o,va pq/s;v,vlda: oxh c1 *y 8–38). (a) What is the linear speed of a child seao,,aq)1 ad/yxcov*pslp v :; vh4dy, gted 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 velocity of the m*pyg-4jy j6amx:m 7l Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sbt 8nf e chef b3ett/(k93ng36peed 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 centrifuge rocvvbz 1 vvk97tv/t30k tate if a particle 7.0 cm from the axis of rotation is to experience an accelkk v30 19/tvzbvt7 cvveration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly a:w1 , (jzvllqabout its center from 130 rpm to 280 rpm :,(1lvz jqalw in 4.0 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 radiubp +oje-7y;ec2sm-b7aa/q eg s $R_1$ 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, as)vdu o6pp9 5dttl 3 ycav:1fw(tronauts aboard the Apollo spacecraft put themselves into duyvp l(t5 tc)p a69owf13v:d 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. 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 15,000kc zfc *05*jti rpm in 220 s. Through how many revolutions did it ttfk0zc5j *c*iurn in this time?    $rev$

  An automobile engine slows down fromu*bj;lbnl1 ddqg8 -htcu-2 q w+gq,y . 4500 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 j 30b8q9rqf zeou-na;i9wh .d xets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutio9z;xe q9 n8r- .hbaq 3fdwiu0ons 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 in 6.1kp1/v6dr:tp0 ne kzos ./jjf5 s. How far will a point on the edge of tjzppe1td o 1 k0s6rjvknf/.: /he wheel have traveled in this time?    m

  A cooling fan is turned off when it is rlgsi(ap a6n15 unning at 850rev/min It turns 1500 revolutions before it comes to ana 1 agpi65l(s 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 the car red:jo n4lu+sq1-xama*v, no t9puces its speed uniformly from 95km/h to 45km/h The ti1m lvx: a,*ao4t+no 9u-qjnspres have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions 7v*fg5dk:k agzjamb*9 /bm.i as the car reduces its speed uniformly from 95km/h to 45km/h The tab9m fb:/ **m7agik z kg5.jdvires 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 bike puts all her weigfz-qg-c2w tp(yr ,,xp oh *7mxht on each pedal when climbing a hill. The pedals rotate in a circle of rad(,p7x -xz*o mcpryt,hf-2 gwqius 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 a door 74 cu .84lgg99h azpfl:ik 1jt5 axm wide. What is the magnitudeku5a 4ilpg axf9thzl 8 .9g1j: 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. 8–39.1,f-qym3 qzvc. pcr9i Assume that a friction f9,1c3qi pyz .mc-vrq 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 hszee6 )wv*y ato6 l.3massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and die vhwzle.t6o 3*a6y )srection of the net torque on this system.

  The bolts on the cylinder h:itth 9or8 h9w;k dk7iead of an engine require tightening to a torque of 38 hioh rid99wt k;7:t8k$m \cdot N$ 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 k5av;k 0r i1h:hutb/i of radius 0.648 m when the axis obi;0a 5uki :rv1htk/h f rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of 1vgz lji.p(jtqt qu 3:7z7l (xinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the x pj1 j(7q3vutqz(il: tl 7.zghub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a vfr7jqwd 9v4;thin, light rod is rotated in a horizontal circle of radius 1.27rq9vf v4djw; 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 potter’s w;q o0 d r8;w1va)p p,bbpm5ufbheel rotating at constant angular speed (Fig. 8–42). The friction forc5wmq;fbb0pb1 d oup vra)8, p;e 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 k4mc3y1yf3q- qe m a+jof the array of point objects shown in Fig. 8–43m a qc13y3mf-qekjy+4 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 9 b0ax*,uqan( )hkalxn: som/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 satelliru.b 2(q q lfr4an4r3wte spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the requq4ru2r3.lr4nq bw(fa ired 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 cylinder with icccy9a l8od8wi5--yku71i 2 s g oow4a radius of 8.50 cm and a mass of 0.580 kg. Cido589kg1c8uci7 ao -oy2 cy -w sl4iwalculate
(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 sw ;nr1:vx(ltjbq5cs34licj;x0 8 f jpqings 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 small hand-driven merry-go-round aajwa2jb3:7 u2k 9vr4r c m7.z tjitym,nd is able to accelerate it from rest tka, muzvicr3:jm7 4b. ttw22ayrj7j9o a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,30ng) *vjy,n rg7tcta d*o1* a7l0 rpm is shut off and is eventually brought uniformly to rest by a frictional tor7*rnjlyvg*ga*,d no1a7t)c t que 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 acceleryt974 z vtir(mates 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 isp(*oha ,(v6mp : zzjcmgx6k4ft/ w.dl thrown 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 acc(v ja,tm:fxh6pm dl.w4zo (*pg 6kcz/elerated 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 eu5tamq0 c*hsn; 6(c ea long thin rod, as shown in Fig. 8–4*ctq u (e6 c;a0m5ehns6.
(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 cos7di. cph-83kpcn gx*nsists 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 four full turnsaq3tc2 c0ns1d (revolutions) and releases it at a spee3da10 2csq cntd 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 nhclwg 8ae+ mlx)90n(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 280f k/-6x5jjqnkdhz-j* kx7y9/ky + a ve $m \cdot N$ 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 wi o8id *nlr e3(wwb:ju;thout slipping down a lane a:ow8l*3db r ;wj(eunit 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun awi ksokfme7f2.;2 0z5 :0pbqwkvtyo(s the sum of two ter 2wozo f:k ;k 705b2qwsy.epf(kitv 0mms,
(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 9 vo2 tnu+ek m-,h5mwzmass 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? Asomh- vtw en9mu 52kz+,sume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fro ae.ojvll.86irpbs ;+)2t.0yfo z f6eu lhf k4m rest and rolls without slippi hp6fe28lf4 z.;r+.vif aeou60.ylskoj )blt ng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically onz6+o;b:t*k c4mvezy q 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 conservatio 4+cm t6 yq:voezz;*bkn of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on r.-5dckv0*bz bn w-ggnjj vr(e 0oa)qqk*r87 the end of a thin string in a circle of raer8nrkq o.gg (*) 0v-jj 0rbw 7 bnaq5k-dvzc*dius 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-anldb4 o;t 3p)kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 150bnd aop3t ;)4l0 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 cq:u ncn f 7zg1kl;8 ,ccoe*/da platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontfu /nq,;cc:lo8z n *17ckgdceal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce dr ,-,ck 9zs:pbo j0upher moment of inertia by a factor of about 3d0s: z9jpkopr ,,bc u-.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, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1.0 izc+z s70i i6t(labf*9ocj(r +tzh8xrev every 2.0 s to aizis j ftz6*9o zcbt(7ch+l8( +xrai0 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 arou9aw xmmn*vkvp7bu8 )(l5 l7 lxnd a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of m 9 (bvmx7va78x*5wnk)lpuml lass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angul,1 ,x syambuo 89csfk/ar momentum 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 the E t.9 yk-(mywf8zzpi)darth
(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 4(qtncas8jw2bb 9l * kan identical disk rotating at angulklnb j(t a249q8 sc*bwar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 29td,a1*z kmna.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 merry-go-round v1 qv58 bgui9cplatform of rad5qv ic 9u1bvg8ius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-r .qjbl.4b9f .cx)l sedound is rotating freely with an angular velocity of 0. q .)dbcfsb. jl.l9x4e8 $rad/s$ 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 0o(/ 0hp d-p1 -plg9hto.v +vrammdpg dwarf, losing about half its mass in the process, anhm h-pp vl tpd1.(o0o-p0gmv9 a+/dgrd winding 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 vjy0rh : l.cmwx2x, b9o/fhm gfi9yi5z w 0r5*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 ycv8ucm*o1od4u t 0 .6d8yyhc $ 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 platfop y2;k*r d *nd6biixv 3ph 5h;uny+tm0rm, initially at rest, that can rotate freely without frictiir k63h;+n2 pybudiv0mp*;t dx n *h5yon. The 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 the edge of asjrv/ n 1dvu kpk bk;750q,cc0 6.5-m diameter merry-go-round turntable that is mounted on fru7vq0r, ccb50vk kp ns /kjd1;ictionless 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 wi+lm m 11(4ahgmj9otdl th the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person(mljd h+9gla1mm o t41 without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Ear*tv 9n6u5 fcnktwrz *(aj k8-lth 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 latter case, treat the Moon as a particle orbiting the Ef 8an*6wl*5tvzk u c(9knj -trarth.)    $\times10^{ -6}$

  A cyclist accelerates y r:eua,jcbgtx2):b;d/a2 g:ql 7tor from rest at 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 cylvzm;wd,7ng o ,inder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval an wogz ,,v7;dmt 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 h sxi(snb(+e x 5m:4xucug(0 omass 0.050 kg 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 the end of it0ms5xc:(+ehx u nxi4 obgsu((s 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 ilzvmg:vw- ; /cg7d3+2x eoz +a qjptd*s 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 our Sun, but with mass 8.0 times askwegqf;s3*eomj-14d,zue8 jh: s; g q 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 speedz;qfe4: gsh3 ek*-u jej18sq; mwgdo, 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 m n/in)1et7ycgv+ ,gsg tb0qpl .9iz6low-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 1.50g6l9 i iqn,s.+ )/mecnt 0typzg7vbg1 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 illustratev8, og.kpa 2phcz9* ads 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 nvu.f40 .m i2kmtxzk1surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length t,*+ka afilc. L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–5, +t.c iaal*kf4. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the f ,q6js)-gj * odmhjq(8;ioun /o8 uxvwloor, and we want to exert a horizontal force F at its axle so that it will climb sniu(/o d -j;qq*86 ,vmgwoj8jhu)oxa step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with spg2 2kmxj1 jcd8+wc2cd1 wjva g8n5+wveed v=4.2m/s on a flat road is making a turn with a radius The forces acting on tm2 w1c2jacdnd1xjvw2 5 j kg+g+8 8wcvhe 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-kg rock into a sli3) 1bd tq8gqa1npo(qr 2lhy+fng of length 1.5 m and begins whirling the rock in a nearly 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 fg rq+1l 38 bq(yaqfn2ph)1tdo rom?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as t( 7 nelvqu+pj:hin rods, making reasonable estimates for the dimensio:lqn(pe7uj+v ns. Then calculate 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 which consists of t5 uqyu 37q.9ul2wroo mwo cylindrical plates, of mass5q2w ou.lqrmy 79o3 uu $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 lo-z8gbc ,3ty8m r:xxof ab94x wpl9j bxk;v(0f oped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it w xgmyvc89bx b9pzr 4a-x8f3:lx, (0oftbk j;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 not assulg0)p7z3cvjv me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the ca66(m m em6/e)tafg2rbiyegv5r reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accerv5)g( t2byee6g fe6a6mm /mi leration 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