A bicycle odometer (which measures dip )e io/y6qn0h4yrr8i xe :e)mstance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyc y8x /iio64m)ye 0:eeph)r rqnle with 24-inch wheels?

Suppose a disk rotates at constant an5/2z (1ygolyg9gs w-qi k qq0mgular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s an2k/s y(0goyg 9 iqmwz1l5q g-qgular velocity increases uniformly, 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 body be described8 gytau) xn5.1:pfr;bn(.a l4qvrf du by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forceso,w-) sy *eei? Explain.

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

Why is it more difficult to do a sit-up with your hands behind yob/,iwqq nr/8 p+ e9kyd2fi3dtc1f:ltur head than when your arms are stretched out in front of you? A diagram may help you 2c:fft1 /wr d8/ eypki+dq b3q,tli9 nto answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pps:*en)j7by sedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why?bjye 7nps*s) : 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 lower lee41n9d6lpe nq; ibb e7gs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatiqni 14denel;b9 7pb6eonal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narroi x46q8w;crab*wyqk /w beam?

If the net force on a system is zero, is the net torque also zero? qh8d)djyghg my3zwl(.b 7l3 2If the net torque on a system is zero, is the netl j d8 .wm) l3q2dgh7h3yyzbg( force zero?

Two inclines have the same h do+zi+0d f8qwr0o8sn (x a.dj*mmop-eight but make different angles with the horizontal. The same steel ball is rolled down each incline. On 0r m+(n0m-+*ofzwpdqxja.8 ddoso8i which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously sta9hcn( dyzz3y wi. 3hj3rt rolling (from 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 has the greater spe 3cdyyi39 nhhj3wz. z(ed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius an 9ff5nxz b(;,ocgzfy5 pn at(8d the same mass. They start 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 the greater rotational KE?tozf pa z;g,nc 9(y5f(b8x n5f

We claim that momentum and angular momentum are conserved. Yu7.e 8 oev)bquet most moving or rotatine)qovbu e87.ug objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Ear t73c dg 0;eacyvco d*wf.43juth’s equator, how would thi 4j*;c.au d3cf7 ot0gdywvce3 s affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any inigqgl4h a(1tk8b 6 pml5tial rotation when she le( 1l 8b5pqk6hamlgt4 gaves the board?

The moment of inertia of a rotating soli)-fkg ba6 hg+cng1rd p4)z8am d disk about an axis through its center of g)4rb cgh d)aakg-p8nf 61zm+mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstr) akcjf;8 v2vk8vpx 4ietched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay tf j 4pxic88)2vk ;vkvahe same? Explain.

Two spheres look identical and have the (sy j d9fs0uzyvq. 5cxq54v+qsame mass. However, one is hollow and the other is solid. Describe an experiment to determine which5jsqvusqvxq0f (9ydzy c+4. 5 is which.

The angular velocity of a wheel rotatih wl w2a39+luxng 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 accele l2 xu9hlaw+w3ration 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 standin4h q46sgeyxjgjizi+r;1su ; 7 g on the edge of a large freely rotating turntable. What happens if yoghq6uj; si z 71xrg+iyje4s ;4u walk toward the center?

A shortstop may leap into the air to catch a ball and throw i3 ) yztumvnef6-1d qf8ult+y)t quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legze 1fmlvyd y 3t8u+)uq)nf6t -s rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatiovq( x e8:iggf ag5r xoj)-/dp:n of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to v jxe- /d:(p:og5g8)qfrxiag keep the helicopter stable.

  Express the following arznk dv,ne,(0xz1r,y*jsvd 1s o4y(z ngles 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. Calculat-4 ldmxlb* +89rekh. vmm5jpd e, using the information inside the Front Cover, t*h8mdm rl+4d-vexlbm59 jp.k he angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bepr(j upgv ..;q 4yega3am diverges at an angle(yrq; p3 jv.4ua.pgg 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 mmle; p*kwop k ;4k::a0;bupsyotor is turned off during operation, the blades slow to a0 mpklwk:seb; * yu ;p4:po;krest in 3.0 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 the ball mak)jb9dyhg4n+2kidt j) es 15.0 revolutions, what is its diameterb 9dj yd j)k+2i4n)htg?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Howq7 q8wdqiodv aldn7 f0/88rj2 many revolutions do the wh odq/8dai78nvwjqrfl8 7 qd02 eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter vk 6v n bga5h/-,)jotlrotates at 2500 rpm. Calculate its angular velocity iha,ko)lbvv-ngjt / 65n $rad/s$ $\omega$ =    $rad/sec$
(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 revolnj73e86dk dny ution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seate d687enknjd3y d 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 velocitf/:xa,,nn nbv y of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a 0j/(rpvl vc9 mmma)+i-wr y8s d4.wdzpoint
(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 min5n 6svcmui4u 5+ky- p+x( ea particle 7.0 cm from the axis of rotation is to experience an anxe4v p(iui6 u-cmkynm++s 55cceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abojocc7 l 0vy8a*8zqt7 s;o+ lghut its center from 130 rpm to 280 rpm in 4.0 s.ojy h8 gacz ;voc7+tll07q8s* 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 4 y jyzt6i60n7y yho0g$R_1$ 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, astrona1ha:4am;yq5rr ha u8c uts aboard the Apollo spacecraft put themselves 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 81ayrcqma5ah 4r:; uhrevolution 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 151 boi)irn/anw +d1/ zx,000 rpm in 220 s. Through how many revolutions did it tunr bxd/+)i /i1 1nzoawrn in this time?    $rev$

  An automobile engine slows down from 4500 rpm 7p )e lqsr.4u.ac37 ft(c ixpsto 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 whirling “b : oig3s+0u5knfmji/:euxy )human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before3ifb o0 kj/::x5uum +egis)ny 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 diameterfhmm*i;2eui/ .aybv u8t dp78 accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel 8 i/ ;evf8u.m uhatymi2*db7p have traveled in this time?    m

  A cooling fan is turned off when dhf ;ci u:dqypg*,f)n;s+p 9xit is running at 850rev/min It turns 1500 revolutions befofu) f:sp diy+;pgc n,hd9*xq;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 6.5 s;x0e-g xrx (aycr /o2p*,wpvt zay5 revolutions as the car reduces its speed uniformly from 95km/h to 45sz*.rc(x rvo2e/ xaxp- p0ty a5w;g,y km/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

  The tires of a car make 65 revolutions as the car reduces its speed uniformlya)uiuq )tslgwg : o1xe6 .5dn. from 95km/h to)l5:g)uqwex1. g6ond.i ts au 45km/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 bike puts all her weight on e *g b x56v.bgm)k;t3md)alhnoach pedal when climbing a hill. The pedals rotate in a circle ofxv nb.bktg* )hmg)d;la5m 3 6o 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 a door 74 cm wi wd pjclqmucr28x2id4y o5c5 mp4fk/8i/n 2;ude. What is the magnitude of the torque if the fo55p8uli//cj mxcdw o4 2k cr mpnu42qf;2d8iyrce 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 8dfnse1yh42ng.mlb q.6 aks7 , n ijiusq95+p axle of the wheel shown in Fig. 8–39. Assume thatmyi hq1 .6.,n4inf9lse b257gak d spjn8+ usq a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass ge 3m8ugw w+9k37sr snm, 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. Calculate the magnitude and direction of r g89+n3s 7e mwg3kwsuthe net torque on this system.

  The bolts on the cylinder heaibp9k vh;6idj7 up 72jd of an engine require tightening to a torque of 38 9kb jh ujpv; 7id2pi67$m \cdot N$ 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 +b g4h (gdmxe610.8-kg sphere of radius 0.648 m when the axis of rotaxd4h +( bmgeg6tion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66a d:vur8, y,(as* ddfs.7 cm in diameter. The rim and tire have udva,dry8s:ds f( , a*a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of wjc )4kxoi. k)a thin, light rod is rotated in a horizontal 4))x w.co ijkkcircle 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 potter’s wheel rotating47yk tmxra gb,we28nmqh.6d; at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N4r .bydkt7;6 ae8 hw2,nmgm qx 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 in Fig. 8–4b fypal5) 4h1i3 aboi1 45lhaf) pbyut
(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 massel 9p (wmhh9/ceou/j zfxq(, ( 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 cym k/iivivs 22*lindrical satellite 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 required steady force of each rocket if the satellite is to reach 32 rpm in 5msi2 v/ki2 v*i.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylbe80vq asmtmj+s 74u5inder with a radius of 8.50 cm and a mass of 0.580 kgu 5vma 7b+0s8eqs 4tmj. 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, accelercjkw)xf248q a ating 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 tangentim+eo87di aexv pz*2(g ally 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 pvo*d(xez 7m gi8ea+ 2the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off a8lt-j pzqb3we, ha( s23;gdoynd is eventually brought unif3,wq ol ab (3pdzhs- jge28t;yormly 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. 8–45w y8tz-j4i 7quz.ytt; accelerates 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 .rj4 ite ,5j*jauq3kg solely by the action of the forearm, which rotates about the elbowq5 j jk,a*.rgi4j 3tue joint under the 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, as shown iof9jko i t85-,zd .pbrn Fig. 8–46j-op,5io9 f rdzbkt. 8.
(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 consis1iur c3j .xgkzj -*/uygd:kl 7ts 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 turns./z, q ;aq) pbl0kebws (revolutions) and releases , bl)/;pzqk.wbaes 0q 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 has a moment of inertia ofbow e+wm163q y $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine devv0u iesoi ,-;yelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slippin-:*6kn xdnwb ng down a lane at :- xd* nb6wnkn3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect t7x1;2fiqa)h; ehijy lo the Sun as the sum of two te jai1f2hq;xye ;il)h7rms,
(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 ofs58dk (vsvlosa 1/ fe- 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.sva v5 ls1d8/-(ke ofs00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 5g7rnvvp hr.2 kg starts from rest and rolls without slipping dorv5g7 npv.2 rhwn 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 i2mq2 nh 9f:1e /e+uf2wdftol rs balanced 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 co:1l f2 e2u/qmrdfwt2ef9+h n onservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-6lre ,8iy itx1kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed oe rtil8 yi61,xf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2rew-zgv4k 5jf qf +11u.8-kg uniform cylindrical grinding wheel of radius 18 cm whjg1kuwr vz-1fqf45 +e en rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his m(*tdzn)z o4xwbzibp,w3 k8; side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal poio bp4xw3kn)8 ;bmzzdzw, (t*sition, 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 her momenlyyi7uhp vt 03h1io* ,t 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 whei30h h up1y7,*it lyovn 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 rot f38kx/seyg n1ation rate from an initial rate of 1.0 rev every 2.0 s tg1ek8 xy/ 3fsno a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center9,q-euzpja*yaf *g gq35f6j r at a frequency of 1.5rev/s T r 6qj-5ggp9f,ae *3qaujz*fyhe wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinni+4 h- nsye8wgwc; os1xng 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 g)v,m x 8ecg*hEarth
(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 qn tpbc,h,po-a) 2)y u+ t/nfeonto an identical disk rota)/ tppbuhf-e,t) +oac yqn,n2ting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4te+hfion7p8f66e q d4 $rev/s$ 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 sta4i,yz2)v x:0hvnsw ujmxa,p(nds at the center of a rotating merry-go-round platform of radius 2,sa0wj,z) 4: (phvnmv ixxuy 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angu5kgqa)dj 8w ek4 qg57hlar velocity of 0.8 agh8)5 egjw7 kk5qq d4$rad/s$ 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 i-9vqgk 5yg-h*y 1 bfiinto a white dwarf, losing about half its mass in the process, and 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?(rouny *hi g-v9f5-1bkiyqg d 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 elpwq7y g1y/0 )/ pcnagxcess 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 e;ptw :rxc/6z $ 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 (ch tzfdl j-.oz0bktvm5:erh m- 2*a-rest, that can rotate freely without friction. The moment of inerti:dt*-b0emth(ljf khz.rza- -52m c ova 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 6r2 )iup ky1vk vu.c,6 ik-u1ga* yubgthe edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless beari ug2r,y v*ab1.iypugk-vicu ) 6k6u1 kngs 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 roh8l 1bn.rf7vkgte pj+*:-s jmpe lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from+pb 7 esh-jfl8*mr 1v .:ktngj the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces7bn 3mff1:l8 ykqq 1hw the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to wn: fqh3m8b1f17l qykits 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 oxy u men ce:(h6utfr r2 -)f0.rp2+duef 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquire 4 jy9 mptd6wq7q wrpun7p 6nm69sn2s8s a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliver9qs2nnuw nq7p d js6t6 8w4ymp796rmp ed by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solgfd9hc3:sd 7antww7f .y v ;3w;b fjw-id cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg;3dw7:bw f7w9.vjngwsy3d ;fa f-htc and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how p05*3c0luy a6 .omhtnncor3k 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 ourcun/nrt7-5: y c fj(pa 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 an /cy-r( up:f5 cn7tjno angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storeo9f49oxdki;cy4x9gj u/ b0cod in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”d99yooc4 xfx4j oc0/9;b uk ig
(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 ag+ )w9lsccgb :v :4htwn $H_2O$ 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 surfaczc3sr,)4go ( kx5gxj pe at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignohc9t.1j *9q dr+cufb ire friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as s .+ uicb91rhqj*cfd9t hown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically c gvlsx,n.6.x19nn pa on the floor, and we want to exert a pg ,n9acn. .vn1 lx6sxhorizontal force F at its axle so that it will 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 turn with /5c fxt -l7wlma radius The forces acting on thc w5ll 7/xft-me 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 sling of length 1.5 m and bcnfdqjb0: y16egins 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, 6 qcjbd f:n0y1and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid */4v1fozt lcn cylinder 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 outst4 1nft vlz/*ocretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly w *v+sp;0-x atcwril7 mhich consists of two cylindrical plates, of ms0lt+vx;a- i7c *pr wmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 x6jk*:kuj0rr fw 1hw 68u4dvgalong 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 without leaving the trach w j urvw0*d6146ujkgxkf:r8k? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu+ q/yv.dbv;egme $r\ll R$ h =    (R-r)

  The tires of a car make8g-l m sfj.vw1 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration ofvjf81s- w.l gm 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