A bicycle odometer (which measur68eky -kjqfp2es distance traveled) is attached near the wheel hub andyk8kep2j 6- fq is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at86sn( *y dc6efi aygx* constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity i xi*ngy(ad6 *cef6 ys8ncreases 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 described by a single va+u 6q) xsolhhz;f 7px7lue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater52kdreg3 unj8 torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands bep zd1s2/ xg;1 chgojun6 h2nt1mn1.oahind your head than whn2/1j1nx gd2zs uo cha1n;.1poh t6mgen your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has se0 (s 85old ciflnq3.wns0by5x ,cx:gsven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocke0,foxn gcl0sbq3l.scx5:n 85sd i(w yt? 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 lower legs with flep; 6*yqj 24m iikwb:ogsh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, ex m:pi4 *bywog;6ki2 qjplain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lon63i9 jb1saeq)xh ct 5ng, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the nejolx ;qk7r /; lk8tc5mt torque on a system isoqkj k8t/;m l5l 7c;xr zero, is the net force zero?

Two inclines have the sameexr ( 9y(pmy-eg +viu8s7ee-h 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 bottom be greate vyexu(r-eyh9-e pe 8s+i7( mgr? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclindlpj /.za.6nq e. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greatnq..zpl6 d /ajer speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sx lka:ag2d+(i6v x6d rtart 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 ti6dr( xdax:kv6lg+a2he greater rotational KE?

We claim that momentum and angular momentum ari rsn ,::m.epae conserved. Yet most moving or rotating objects eventually slow down and stop. Eesa:i. r,m:pn xplain.

If there were a great migration of people toward the Earth’u.ugl xuq)ue3ua pp4 z:5+8 vps equator, how would this affect the length of the dapu.vp):z u8eqgpual +4u3x5uy?

Can the diver of Fig. 8–29 do a somershnyryq4t p eodn4*,b8,2f 5pdault without having any initial rotation when she leav,nepyq4t 4yd hd,5 f2 borp*8nes the board?

The moment of inertia of a rotating solid disk about an axis through its cente qhq*1pi4ag (3u4aay8nfpl 9b0nb o u*r of masp84oyf q1iugh u3a( n9p4lbnq*ab* 0 as 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 ei4qyml k h*h8hfu2 (2nach outstretched hand. If you suddenly drop the masses2 nq*hyul48hkim hf 2(, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, oneqz om v:)/d-ne is hollow and the other is solid. Describe an experiment to dn m:v) /zedoq-etermine which is which.

The angular velocity of a wheel rotating on4-ure 1kt -kzml/mzo: a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the toz:1-oket u rmz -/4lmkp of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edgeq1jgeh ;a3/ le1kob+ p of a large freely rotating turntable. What happens if you walk toward 1;hkj1b +/qleo3pg ae the center?

A shortstop may leap into the air to catch 7daezof;/gxrp4tj7 7.b6n -p db i8oma ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposit o/gpno 7d7rz.m8ib6b pe4 t;jxaf-d7e direction (Fig. 8–36). Explain.

On the basis of the ld,lvzp)2oau6 6a qk( raw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller caa2 6uprol (,v)k zq6dan operate to keep the helicopter stable.

  Express the following angles in radians: (a) v-qv mhb7k4/b30 $^{\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 o iqvyn1 x1f8/ef an amazing coincidence. Calculate, using the information inside the Front Cover,n/ x81 q1eviyf the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dink1r aclb(52hverges at an blcr1n a5(2h kangle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotat rkytz9,d99vqe at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0,vqt9dyk 99 rz s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor ;e . g,n;ou7trclnhe 63.5 m to another child. If the ball makes 15.0 regth, 7 neocn6 elr;u.;volutions, what is its diameter?    m

  A bicycle with tires w+hmu f7f/vm2i mcdrf 0h-2 q5c-6tgs 68 cm in diameter travels 8.0 km. How many revolutions do the wheels mafihr7mqgtc vm+0w2uc- 2-s5d 6fmh f/ ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its iq8+ch69w6te0st sdp angular vhst6 +sicw6ed9 0t8qpelocity 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-round6 2dd)az jbb (51gpxrz makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the li1xdz)b6rjd a5 2bp(g znear speed of a child seated 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 velo)2 f3by)qf*v 4jvghwl city 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 speegpwu.z c/zga e: 4occt-..17eb g tg/qd 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 centrif-e qc.kstv 3t8l1e;nwuge rotate if a particle 7.0 cm from the axis of;w.tcks- t8l e3qn v1e rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleratesmh, obnfb. 2,1gpez,a uniformly about its center from 130 rpm to 280 rpm in 4.0ezn2m ,abp,.1 ,hg obf 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 radiu7zw77n )9obyn tx1aya 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, astronauts aboard the Apollo spaceh r0n40z a )sqic4/ki ;tyi/mycraft 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 revolution every minute during a 12-min time interval. The spacecraft can /rniyhm0qt;4 a0yk ) 4/ iiczsbe thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2cak,qae lck ,b2wvyc) g;4 2y/20 s. Through how many revolutions didg /,2 wak 2c4ycyk)vcqb a;e,l it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to s.qaeu1pw0-wu ( a( (xif 5ola1200 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 for0xbr mo iph)t)k-k -/zc0ief3 the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complefkk r-m0 oi0i)3ezt cx hp-b)/te 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 acceleratex/x z ddyb,/nbt2yrsgi, mu (i7pn64, s uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? xt(7b,,6 4rgsyym n,u bp/d/ iixn dz2    m

  A cooling fan is turned off when it is running at 850rev/min s +v7,i ysi:glIt turns 1500 revolutions beforeyvi+ gis:s,l7 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 6i+x9hiztv k tqniuz,0t +o1( 75 revolutions as the car reduces its speed uniformly from 95km/h h1t9 nu(i,+0z q 7okvtti+ixzto 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

  The tires of a car make 65 revolutions as thy6 gw5 bbpstj siu+n0(,8kl0ve car reduces its speed uniformly from 95km/huy +lswv,k0(ijbsg bt 5p860n to 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 0r iq/p+7b5+;0 aa 7sos0vhivoojghkweight on each pedal when climbing a hill. The pedals rotagih h+/v7aip0rvo5;kaq0 o s70 sb j+ote 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 a doo mkx(m o836rbnqwa (f(r 74 cm wide. What is the magnitude of the torque if the force is am8w(rfx 6 b(nqm(ko3exerted
(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 aboug1:f4gt 3j8h 4na oregt the axle of the wheel shown in Fig. 8–39. Assume that a friction too:tf 8a 3g gg4jnrh41erque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are0z k4lws dxj.5 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 axl0j5.z sk 4wdnd then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighgv w3tm,fh4 t1tening to a torque of 38 w3 14mfvg,tht $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the/zfpb1 1 ot,)*fa schwk8xx w+ axis of rotati tfw 1oabxp 8hzk1scx+w,/f )*on is through its center.    $kg \cdot m^2$

  Calculate the moment of i.lmw7 o27 * aywb nj0mz+1ljsinertia of a bicycle wheel 66.7 cm in diameter. The rim andwm0za7jnm byo7 + s 1iwlj.l*2 tire have 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 a thin, lio4)f t*:nq+2eejbc tx3c nfw+ght rod is rotated in a horizontal circle of radius+tq+fwobn*tf xc2e:c3n4 )j e 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 pottemn* d mtqp;n*mukn98 v5tyk5 eq*qc45 r’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the cl 4km n*kvqptqn5 5*;*uedm8 5tqcn 9myay 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 in ynwpqbnuu7. yw ry:1 ()sp ;q.Fig. 8–43 abo n;wyy y.rpus wnpu q(q71).:but
(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 oxygenhk 9*v isze).vf*-oyxj sls/wq y(3 2e 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 spinnin;q +0g) ghnirrg at the correct rate, engineers fire for g ;hgn+i)r0qur tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder wito4.xslt t-(ez7 vgrr -ex-t hq(zo,8k h a radius of 8.50 cm and a mass of 0.580 kg. Calthr-,tek(reg.4x7qo-v8s z -ot (xzlculate
(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, acceb4g1;d6 3 fidu3dkvdtlerating 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 tangentia mpp*srz*h g +v3f:udnx3s0g -lly 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 o*rm3 vppu ssh+: gd-3*x0zgnff 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 rotatingcu gl:nnhjedthin 5-9db(43g+ t7 5nr at 10,300 rpm is shut off and is eventually brought uh egc+(gnj7l- thnd :r45nt5b nudi93niformly 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. 8–4s7pn+ty(g o0s 5 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 solely by the lpwj9 glkfb5daoej.5)*8f/saction of the forearm, which rotates about the elbow joint under the action of the triceps muscle)9ojj/lge kf58saf p.*db5 lw, 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 lp tk sf-/q*.frod, as shown in Fig. 8–46..kt lf -q/*pfs
(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 conb3 sr ww .vix508wxxo7sists 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 r pewp34;xe(tt pi-rw ,est within four full turns (revolutions) and releases it at a speed p prxw tpw-t3(,;i4ee 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 inej-jq5 k0 6ysqpqo lwmc8w:9a: rtia 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 develon b+p,qncaf)b/8kz3v ps 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 slipping down a l 2w-fr+xtl vgzx.q-7d ane at 3.3wg+ l-r.dfq v2-xt7 zx $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ead5ts.vu:nh (r,e: zeqrth with respect to the Sun as the sum of two terms 5qrv:h,e.sz( teun:d ,
(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 mi -ko4+l37itxpm s) srass 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? A)rxktilsim74s-op 3 +ssume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls witsguqd; f+bp7mqa- ac+gf*8:o hout slipping down - uosa:mfb;87pg+qg aqd+c*f 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 3n1v6-nfgy 8o ,a :8hqsdu yuoon 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 conservatuou f ,6gdsy v1-8qhn:3ony a8ion of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a th6irle9v why;d v3:df 7in string in a circle of radius 1.10 m at an angular speed 6r;y9h3lfe wdv:ivd 7of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindric a-v wnzn gcqx1.e+yg3 1dt,4wal grinding wheel of rgvw1 4n3dneg,. z 1a-twqcxy+adius 18 cm when 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 side, on a platform that *t6gsr*wc54 8 fyuozupeh-t( is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the sppu8ry *gc( s-otueh*54zf t 6weed 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 moment od1r ,jic:)j;*k zsq apf inertia by a factor of about 3.5 when changing from the straight position to the tud: *pjq1i k)z;,acjs rck 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 rotatjmcjto+6 j-9v,o tmk) ion rate from an initial rate of 1.0 rev every 2.0 s to a finjk9m,j6 )v c+j-oto mtal 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 h.krqd-8tao8v ik5zr m ,nr0(na .7zp through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.d .0 hvakrqpr( k,.mitn a8or5z78z-n0 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 ,y,hlb( )yyq7i j.bkrmomentum 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 th t592x8my8qj;e j.kaway 6mytuegu 81e 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 mis1a /gy p2jrz4jb::q +i(jz goment of inertia I is dropped onto an identical di:(:zq+gyjgi41a/s p 2 zrjjbisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atdu (t iee7hbjdfl*0, 6x )3zezik* ez+ 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating mei / q8tfx.9ibtrry-go-round platform of radix/9ift bq t8i.us 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 frrw */d;bdp, kyzr1jvto6h ; y ,,vgxe0-i,g wkeely with an angular velocity of 0.8dd k-,ok/rv ip;h0gywbrt1g* ;j6xv,yz,w ,e $rad/s$ 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 rp:9 u *a4tmo1 goa tl-z-snq(about half its mass in the process, and windins:ut4r -1a 9l *a-tqn(opmzog g 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 excptu/6o e0 ywx3tfk02b ess 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 3: fhixa5 w6 amuh 4,.rxknaw1$ 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, ix5)7 -gn (e-mhf bbeyjy.io,c nitially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform isbiyn fje )eo7x,gm b. -5hc-(y $I_P$ 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 vzdl* rwz)be.kqu-o2+d:b/y diameter merry-go-round turntable that is mounted on frictionless bearings and has a mowdl)b +k- qdzoy:b2/*urvez .ment 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 grounde-a/ 9wcpbxs6 with 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 without slipping. What length of rope unwinds from the spool? How far does the spool’s center o-xsa96wceb/ pf mass move?

  The Moon orbits the Earth such that the same side alway-2n b59apqqop s faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latte o qpb5q2p9-anr case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates froxgalj+4.zuw tzhgly2x *tb ,t).4j .im 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 ofp 56pro lv9zezhss661 a uniform cylinder of radius 0.20 m acquires a rotational rate9r6hlsp56 op e61 zvsz of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical 2ovwu)6(znluq s /, ppdisks, each of mass 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 l(6u2)p olw/,qus vpzninear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular sp,v:w44)r/cat-vqo fkaj yr-seed 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 ofm be pb,cd*i7aat2+ r+ our 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 p r b7t+icp,+2 deabm*arocess, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is zk59yvf/:ef y6fr9s t+m /ew dfor it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and v fwyfe9mk y+ t9 65de/sfzr:/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 illustrateq;f,rf-h cql 71 bl+kis 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 atunzl thgp3y:l ./52wx 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;ge. .f :9not;ydot fo., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then ofoe;. gt odfnt y9;:.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 vecv)lb /hadwhe tk i95q)60mbu e2gv//rtically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests)t h vub2i/a/)0eevwl c9 q6gbh/dm5k (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makqoiip+- si*nl0cur))e60 objing a turn with a radius The forces acting on th nj oe6ub* 0i0po +cq)-rsil)ie 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 lengt:s1mby72f f* mj8oze 7c .turqh 1.5 m and begins whirling the rock in a n.ym js8z*umo :b1ef c 77frtq2early horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as6v gvq si-)t3rlajfi3k *t 6q1 a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretchedt *3j-6vi fs)3 16aklvgqtrqi arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of rvcce3hoyo5-c/ +f5. t6vy bh two cylindrical plates, of macy.bcf5ovy / 65hr+3v e-ot hcss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped rough trackzb1:cfo-+xt u of Fig. 8–58. What is the minimum value of the vertical height h that the marble mxzo-b+tfc u 1:ust drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assuj 9: nu je h0l)z)exazs4y1q:ome $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed l9jy4u,va u0yuniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleratioy,4ualj0 yuv9n 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