A bicycle odometer (which measur7r:1llxelt*m-u)q- oy ;y e tces distance traveled) is attached near the wheel hub and is designe;q yc71elox- ) l:-yml*ert tud for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on thexydm+h5e /v(b rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either coy/b (dhv+e5xmmponent of linear acceleration change?

Could a nonrigid body be described by a single valuewm :z- x2p/tyw-uq9c o of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.-q /qv oll :sv1lj, ;weah5av,yrv0c*

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 u1ijbiad s ymy2i;w-o4;ol7 + hands behind your head than when your arms are stretched out inwmo lib+1i4 ioy;dju a;2 7-ys front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and u. zz hq3do;:ethree at 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 sprocket o:q; ezdz3hu .or a large front sprocket? Why?

Mammals that depend on being able to run fast have slendl,sipg;dd wq/5m rr /fgkk,-)er lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamick, fkdi/p)d;q g-s/wg5rr m, ls, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a ldx3 6 s8mepi-kden4v:ong, narrow beam?

If the net force on a system is zero, is the net torque also zerd /ap( ,fl(9ybh2rurgo? If the net torque on a system is zero, is ther , fg(pbld9rya (2uh/ net force zero?

Two inclines have the sam a)t:,+w53l x w sxjo-;jpmnjce 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 grea;:3sjwcot ,5x+xa jj )mpnlw-ter? Explain.

Two solid spheres simultaneouslc0 vt-x/cg;z ,hth9zmy start 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 speed there? Which has the greater total kinetic tm h tc0-v/zh9;,xzgcenergy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They star6 omjcy/ uv8g-1+jiknt 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 ty 8jino+ck-6g /j u1vmhe greater rotational KE?

We claim that momentum and angular momeb56i8e q5de n ib*-udyf(a.b-cqxihn5;u2mq ntum are conserved. Yet most moving or rotating objeb qye*u aqhnd(unb5 cdi5q -e6i;.5 m fxi8b2-cts eventually slow down and stop. Explain.

If there were a great migration of 8(,hpi6qe ddmyyzst + /:x;kr people toward the Earth’s equator, how would thy8(zp;,ri6: md hq+ ydsx/ kteis affect the length of the day?

Can the diver of Fig. 8–29 do a somer p7qhm7ivg+;s3wsan. sault without having any initial rotation when she leaves the boasig asp .hvwn3; 7q7+mrd?

The moment of inertia of a rotating solid dnt+;gezyjuy;h.p(e /ez : )bgisk about an axis through its center of mass (eg+ hg:n)ye zjpb/;;yet.uzis $\frac{1}{2}WR^2$ (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 sittinh pl6snzy ,9x)nx*y,rg on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the n)r,yx6xl* hsp9ny z, masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the sar6 vv ,(3ctkp8 3zfi7h6qc yyzme mass. However, one is hollow and the other is solid. Describe an experim6kzih t,6 (3zqvpvy r3cy8 7cfent to determine which is which.

The angular velocity of a wheel rotating on a ho.(y)q2dodc twbk, b g*,tc h;vrizontal 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 top of the whee ,2y dbb(g*dwckoqv.ch,);t t l. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotag1t hhbcvt45,:fb61bx)q cc lting turntable. What happens if you walk toward the cen4bc1 ch:) c tlq,t61bgfvb x5hter?

A shortstop may leap into the air to catch a ball and throw it quickly. As he thy(pmr s(+pe 6k6dok0 grows the ball, the uppeosk66(mp +p rgkyed0(r part of his body rotates. 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 of conservation om,;phyqt c4l 6f angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss o p4yhtc,; m6lqne or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglem7 kxcml :wj2 o2dcy/ nfoz,7l5d;hd;s 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 v lp4kktg f,r:2wj.u4 coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of jktuw l.2 4p kvgr,:4fthe 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. Thewj5 ,hoc;qn j+ beam diverges at ; 5jowqn,hc+jan angle $\theta$ (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 m733fta lu3, n whfyg ;l89dfeiotor is turned off f ;, 833ai7 hw9ledtynulfgf3during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a leve. y7+ae jaxl4al floor 3.5 m to another child. If the ball makes 15.lxj.4aa +7 yae0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 6sd;agz8 p:)hkc0ts5lft+q9itc* hkkm. How many revolutions do the whe*phkd+aq; cftszt h: 9ik5t 6l8gsc )0els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpmce2amh k99ilz(3b* tu px-bqoo.h 8*g. Calculate its angular velocity iu8xpeh i*k cqt9bzl-9 .o ho *32magb(n $rad/s$ $\omega$ =    $rad/sec$
(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,by1pe6 : eds-gib:7 +aljk kd one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 egbd ik y,ebks7d+:6p1a- lj: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 Earth (a) in its o2sq 3la,(mx f .fyni4rrbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speede fx+3e) r p(qihp-;kf 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) muwc f nkmnq :az*ix;902st a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 10n mw0ckfa9* q zn:x2;i0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm tos-aiqct x 29t)qkj9 8h 280 rpm in2stj99 )aicqk8x-t h q 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 radius ;o y9 -(mxx. r.rzhlwtm4 x9 r.zir.ku$R_1$ 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 spacecr*lf)ka h7r-5oca3bt saft 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 spaca lc*bt7-shao )frk53 ecraft 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 rea u,h p8c.0nsgst to 15,000 rpm in 220 s. Through how many rev a0pg.hu s,8ncolutions did it turn in this time?    $rev$

  An automobile engine zo h,(ll9d8dr 2s nb8*ig joy): o4ubv,pehf-slows down from 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 highspe a4thoknnxqf)yaq g+pw*si.( -;2xw*ed jets in a whirling “human centrifuge,” which tao *(4)aynkxxqnwg* qaf.p2sh;- t iw+kes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 36 adkxh.cxyzm oh3hp0 c*+8- h.l5vv3u0 rpm in 6.5 s. How far will a point on the x05d3. 8 mvhhhh+. vak3lz-yux poc*c edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/vli .5rz+wj7 rc d(,3 s*jerezmin It turns 1500 revolutionwerz (r,ldrz 7i 5*. jse3vc+js before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fmw8+cbyva so(7m /-cyrom 95km/h to 45km/h The tb v-+m(cs7y/wa cym 8oires 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 redvkg 4xryr0+sic1t03qg / e4isuces its speed uniformly from 95km/h to 45km/h The tires have a diamet3rix0/gs 1 q +r4cvitg0e4s kyer 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 each pedal when climb.k4s0/ e fg4hu t*teawiu8w-ling a hill. The . aw w i/ e8ge*ku4s0-fhl4uttpedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force ofaa+swx e(4v67 cec2pzn-l,g06)uja agrfy 0h 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the fj7ghv0+xu l r-4gea(cy6n , 02f sepzwa6)aacorce 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 torqupn96zmt xta .2e about the axle of the wheel shown in Fig. 8–39. Assume th9x6.pn2a tt zmat a friction 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 masslypb0dl2npn s; u3 *4caess 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 the net torque on thisnsl py a 204uc*bdn3;p system.

  The bolts on the cylinder head of an engine require tigh4jk7o way8s q3tening to a torque of 38sa87ok 3 4qywj $m \cdot N$ 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 w 5* 3vdvnws)u) lo,3qr3rmx mjux.e 4rhen the axis ofrvr ,j45 ) xxwm lmqude*)3v.sn u3r3o rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The: tt;r+;ovpzb rim and tire have a combined mass of 1.25 kg. The mass of the hub can be r ;b;tvt: opz+ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontal rc 8tautrj.( *ekpwp22e:zo- circle of radius 1.2 m. wjtrep .*e 2(u:c-akt2p 8orzCalculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant anguc. 3)ggeb ug2ilar speed (Fig. 8–42). The friction force between her hci gu.g2g 3)ebands 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 inert .eilvr ;y/zz6 bct*.xia of the array of point objects shown in Fig. 8–43 abou. ry6v *z.tizl bxe/;ct
(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 atvie6 x6(/dl , g/ltbg8) authta*bmy :oms 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 spinningkwn ig*j+vruo0/ y3 /c*mbhy - at the correct rate, engineers fire four tangential rockets / hg0i n3v r+wy/-bmk*ycuoj*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 a4 84llkot pcgai6o0-cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cal-o4l kalta p6g480oicculate
(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, accelerating it fr vtp6/p4 / 9gd,kqpvklom 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 tange/o. x s0r6oa0 v1)rxqgq8ii ujntially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecti/ )jaiqoq o0 .8rxvs16x0igrung 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 a) 12 bcnzwht/ olfd9+lk-:xnind is eventually brought uniformly to rest by a frictbn9 2 lnzol-w/kdxcth+:f1i)ional 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. 8–457jxtchq k;i2+ 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 isfc;0yfm: nkh jqi5 )s87v0j o,ybv(ox 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 accelerated uniformly from rekbc7fi;,0vm5xhs 8(jj f:o yy)0 qn ovst 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 sho-bdz l4 z;tz)swn in Fig. 8–46. b4)z zd;tl-sz
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of twz- uq 71/7-vqj fh9ac3.rn xxz daq*tto 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 r8s mi c8ezsi 0q.:9kflr3 whe+est within four full turns (revolutioc9 +eiq:m 3ielw8rz 0s.8skfhns) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a q;k38fukz 7dtmoment 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 develops2o.zfqfp t 0rua8 -x9s 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 dowzk4qvk4, xcez +rc1r 8hebr2- n a lane at vx- r 2ze4r1,ec b8qr hk+c4zk3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ofg x5jtjl57z s4bph8c v o1k.v1 the Earth with respect to the Sun as the sum of two kh5x g5z4s8p1j7 o1 b.cvljtv terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net w:w6likc6yqsu3 5u u ,hork is required to accelerate it from rest to a rotation rate of 1.00 reu :kih6qywc,5 l s3uu6volution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roll j* lhw 99)w9myvi/ydbs without slipping downvl yj i9d*hwmybw /)99 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 on its tip. * pbu/ ftnb;rj)( hg me:+7f1r9fppooIt starts to fall and its lower end does not slip. What will be the speed of the ubob(*1+7)hp p e fm;pfr:rogt/fj9 un pper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end ova5 uswm+wf+x-pex k.. dm *(sf a thin string in a circle of radiu dku wxw.( + m5aes*fsm+p-vx.s 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding9m/w dimv kef,+2k 2nb wheel of radiu,29vk imwk defbnm+2/s 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 platfo pi kb8ntmpd/.i.e2yty 0/0vfe-pi ,grm that is rotating at a rate of 1.3rev/s If he raises his arms0y0gveit 8e..pk itb- yf2 /dmi /pp,n to a horizontal 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 her moment of inertia vv0uq9: jz:7 yjdkq+m by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in7: m9v j+k 0uzqjdv:yq 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 jz1u1tg bd 5yj)g3:+m0em h3 o1g dbovrate from an initial rate of 1.0 rev every 2.0 s to a final +1oevug1j0 3gydd m3g):5 bj 1tbhomzrate 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 throwsra7mwqd fqp + fo9 0)*4p2peugh its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass rpp4q02o9)ep s 7+wm*fwfdaq5.0 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 angula/hsui+ (3ebu-u7s sks r 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 Earthefhp:v0. aksa5 oiepma 62)u(
(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 an ident 39fnt ej6;cvxical 6fex3; n9jvc tdisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4qwrjh+ x7rii7q; f/l+ $rev/s$ 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 ktr)suk;xh0rdvjdi7xx j3 (;-g stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia i3jhxr 0)kjd7(r ;v-t;xdsux920 $kg \cdot m^2$ 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 angular vel xh i+ :rr-ezmq)p+gf+ocity of 0.r+riz:h)-xg+ qm p+fe8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half itshulw6(r p;:2tm1 6 g4ccllyxy)u mb8n mass in the processxw6l; )mm2uc y8yn4p :ll1bh 6 g(rctu, 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?(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 o 3( 9lhrlsu0p5. vk34q2macq2rkruao f 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 jxl2m 2 d(bb vw.0n1yt$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, thao3 h 2z1o(showt can rotate freely without friction. The momeh23(hw so1oo znt 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;57x ufjuop9 u a 6.5-m diameter merry-go-round turntable that is mounted on fricti;7 ufo9uxpu5 jonless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of ok :v npe4*z ;o4jynbsjd62n/the rope lying on the top edge of the spool. A person grspj 4jb2;v dzn/yne 6n4ok:o*abs 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 of mass move?

  The Moon orbits the Earth such that the same side g-,tt0y ea acmq.za(lwn;uhc8d-i / . always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbitalcm.,ial.uny waeq t ga0(z;--h8/ d tc angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at hn4k) .sqsz6bdu39fp 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 cylinder ,e/zd6 qjfd3 dof radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculat/d,jd eqdzf 63e the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disksn*mrs.m h boymohumd m/s, y6uz,/ (qv5x l8;/, 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 linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from5,m lry8 qdh 6h s(mv./ ;xnu*smmoy//uzomb, rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the ree)9kartbxv638 l 42 iqlabs3 kv)3jvq ar 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, b. rx*,i12j5txb nry tk qyx14gut 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 xi tjrr*,y 4t 1kn.xqy215xbg 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 for+.350iyyokqp rfv dc 9 it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total ma5c3 i.dfkyo q0ypvr+9 ss of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an:08gk: z p8uf9zoxauf $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at spe5 t zq;foyid3cg:xx*6 ed 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 (5cowh2hn; dr* mvf1 i5i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod.ihwc*fr5nd51m 2v; oh 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 l3fxr. lx;vvoy 0tzjgf2n /0/standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will cl glnf /. y0xr3tov/0;lz2fjvx imb 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 wit7jh m8i15u zl9umfh*f*pf c-+ dl,f kdh a radius The forces acting on the cyclist and cycle are the normakfuh, -dc98hm l1j zmulff p5+ *df*i7l 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 ayqp a(j92 ple7 0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque requ lp9eajy27 q(pired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her x1*b2 svenj0b arms as thin rods, making reasonable estimates f2b*vn1b 0 jesxor the dimensions. 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 consi; i .,gbaa9htjax3sh (o7bl 3ksts of two cylindrical plates, of mashgl.b;o3ijkstaa (ba39 h ,7x s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a67ksk:z qy43 : hkf0z*xfwzblnd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it fksz:kzyh3w :bq* f z70x6l4k 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 as9 dp n1f s)05zi+t(m0xlab (*)bjtuoxp dg) dksume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as iv 6i:q,s fbx7o 1tyv11uam*mthe car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the anguvmqi :1aoi *xfbt sv,6uy711 mlar acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s