A bicycle odometer (which measures distance tr( s25gf dv p. ac989lpmlm4e7zuiu2avaveled) is attached near the wheel hub and is desi95.fpmc sia48u9z(e72dvglu 2plm avgned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatevt4zp 51ptxnbm 9x1:gs at constant angular velocity. Does a point on the 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 component of linear xxzn1bmv g41tp:t p95 acceleration change?

Could a nonrigid bodowb:.ewlo8q7s0 o3u ty be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exerpjin.1l6i0dh;y-;+ f xa ctuxt a greater 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 6 ,ld4vecg 7jcto do a sit-up with your hands behind your head than when your arms are str74c j egvdc,6letched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheeliiy/c:2tc ofve7.90hxr h 8ng and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket?h. oic ctvf:20gr y 9ehn/7xi8 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 le63y q8eggm39ouyq u+wgs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotation3woe yyg9g uu +6mq8q3al dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a tqq3nu 2la ev.yx9,r2 long, narrow beam?

If the net force on a system is zero, is the tm. bg;yjjw6 u)6g1 aznet torque also zero? If the net torque oj bzyg; t)wj.66uag1mn a system is zero, is the net force zero?

Two inclines have the same heighq3e+,/;qalusp:* po8 / tbmdu:5gwqjg.jv wy t but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will t gq+bue/qd j*pysj.5wuv,mg8/:3otw:ap ;lqhe speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. /pc:)r(w a silOne sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incl:/ wlcisa)rp(ine first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same m2k*indg. mm2rkw; k3uass. 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 greateiku; w*2gmr3k d k.nm2r rotational KE?

We claim that momentum and angular momentum are conserved. Yv6l ) htdo;maq:y3l7dxb; 9vqet most moving or rotatingv) 3dl tqm: h d69layxvqb;;o7 objects eventually slow down and stop. Explain.

If there were a great migration ocf8wc*bk6st ++u t0msf people toward the Earth’s equator, how would this affeckb t u*f+ s86cwt0+scmt the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any igvno+ d+n(rf 9yb7v/mnitial rotation when sh( +ybv97gd nfvm+/or ne leaves the board?

The moment of inertia of a rotating solid disk /ya34hhb )49hsnklz uabout an axis through its center of mass /nhhy )bh l4z3u4 k9sais $\frac{1}{2}WR^2$ (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 ms1uau01w. qmw*1xp mholding a 2-kg mass in each outstretched hand. If you s umx1*p m0wu.1mq1awsuddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However,t ww-ct 51vmq7 d0vdp3 one is hollow and the other is solid. De q31v pd-5tcmwtw 7v0dscribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In nyo*vfa+1tv+tb *cvdvn5f 3)7)qtu uwhat 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 ttvnd1) 3+7* vuu5t) cqav+yft*fvnbohe top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. 9nr7,5cvbka c:xb:r 5cge 7cmWhat happens if you walk toward the center?cbe7nrb gc:a c 7cv:,9r5k5xm

A shortstop may leap into the air to catch a ball and throw it quickly. 6) )r pw.-yteali)9isptu)klAs he throws the ball, the uplk)))li)p u9.ti tysa6-w re pper 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 of angular momentum, discuss lhtk+pko ;+0u why a helicopter must have more than one rotor (or propellerko;+ p0tlk h+u). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles 698avcjs u3tz: .i/p/ofscl fu.0pei 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.rno9x4x (63 tunpxa h-d72y,vhozuy2 Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, a2xtzn236,o u y ox7pnha4vu9xhrdy(- s seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,00 0z42y36zn4typ8ht:mg b.,f4bn ybv w5 ovu gh0 km from Earth. The beam diverges at 0 b5 yw6nvy 4u 8t.hfvoyh:bz24bpgtg m4nz,3an 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 motornvm,b -8vo8 k jo/oz7m is turned off during operation, the blades slow to rest in 3.08mz n/8 voob-j7okv ,m 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 b2pp 04 dx-otl6xobh,wall makes 15.0 hp,loo x-db6t 42x0pwrevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolu)ubf .1q, k+uj:cbuhqtions do the wheels makb.,hf:bj +1)qu uqu kce?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Caltcicuihhb,o673 k m39culate its angular velocity inkbtuh ci369i3,mohc7 $rad/s$ $\omega$ =    $rad/sec$
(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 complch.32 /zt,i adqa1du1 ,ohbywete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from h ydbiq/daa .12,w ho1u3cz,t 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) i9p e**/ euybyt5v1 vlxn its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s hxky; e+h,+gu+j gugw9*ok5epeed 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 cen3cwyqxoljii )tzj8+* 1jj /z:trifuge rotate if a particle 7.0 cm from the axis of rotatxw/+jij1ijy l oz q3:ctz)*8jion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly ab0 m.i cq5om1v,.psm13ei5qs f ug0wkx out its center from 130 rpm to 280 rpm in 4.0 s. pugfm0s1q s1vewq. 30m x,ikio c5.m5Determine
(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 radius4 zn7molr2m+ w $R_1$ 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, astrona -veid3j7yd8outs 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 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determinij-37odd v8ye e
(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 frol(87.;c, ux(qz weqt, hci pecm rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time qce(pccz q.;ie(l,7t,w8h xu ?    $rev$

  An automobile engine slows downhf9o46dq65om+o dqmg 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 highspeed jets in a whirling665n jpn-.j) mpf -zukpwni;h jtc+x9 “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching fp6-xj)5jn9zjw-ck + uphitn pnm6;. 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 acceler pepw.0)u op:rates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a pointer ppo.0w:)up on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500.ht6 tshf +py6 revolutions 6tshpy6h. ft+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 .;x,p* .l9gdu km3sc9 djjpidrevolutions as the car reduces its speed uniformly fr; ugd, .*dsmc 93 ipklxjd.jp9om 95km/h 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

  The tires of a car make 65 revolutw x*+ab1y0cz9 b rtid2tyqi / *g.lps:ions as the car reduces its speed uniformly from 95km/it 2x :g9b*rlyw+y z*aqs1d .b0ip tc/h 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 aisz,s,0 swhm:)kh-c3ye+: m xh jvcu9ll her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm.,mwvhm9, czshy0 +:: -x3h s eisjk)cu
(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 enc6mq(nf;:yr :+6 hyab ruuk5 rd of a door 74 cm wide. What is the magnitude of tcqukar 65 (yh6rmy;:u: nfb+rhe torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel wo2ek/wsii0 9 shown in Fig. 8–39. Assume that a2wski0ei w9/o friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, aqy+ w hs-lhhya.9e0,ere attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positah0hl., +s heq9-ywey ion and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 38s70qzh j1dms e 5pgf8 3tyhp*ru5hx4 8 y4pht510sf8xdu8mr5hseqh7jg z p3*$m \cdot N$ 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 sphh t)hk6h8 -(b gz+fmmc9koz0dere of radius 0.648 m when the axd hbkzf-t6h +kmg(h8o0m)9zcis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicmj6z05 pte5u6h r2 hfuycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The m5ruthz66mu5 2fjhp0 e ass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thifhh/ 9(jjnj ic8x-p;nn, light rod is rotated in a horizontalnjch8f/n- h; xjp(9ij circle 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 rotatifc6k q/hs+d2z ng at constant angular speed (Fig. 8–+26hq/ fzsdck42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment(ld igv93t7j hs yt(8bamen91 of inertia of the array of point objects shown in Fig. 8–43 ab d1ijtly7s(a(tv39hbn e g98mout
(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 cpd/bkqxi (b* nxm28(wd rz8(sloc8,yonsists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, e3,hc(txh lk x*ngineers 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 i(3htl x*hxkc ,f the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinde(vm4h5e wo jp2r with a radius of 8.50 cm and a mass of 0.580 kg.e 5mp h(2wvo4j 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, acceler(,o 9fmnacw y6ating 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 tangential19c6 3gbc)gzn kz0v d*xitkl)ly 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 sk0)gckvzi3gn9ztd 6 x *b l)c1. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at .kmlqpob5-o5 jcxh 85 10,300 rpm is shut off and is eventually brought uniformly to rest by po8bqmx hjol-. 55kc5a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-k7i5bn1 m 2xwhaix)- nmr2h:cng 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 6spys(qwl, o; op:2 irthrown 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 unif rp:psi( ,ls6woo;2 yqormly 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 thiuj1/p)m c,mx:zma7k rn rod, as shown in Fig. 8–46 au1kczpx: 7 mmr,)/mj.
(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 n 4798l;dv*cb3amaamfsi9ro 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 thec2p4:hv6 o3 nqysf u:l hammer from rest within four full turns (revolutions) and releases it at a speeh2:p: foy43 n6cuqvsl d 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 hawjnlfhez5* g*8 4u1 tw;zne9 u 4;ke7xrxf6o ms a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine de+ rmo,e:mvvb +izl f7.velops 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 slxzqxb o+ z-9x*ipping down a lanx+9box*x - zzqe at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the S4mwnfoy 0eo8c6n; d0mh w-tx,un as the sum of two te wxh ,y4ntdo 86wnfmc0; meo-0rms,
(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 radiusg+gzttg:- jz;gf ; ke1 of 7.50 m. How much net work is require- g;+fgtztk g;gz:1ejd to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withf(d:z,vp 2:imb qc y0pout slipping down a 30bq( 2 fyp mpcv0d:z:i,.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 timbv1b5;9my6/qmo d3vz s /rpsp. It starts to fall and its lower end does not slip. What will be the speed smmos6pyvzvb/5b ;md9r 13q/ of the upper 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 of a thj9+lzi sv4 ev1in string in a circle of radius 1.10 m at an angular speed o9sijzl e v14+vf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrieb;.* pi+ j j+uxtz;oacal grinding wheel of radius 18 cm when rotating at 1500 rpm a +p+*bjtzi ;.je;oux?    $kg \cdot m^2$
(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 is rotating at a ra dv3g-jw;+c wif3pl/a te of 1.3rev/s If hp vjacl;g+- 3fw3wid/e raises his arms 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./ ip86rd*s8ayma hvj .h63q5 gupwh4h 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight .pp8*au gsayd5 v 6jq3/6 hh4i8wmhhrposition to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from a(8qu-8 gdyrvjn initial rate of 1.0 rev every 2.0 s 8 udq gvr-jy8(to 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 aroun:ye0xn eln ) klfx75:yd a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat n e:5k7nfxyl)y:lxe 0disk 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 moms uz ug) +g9thg.d3q et9;e z3ve+e5jcentum 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 Ea db +bu0yj8 bddz7o0)zrth
(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 * ios0kcb-;a*gtci:b z*ej96ood3 vs moment of inertia I is dropped onto an identical disk rotating at angular s ;oko tc 3i -*bsd*ozi*e6jva:0gbs9cpeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atw2te.1 5w5llq7deba jlf2n5y 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 thi cs2gxlo-e6* e center of a rotating merry-go-round platform of r2ioxcg* 6l es-adius 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 angular velocity6l:1, 5wi;cnxalfq xu9t t9 no of 0wua9:x6 ,cn9to ifqx 1 ;5lltn.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a wh1. 7izdjindgo 1/.sgk ite dwarf, losing about half its mass in the process, and winding up with a radius 1.od/k di .i 71s.ggjz1n0% 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 excehpd5z 1 ;*vmruss 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 *+hamim sp6rq1rw m*w ,h*)my$ 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, th5nzl cbublc4m12z7jz-.nc ,s at can rotate freely without friction. The moment of inertia of the person plus t12cucbzm4j zl nns, bl- .c5z7he 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 stand5uhdzs c z1b q*2(9eizs at the edge of a 6.5-m diameter merry-go-round turntable that isq*b9zes 21duz(h5 cz i mounted on frictionless 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 thcz- 0+ 1dynms/2uav fy7l)yjve ground 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 of mass movf2-myuz)v7cnl+/ 10 s dyayvje?

  The Moon orbits the Earth such th1uuaifw2w;ga * xg;o,8(jneeat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the la12;fuejx; g ew8oawin gu,( *atter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ofpl6yvi( 7b/uawxt ; y8 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 cylidmduthqpu49 qep6ox (s n4f)uyrax*z,k-9*1nder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval aquf)u4-p1*ntqr sz4ku* hxpoad 6m9 (xe9d,y t constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid c*asv2d,anywl-*mv5v h v 2dk 0ylindrical 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 and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it revwv22 l-*h5kamndyv*ds, v0a aches 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 spee/x3ic-i)fogd d of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 timkco lj+e-abn,/8+mi r es 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 rotat,nr 8-+bemiloj+ck a /ion 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 for it to use energy stored dh3,7ty7 kualb.f+4b d+j0vj bkbli. in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, usjbkd7ublb k0 .,fi ld+j 3h t.vya+b47es 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 illustratz/11ay nnh,,pa g 7z ;po1ni jt01munqes 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 at speeh)b y e*75pr5ghejuy3 d 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 (9fwf b7+gbc u64fp t1qi.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held ho6g 17 u+tf4wbbfcfpq9rizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R.ts 0mo5ig/ujkwc6pqd82w 2 / q It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it wjdqgk 6 t0 ui/c5 /qs82mw2powill 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 tujfyhj 9c z:n zr28ir30,bc-pd rn with a radius The fcnp0h2: fjdi,jzrb 93z8 cr- yorces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins whn nc0txiac:2,pxb7 r (irling the rock in a nearly horizontal circle above his head, acceleratingc7rnb,n xt2a:(pcxi0 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 as a solid ;m xqzpd(hf+ e12g 3wlcylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio f(31 2mwq hx+dgep;zlof the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pla:l. dxs d:mh5htes, of mass hd s.mh: 5lx:d$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Figk;ixf;u qs7 i8. 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 withoxi87k;fquis; ut leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asxd/5c4.g7wx z*aqf. y7b,uh 5h r yemusume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly tbvpweixmh/(01i- s* from 90km/h t(0 him1wpevib st-*/x o 60km/h The tires have a diameter of 0.90 m. (a) What was the angular 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