A bicycle odometer (which measures distance traveled) is attachwu ll5t by2905l1cvz wed near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch lc9w yw1bzt05ll uv25wheels?

Suppose a disk rotates at constant ano:ek(/ 9dabn c7po;io gular 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 eitoo /b9 (co:ndpe7;ik aher component of linear acceleration change?

Could a nonrigid body be dzyjo1 gkbn;f1t2: +b zescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? s7zd:fd j96xximbh+ *6a2s dzExplain.

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

Why is it more difficult to do a sit-up with your hands behind your head rr1:p,:ulrx 3;fkhklthan whexpf: :ku1,r l;kr hl3rn your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel 5*w;k zj cbwv fgc+1cl76ra6 land three at the pedal cranks. In which gear is it harder to pedalclj+zc1kf w67vr*65cbg ;wal, a small rear sprocket or a large rear sprocket? 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 fasf6ch lsoywgl; 6333fzt have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass isyf z 6lh;3f6wso g33cl advantageous.

Why do tightrope walkers f6 hz tf(zw./z(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zerof*o 3d,j usz7x? If the net tor*x3 o, fzsu7djque on a system is zero, is the net force zero?

Two inclines have the same height but b .0cj 3dxkdpt9kfu:: make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed oj9d fk 0upx :c.tk3bd:f the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from re,k55b:* 8awnsrq w 5v2dmlc isst) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? 5qcsm i5k* lwsv8:b5nw2, dar Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radi9vm(d)d0dy2x zrm: o uus and the same mass. They start from rest at the ty2uzv() mo0d 9 xddrm:op of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. fa .0zywp9t( mYet most moving or rotating objects e 0ztywfpam. 9(ventually slow down and stop. Explain.

If there were a great migration of people qc-muikf*6,)tncrb+y u z- /j toward the Earth’s equator, how would thin,uick+tu/ rz)b m-qf6*jyc- s affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initia w w2rvyx(-msd)8q7nf l rotation when she leavesv-q 7sx 2(yww8frdnm) the board?

The moment of inertia of a rotating solid disk about z )8bj)2; z37zfwkli)tjqd oqan axis through its center q;z)tjfbq))oj7 8iz3 zw2 lkdof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg ma.;/ bixy jdl1ta6a.fqss in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay;tax.6 j abi /lfqy1.d the same? Explain.

Two spheres look identical and have the same mass. However, olmm;v/h t d1(gne is hollow and the other is solid. Describe an experiment to determine which is w d hml1/tg;v(mhich.

The angular velocity of a wheel/mi -cx;cc v s03pc*ixx:m e+k rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration poi :;c+xciic3 m0xvemc*x/k -spnts east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. j2aqj)4v w2;dnkmt pg yd3 w+l vb/3x2What happens if you walk toward the+b23plt4) ; gjywmqv/xadkj wd2vn 32 center?

A shortstop may leap into the air to cat 1afwpob 1f 3f-m z7wupytlwy.p1 w(:3ch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If .wp7pmp3( u1-y ly w13ww toaf:b 1fzfyou 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 momeop 8u2iyzr-4hntum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicoptpo2i h4u-zr8y er stable.

  Express the following angles in radian 0thk(-niuy d/s: (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 b9n,ua+) o q35nziulemecause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diamet9zl q+enu5),i oau m3ners (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at tu4:egit7s jf - q fel.1(eh:i.9xlih rhe Moon, 380,000 km from Earth. The beam diverges at4teh j9gi.flq 7.(1 ::ruxflhieeis- an 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.ri.+zg 4r/hzvpx6u2 u When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerati6p+x2ir.zzhu v gu4/ron as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level frqkeu:q0kgft- *:m s7f) n )syloor 3.5 m to another child. If the ball makes 15.n: f7sk* yq0eq ktfum-g)):rs0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions dl4f 0dyiu xm-ty-0*(o .mp d +bdeh3mho the wheels ma.xm3fthu y-emo *i00 d(p lbmd-+d 4hyke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates n7bhupjo+x.r1f6c 7z at 2500 rpm. Calculate its angular .b7 z6pr+ hcu1f7xonj velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round io*4c4- xrbma o14 fwimakes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child orf1 axbim-4*ioc44w 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 velocity of the Earth (a) in its orbit ar6l xit9e 28j8e(m:1grdfl-kgfm o - lsound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed k6(s9zd(lpl q of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis of:r(;r dmlzp g) rotation is to experiencrdrg)lmp(: z ;e an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13su8* y*az q,co0 rpm to 280 rpm in 4.0 s. Determiqc,o* 8yzsu*ane
(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 radiu6;qim,hfab- . 9*uj * jzgyftrs $R_1$ 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 sp2nm9 imdwc1e4b.n* na ngl(:gacecraft put themselves into a slow rotation to distribute the cwm2.(l 9di4nannge:gbm n1*Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in t(;5ik-e 14 cxqndlj w220 s. Through how many revolutkc1qe5x w;j it (l-4ndions did it turn in this time?    $rev$

  An automobile engine slows down fr.kz ufve79*n hom 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 whirlinqr*2p 5 5 wrt xs1bfk21czxbs8g “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutionsxw8 2 1*ckts pqxs2r5rz1bb5f 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 accelerateq1pqg 5fll/+sg/)ia vs uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveleg+a)s/l / 1p5 fvqqlgid in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turnorsv1x7eaj40 j :/yqcs 1500 revolutions beforesxc/j4 r7jo qa:1v ey0 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 reducesw50q/y ,jvurpriv,5 s its speed uniformly from 95km/h to 45km/h The tires have a dia05,/jur sr yvvw5q i,pmeter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fntq*m,o6 ,hqql ;/ vtcrom 95km/h to 45km/h The tires have a/*,ot lhtqq6cm;n q v, diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a h j9wdj htploiby61 z471wl6) em;mb4till. The pedals rotate ihlmyt7d t1m 9ilwpzjw)4; j 61o6 eb4bn 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 door m: 6l;m2npghd74 cm wide. What is the magnitude of the torque n6;g mdp:lh2m 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 t mm/6) x9 rag)nqk.ngumzl*5qvc j66 bhe wheel shown in Fig. 8–39. Assume that a frictimq5 luvg) xb/6z6 ).m9gq mca6n*jknron 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 massless rod whichr6i(l0t iney 0 pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcul ryiiel(60n0t ate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenint1.d xw2oszokj(*ab+l4r *hc g to a torque of 38 4 .hcsrw2bl+j1*o(ozkd x *ta$m \cdot N$ 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 u,lyk1cxz 2 ,dlj26 zr5 i(iuxaxis of rotation is through its center. ,x5r6, ld(k2zilz xuy1 j2uc i   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 660bqfn6vd7rzpl 4s :yo 6g +x-e.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (rg lsqbz4+op 7-y f ev6nd:06xwhy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a tf0mm f w();hxfy1crt*hin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculaw*x y m1(f frf);m0hctte
(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 angu/q*mcvhj i85q(6fvx qlar speed (Fig. 8–42).8fqq iv5/ h6mcx j*q(v 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 of inertia of the array of zwu( 5ael75/nsb f4 2aiyb,uqh brxe*+nw+-npoint objects shown in Fig. 8–43sin e4x* 75a5w+ zl2b u h(n+/beqaywb-r nu,f about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mas9j .yoqav1gl8 s 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 cy+:bhrm,s spx 7lindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg+s bx7rhs p,m: 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 uniforyp(9(gy cre 5gm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculate p9cyy(reg5(g
(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 nng;z v1s12jhf ,es2( ,huqgxfrom rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a sm r( 1r+:d *ztyp((ide pbq:kr aj9x9wxall hand-driven merry-go-round and is able to accelerate it from rest tjpra z(: dxd91(rqyex:(p9kt bw ri+*o a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brought e,hm k*ar1tq.7;hm- osoye0o uniformly to rest by a frictiona 0; oohs7ea,e my*q1 .rokhmt-l 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-kg bal*p 9(-gii6pppu;1+dxkn xjv8id1 wl ml 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 ;39c q-2a7dd5g l-ecbmxd nm naction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–3a ln;ebq2-mc-7d59dcdx m ng45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod nafiodq* .ma5i4qda51ne* 6v1+svbnm:z vk7, as shown in Fig. 8–46.q aq f57v mz:n.m61 ed5sdkn* nao4iv1avib +*
(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 rk4mb3,v; hhuo3 xf86qlp u3n two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns wn9 91+bltz wlu* bd)q(revolutions) and r9+l9)lw n u*tbwzq1dbeleases 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 momenn0: l 0iuvej7et of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a ton; q.0uyjx 6 nmr1pzd0rque 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 do(e76akvj t(cuwn a lane at 36(vja 7tku ec(.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wiu- trmto p,joe(1ntkh)0nhq, *vv /(y th respect to the Sun as the sum of twypqt(h ) ,ohnm/rj *,1ek 0ntv(ouv-to 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 /ysns+4rwy u g6 1s9/soc6rbz4pqo(pork is required to aossry4q rso4(9y 16wc+z nspbp6 g/ /uccelerate 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 rps(2 3rbkk; oig,f:gtolls without slipping down a 3:t2prgkgk(oi, 3;sb f0.0 $^{\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. It starts to fall and i*ce bel2fmf0. ve h-,lts lower end does not slip. What will be the speed of the upper end o* elee,f.b2fchl0 - vmf the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentuk; ((hbzyxg m0v6df,b m of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.1ybvh(kf, ( bz;x m0g6d0 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 grinding h*a)l ttvct22 wheel of radius 18 cm wl th 2c)t*av2then 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 is qqq a7p 29frc ;*hqdzod8;m. urotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotat8q 2q;97d rfcmhoq ;uqpa.*d zion 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 momb: l2b)t6 aeosent of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position :ts)leo 2a6bb, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rota8sjobe*qt;7pus 0 e3ation rate from an initial rate of 1.0 uq oa 38es7t;bp j0*serev every 2.0 s 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 around a vertical axis through its cxpgct6d9n /, wenter 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 potten/9p6c t dwx,gr then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skaieap82 (feo (v1ylug )ter 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 momen*o4ay8g2lz4z/ gkolitum of the 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 moment of inertia I is dropped onto av)k 0)z1u1gaw2vb lj/f9tb jvn identical disk rotating at1 /a 1fvuglvv0twj) )kb9zjb2 angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsw(ed8z f5 ,r0 op-xenm at 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 merry-go-round platforswy5/ngxy)sw9- c qp6 x5wcwq-nygsy 6s)/p9m of radius 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 vwunkn)53fsj mczo1j 6d0ec9 7elocity of 0.8 kfc5903j1)cdw ms 76jeo znun $rad/s$ 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 collw9k.nec,v8x8w6ae i lapses into a white dwarf, losing about half its ma .8c8e, 9n ikaewxwv6lss in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 9 9z3 ckdwijhsb/pt7-$km/h$ 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 fh6b ss-h:4 (m2q ovrm$ 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, that can rotateynq2czcj ) +* thnp20w freely without friction. The mome )qyhw t*c2n+njp2z0c nt 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 th xwfb;r:y+055zmm vjue edge of a 6.5-m diameter merry-go-round turntable that is mounted o fw+b vu5myj50x: ;zmrn 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 the ground with the end of the rope lying on fl r ,vo ug.4hhj02+vjthe 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 tho20r,juhv+f v. jghl4 e spool’s center of mass move?

  The Moon orbits the Earl ,bqrwpz ojv+ ow860;+ 0zurx)q1cel th such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle oro qeww qcb6 xljp0+ rrv+zu ,)o01zl8;biting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate o.4vrdkrlo: .lf 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/p:e , jwft.gebnz-s)id-yo5 uniform cylinder of radius 0.20 m acquires a rotational rate of wdnz b)y ei.o:-5jset-/gpf, 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 k2kff,l jfc*n3qt7c-of two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.0-jlkc q fcnt,7f3*f2 k10 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of(;ol3p1hc4;ouq qg ni 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 timesr5 iqdt.df4i 7q0 lp*m as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all tir*di7q.d fmp0l45iqt mes, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a loc/y-:vzxdmt3t 3y r+cw-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a f-mrt3v xc3y:z+ /ytc dlywheel “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 ah) w(l e/el+vj72b tvnn $H_2O$ 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 r*ykno;th2g9mxbvx5 :z2uo de2s16 rsolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e.9 ,rqyl hqv:wh0)ivv3 , 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 3qvqwv) r 0,v 9lhiyh: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 verticash1a-wu z:p+wlly on the floor, and we want to exert a horizontal force F at its axle so that it us - wza1+:hwpwill climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with s+j yutp53jek -b ac6a)a:3 d+xq +hfewpeed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cycfq3tjk+:y abp 3 h+a u5 jdxw)-+6eaeclist 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 g ka +, 1+5(qtkuyycmrof length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, acceleratinktga+ ,cq(ryuk 5+my1g 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 cyl ic0)o -yhij.finder 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 outstretched arms, and with arms held tfhc)jio. iy0-ightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, oftn4p qs2.1pvsn du-6mv4p ,ip mass s42sn4 pi .vpt-1p6qu vp d,nm$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alm b a8sn kte9zrd7-l)2*z8o;kcoss k ;ong the looped rough track of Fig. 8–58. What is the minimum value of the ml7bdokzs8)9k -sk a2;*znrtc;eos8vertical height h that the marble must 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 assj-ots (vg2u (,lr.oftume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifor. 8zco 2gp6dih33gmgvmly from 90km/h to 60km/h The tires have a diameter ofvgm8g6gpdhc3i3 oz.2 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