A bicycle odometer (which measures distance travele 4xbv,y d8b7ffd) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wyvb bdf,fx 784ith 24-inch wheels?

Suppose a disk rotates at constant angular vq1vicmrt*-jna a):vo.o ey :(elocity. 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 tangentia:m(-:oa.i1 yte*o)njqarv c vl acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single valqbbh n6(w7u0c ij(d4 zue of the angular velocity $\omega$ Explain.

Can a small force ever eot9rse0fsb+ss m(yz:; :. 5nahc3xmwxert 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 to do a sit-up with your hands behind your head than whxtgl ;px-a0i8izb8n0 en your arms are stretched out in a8ng;xxlz t8b p0ii0-front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and th wvf8w/d bi-lxt5qo9 ;ree at the pedal cranks. In which gear is it harder to pedal, a small rear sprocketwiqv;/ bo-xlw9d5 8ft 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 fas5- tdt z;l1lntt have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain -z51lt tn;tldwhy this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) 7bpb;n bx;c3icarry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the rh31nx f31 zopnet torque on a system is zero131px zronfh3, is the net force zero?

Two inclines have the same height but make different angles with the horizontalpsq / (gv)tei5l*q5sq. The same steel ball is rolled down each incline. On which incline will the speed of the ball at thel)5q spe v5qs (*qt/gi bottom be greater? Explain.

Two solid spheres simult, avjl9/2o,+ w: ve rqudbat,taneously start rolling (from rest) down an incline. One sphere has twice the radius and tvvo jleu,9aa+b,dt ,w:t2 r/qwice 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 energy at the bottom?

A sphere and a cylinder have the same radius and the sxqelm 5mapvp5dfb85 z p/mn* ph:79w+ame mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at tz:w8 n m* em/p5pvmpb 5 pq57dah9xlf+he bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mvyyw*p9*ow9 odse6 m*ext+f 5ost moving or rotating objects eventually slow down anyoxy*vt +9f6*wm5*p9 seo wded stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouldxz4 eig y ktp*6i:6st- this affect the lengti tk z*6s p46ie:gxy-th of the day?

Can the diver of Fig. 8–29 do a somersault without havingr5x5 jgozcnyzqc /46 1 any initial rotation when c/n zzxo4g q55j6y1rcshe leaves the board?

The moment of inertia of a rotating/.okp1rb n; ji solid disk about an axis through its center of mp/;.inbjkro1 ass 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 sitt+w; mkj jpks6*ing on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, +wkj6; j* psmkwill your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeve;feq/b 86.jy f xnrdz x+.4harr, one is hollow and the other is solid. Descrirej h/ f6dy84brqfx+nz; .a. xbe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal ak +)h:jlw g7 b gsaq:x5o2*cthxle 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 whe:x at +gs)h2g lowh 5jk7c*qb:el. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntacjd7iap.q(a7b5p l )mya iv, (ble. What happens if you 7)p,a i(v ja7 l(dmi .py5cqbawalk toward the center?

A shortstop may leap into the air to catch a bst cz2 p o(indii5do34g90 ;vqall and throw it quickly. As he throws the ball, the upper part of his bod2; 0io4 3sizogqn vipd( cd95ty 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, disc7:wmp0pa r l3cuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicoptr7 3 aw:cm0lpper stable.

  Express the following anglh7 k.h0mbgw/ des 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 Earthdofnm;m **4y t.v4kpu because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as st *dun*mfyo ;vp44mk.een on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 sy18 u rkz;z:a95,ulh2a *9l0txiagv7 gy lplkm from Earth. The beam diverges at an8:yguz,k7r9plh;x1aiv5* g u lz92lsa 0 laty 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 motor is turned 1 qjux -k/uhzp:f;,8xoun8zcoff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? u xuzu zqc8n-8hk o,jp/; x:f1   $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chndg 3.ixj+m9pild. If the ball makes 15.0 revolutions, what is its diimnp .j+xg39d ameter?    m

  A bicycle with tires 68 cm my9rfd0,wiucv 5 n(g 2in diameter travels 8.0 km. How many revolutions do the wheels make?5, if vyd(u0nmc2gw9r    $rev$

  (a) A grinding wheel 0.35 m in divdxh+urgi/, 4 .:ibalameter rotates at 2500 rpm. Calculate its angular velov,4g/bih:.ru ldaix + city 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 makes one complete revolution o+ sxf/ u *h7byziu78bin 4.0 s (Fig. 8–38). (a) What is the linear speed of+zhfb8i7/xsbyu u 7*o a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) m:w29bcrhz2a vt;fd8:k y0)z t;z hd ein its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a p4 cc0(elyyd)juy*4m m oint
(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 rv)gs+7unj o cwn8oub(wc,5(zdkw/4 from the axis of rotation is to experience an acceleration oucg+b j) w8 w ,nrkcv(wo/5dsuz7 (4onf 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c.,zmorv + oyxrqn: 4g7enter from 130 rpm to 280 rpm in 4.0z+yxro oq m.g vn7,r4: 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 )j(8m*pimvfii l i*edc), 4hy $R_1$ 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+jf 9ms*ptz)t 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 +p f*9)sztmjtduring 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 t af*a fduc4;6 l7*phifrom rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time tufp clafda;47hi**6?    $rev$

  An automobile engine slows down from 4500 rpm eswx:j8cg5ujp1ca0) 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 streoqa da4h mxchuw1w64,4fw-pp qafg):07g (ax sses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolff4a(aa-wx o,uda6:m40hgq pgp4w) cwx17h q utions 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 k8 dge45ivetlx4ho8vuymn1as/6d*; uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel8xhe1/ ksveagtn 486lv4 u idyd*;om5 have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15c7lh: p0hr1fo4uv6 lu 00 revolutions before i4 vuh0l ucpfo 7r:l6h1t 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 -q my cnb3i4 xc.8,8 neb34hpvhnmq;nspeed uniformly from 95km/h to 45km/h The tires h3ev4-i.qh4 n;mynhpn3cm 8,q 8b cnxbave 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 rev ew(.;ay j2u ijq0 1h.jx.pjieolutions as the car reduces its speed uniformly from 95km/h to 45km/h he jju;0j.1x e.ij (pya.2iwqThe 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 bike04u,v ,7i- j vbvc v3dvlynaf+ puts all her weight on each pedal when climbing a hill. The pedj-4v + ayu c dv,3vnvf0b7lv,ials 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 of 55 N on the end of a door 74 cm wide.4h;usguu5by p ao n o0;a2v3h: What is the magnitude of the torque if the forh 3ash;po oy0a4v5uu;n 2gu:bce 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 shown ijeqd(ub */ t3waza6vs e+g6x4o. lfq-s ( ekz4n Fig. 8–39. Assume that a f- zb6x vjsawuql6g(ea* 4eo4e.dqf 3kz/ts+ (riction 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 e ,4 sgiu)ir i9:cc-xag84vdknnds of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positid :i4ivi-sk,n )c49x8g gauc ron 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 3 48oacmr2lk me3k-ha dnk b; .ac21a+t8dkabmman c;k+c1234a r2.ek h tl- oa8 $m \cdot N$ 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-invn ed8ao 10q1r vb1ii/a4 4ukg sphere of radius 0.648 m when the axis of rotation is thr 81nd0qa1raibe4/1i ivoun v4ough its center.    $kg \cdot m^2$

  Calculate the moment r h5n4qrqv4 n7v u6e0kof inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 17quq 54enkvv4hnr06 r.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated ic lk(6q2qr if;n a horizontal circlfq k(;2 6qircle 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 onc6 de7zta b*r5wyi )a2 a potter’s wheel rotating at constant angular speedbytca7*2 i z)6 e5drwa (Fig. 8–42). 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 point objects shown in 4j;l, r xtszjh78lls7xl+y1nFig. 8–43 ar;1, llllnxjhj8 y7xsz4t +s7bout
(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 l t0-svr ;xg3qwhose 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 satel6+ tmdaop(mje 2raz:*lite spinning at the correct rate, engineer e arat+:zo (*6d2jpmms fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifor u +zi9b*om)v-lz- rqzm cylinder with a radius of 8.50 cm and a mass of 0.580 kg-quz+lzm*ir)z 9v- ob. 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 swi,lge7yc 8dcnca fe+)w0vr/ b lb,u1+ mngs a bat, accelerating 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 tangentially on a small hand-driven merry-go-rs( gxyee;atfx.w,s3 .ound 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 prosfa( gest3xw. ,;yex. duce 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 brouetv 51fl kz; p6u2tux/ips4m.ght uniformly to rest by a frictional to2mku/t6 f5t1;x v 4.i pleszpurque 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-k6ld7bvwg0 w0g. zq1h hg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of thex*hi2 zxexxm3do smx/o 1 6f:) forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. om x)ihx1/ zm3 x2es *xd6xfo:8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a lo7a(,sa2r duam ng thin rod, as shown in Fig. 8–46.r u,a2s(7m ada
(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 two matq-pfnf) 1 i/h p0po1csses, $m_1$ 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 fullpg7 nsr0u-5qf turns (revolutu nf07gpsrq 5-ions) 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 moment of inervnq3wa8bg unya 41(:t tia 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 torquy.fp2 sa (lt.e55ujrxe 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 d,vgb+7ggtf:yc nm2k;own a lane at 3.3 y,c7gg+:2tmf vkbn ;g$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thf; qd5kp 0x8ye5ccjp yt ,j4m/e sum of tw dxcck5yj4j p 5q80;p,ety/fmo 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 mu 8qtocjrm0, ,ych net work is required to accelerate it fryo 08 q,mt,cjrom 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 ma bnnrz ;1m4iwqs/m52r t1 rm:lss 1.80 kg starts from rest and rolls without slipping down a b1r5zsilnqr 2nm r;t4:m/ w1m30.0 $^{\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 ulz-;uwe8mv8 ,d3ch i its tip. It starts to fall and its lower end does not slip. What wizi8dum 3c h,wev-;ul 8ll be the speed 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 rotati.2/2 uls*hloo kd:jio ng on the end of a thin string in a circle of radius 1.10 m at an angula ojo:sdluoh */.lik2 2r speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniformm/ 9j;3 mksll7n8zidx cylindrical grinding wheel of radius 18 cm when rotating at 1500l8 dlzm k;37smj9/ xin 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 hhqbz.fi.de;xp0/ 77 m nsxr :bis side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizo;irnd0 /zb7 : x mfxpb7esh.q.ntal 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. 8eeu3 28 mx4akf–29) can reduce her moment of inertia by 8f ea2mkx4eu3 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, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rategq9e kjtop0hc,,2x/v of 1.0 rev every 2.0 s to a final rate of 3 pvjctk 0h9o xe/ ,q,g2$rev/s$ 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 cemfozvd9 o-:5 dnter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radiuzdo -f9 5:dovms 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)4- 2ve ea lpv9hvf3uxm yk*+e 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 oh-j8z)xcnzub q,y 38 -4s xtlxf 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 an identi 8;3f7 pyvutjucal difu; vj8t 3y7pusk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ao kqkkdg7966 zt 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+l7zttcs83dfh v6kq: platform of radius 3.0 m and moment of i7z3:sk qcl8v +hdft6 tnertia 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 lp6ea:02cbn am1x8ga-go-round is rotating freely with an angular velocity of 0lgx8cbm01:pa n6aa 2 e.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 white dwarf, losing about half its m( a43tr. b7l d ..tj hhyp+bprq;por5cass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angul3 trpc a.;tho.+j(p 4hrq pdb5ry7 l.bar 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 :6;s )eo qoqmuin excess 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 j-l8akbs(q/py z l.b1r+m4 hx$ 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 rotate0 mgkdkj */0y6zev (lr freely without friction. T0vl e zjk(ky*gd r60m/he moment 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 a 6.5-m diame ; /*n4u4pwhywr dnbu/ter merry-go-round turntable that is mounted on frictionless bearings and has ;p /h uy *wn/dnwbru44a 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 wdk(x ;q jza 95tk;)rprope 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 9 k;t wdqx5(rjpza;)k move?

  The Moon orbits the Earo+50brcbr.xgm n f/i (wa(l0n n(3er ath such that the same side always faces the Earth. Determine the ratio(onrwi 5 ab03(fanlmgn/ b+c ex(r0r. 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 orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates*y. ac z0yf-wa from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder on;iul (xsl hwe -y)x00f radius 0.20 m acquires a rotational rate of from rest over a 6.0;(nysixll)wx-ue00 h-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of x x/9l q7;dzc+;gigqna70oa ftwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, z; iggno;qxa7qcf+0 d7x la/9 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 from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wmyy.yf.3a l1a heel ($\omega_R$) 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 masscp)rihk d1m;5, -zhwl 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to under ripk )-hh15w,;mlzcdgo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile k k+:clgn )b;fis 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.gl+k kb;fnc :)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 illustrate s6),d: (bsgp yrajuq+af-s8is 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 mym 2w -)lrzf beqq(t1;c4.zlspeed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fric 5a h)u,1zirvdtion) 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 i)v ,5r au1hzdthe 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.s 6 w+,tyof(he It is standing vertically on the floor, and we want tyo+,6 ew fths(o exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/ts f y39s16asss on a flat road is making a turn with a radius The forces 3f6s 9as1ssty 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 rockn f z(xx75rhg3 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 to (f7zxrxg3nh5 rque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylxy(seh *nzu7;inder 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 tightly zuy7n;x*sh e(against her body.   

  You are designing a clutch asse*sv *dzl buv,6to,n/qzh+ dt2 mbly which consists of two cylindrical plates, of massv /dv*hno+2t uq,*6t,zl zs bd $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. csbqf8.lv77y a6 9w ke8–58. What is the minimum value of the vertical height h that the marble must drop ife6 facv78 9yw. slk7bq 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, bu;rvwtb4c0wjhl f0 / -bt do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its suvncdl+4h 95o x9 ttu(peed uniformly from 90kmuxhot vl5n(99dtu4c+ /h to 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