A bicycle odometer (which measures distance traveled) ise h6j 7m u1p+gwi(+vzr attached near the wheel hub and is u i(rz+h1 6gmp+ewv 7jdesigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angt-03iz gpkkjp.; +snp ular velocity. Does a point on the rim havp j-s.+zpiknt3k;p g 0e 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 acceleration change?

Could a nonrigid bodnckd2 en sahx8xx s2) (rxq19)y be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expltmgjng st30r-d51 7vqain.

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 do3gvr**-q k-fjhl own. a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may.oj*g3h nqk-r vl*fw - help you to answer this.

A 21-speed bicycle has seven spyd0ad1ir/ ;c b fr-e9hrockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sp yda0cf-b1dh 9 ri;r/erocket? Why?

Mammals that depend on being able to run fast have slender 3g8kvm6v7+tc v 0mo2kg- homflower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrg 60t832m v-hvmc+7ofom kvgkibution of mass is advantageous.

Why do tightrope walk48c8ln +g ,wgwcnr1yetc, c;6d)epbhers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net(m2)vmlnn wg v* t +/sl sugof,sj-7x2s.)xoj torque on a system is zero, is the net forx*lnv2 7)n.uvg-js)+ om/,j( wtsgxof l 2smsce zero?

Two inclines have the same height but make different angles with the (ls6 6zea1a sfhorizontal. The same steel ball is rolled down each incline. On which incline will the speed of the bal6 af( laess61zl at the bottom be greater? Explain.

Two solid spheres simultaneou z23wouj ewqbsdgka51/p 9*7 drwc- .csly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Whichcwqw*-7dgu/ 15cjbkw9r sa2e do.3z p 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 t 1rf jacy2 c40ss.04,pq vmx5pri0sn rhe same mass. They start from rest at the top of an incline. Which reaches thexsrp, 0iv40n .mscyr5fc 420sq jap1 r 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 ar70twl3kphdj 9 e conserved. Yet most moving or rotating objects eventually slow down and stop. E30 d97w ptjhlkxplain.

If there were a great migratu73e2uj8of o4av3h z yion of people toward the Earth’s equator, how would this affect the length of the day?j7 efv33oha48 yozu2u

Can the diver of Fig. 8–29 do a somersault without having any initial rota:tdbj,x -l(t mtion when she leaves the bjb, m -tlxd:(toard?

The moment of inertia of a rotating solid disk about an axis throughut0-5e(yyc k(./l 4t uhab utc its center of maskuhl tt/ybc-a40u5 (.( etycus 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* sx;iz 6er/ts)b ept) 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, ori6;r*esz) )ebp xts/t stay the same? Explain.

Two spheres look identical and have the same mass. However, one ia4bk/7 ,1rrw,vy j ddgs hollow and the other is solid. Describe an experiment to determine whik, w1vdy g7 br4dj,ar/ch is which.

The angular velocity of a wheel rotating on a horizontal axle poiniu:- z2 qh2uf,prueh.ts west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points eap2, r2 eih:.z-q ufuhust, 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 freelj h6s/up(2v;qm yd;oiy rotating turntable. What happe(p/yh s6 oqimv;;2udjns if you walk toward the center?

A shortstop may leap into the air to catch a ball :tu:hq cb+l re59yg 2nand throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly 5e2n:ug9ylh+qrt bc: you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the z /yxv9v4b rk 36su (m + z7eqsr5/cawd0o+zaalaw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discaazz3sa6yv dkbrq7os z(+x4mc0 //eu+r 95w vuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles*b .5q yn:ws d piv1y x85g3ahgujg q85gl77wp 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 a1zfw ;sm6td8qs/ra8u mazing coincidence. Calculate, using the infwu8 rd 8tzsms 1;/faq6ormation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fr3bz :rum d23kgom Earth. The beam diverges ab2 dmk :u3rgz3t 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. When the motor is turned lu*k ovnok3nlw-k,52 off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow d,kln uwl*v2 5kkno -o3own?    $rad/s^2$

  A child rolls a ball on a leh6yl,bv//meuf2qada: zj*v 3vel floor 3.5 m to another child. If the ball makes 15.0 revolutions, wh: 36 qlau,*jabd/z mfyhve2/vat is its diameter?    m

  A bicycle with tires 68 cm in diameterxwz6s+u. f8ac travels 8.0 km. How many revolutions do the w6uzxa8s cwf+.heels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angul(uds jr0- 3pdyar velocity syd(uj3pd-0 rin $rad/s$ $\omega$ =    $rad/sec$
(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-roun224-zptuygpg d makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is-gt p2p4u yg2z the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a qtmws +*q5u-;6pxyz++p rnl l) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ocs8ukyh0ns/un b(w6r* /c.d:oxe 9aif 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 7octsh; -vt-w+ .0 cm from the axis of rotation ihwo+ -s-ctv; ts to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accy 44 fuebfr ex-0s0hv(6+wncp elerates uniformly about its center from 130 rpm to 280 rp00+exs fcruf 6yv p4 4-(nbehwm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuseo( 7z b(uitpv c6cjxc84+w ydc34r v, $R_1$ 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 spacecraft put themselvesa8v8wr srpppdm /r*842.2oy 0wz+k+ roxvq me 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 intervalqr0*8v2 pwrk 8ymp4eoovm8rraw/p+z 2+ . dsx. 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:gdli 8m0a5gt 220 s. Through how many revolutions did it turn in this ti i0a8d gml:gt5me?    $rev$

  An automobile engine slows doj8m0utq5j zp:ikp/t 3qq e,w1wn 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 stressesicxz: ,nc35)p aeg;.k9 djrxj of flying highspeed jets in a whirling “human centrifuge,” which ta95:c3nxd.p j ;ca ,xjezrkg)ikes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerate ru r o/)n1:)cv*w ,vj7eyvquon 94ogns uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on7,y)v 9or1 nj*r w)qngo n4/e :vcuuov 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 15007fh+y:e; b rce revolutions : ;rfec+yh7e bbefore 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 j7vc2u x ,t tv9g-zj-hcar reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 9uc jg -tv2,jv- xzh7t0.80 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 i;5 qe(it6:nd9u gj,oxdh sbj) ts speed uniformly from 95km/h to 45k9 xbhqe5)un:gj(,o j;ds 6i dtm/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 putsqmep8/ogmlyy9s//9:uj*eg a all her weight on each pedal when climbing a hill. The ped/*ggqyy9u p://emla9oj8sme als 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 ij:hc4vex+ +mof 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exertejv+ce:m 4 ihx+d
(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 in Fig. 8–39. Assu 0u2p;2cn6 pvo8rxb.g wd;qqume that8 ; b ruc qx6qwuo2nd;0ppg2v. a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of azm n7:5xn5co cpdg l5 fey79p9 massless rod which pivots as shown in Fig. 8–40. Initially the rfngodcp 5 m:95xne7zc9yp l57od is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinderg24t o min7w,z5sn ,ji head of an engine require tightening to a torque of 38 io si,ntn g2z4,7 w5mj$m \cdot N$ 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 wh2xo gus4l +r *.y9iqj;/cumht9n)v p cen the axis of rotat p)ts/92u9vqcj 4; oxc*muhnl.+ri gy ion is through its center.    $kg \cdot m^2$

  Calculate the moment of ine8nb vv ;v 5*mnux gf8h8z3:znirtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mas 8ib5h;vgnz8n3xm z8vn *u :fvs of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the endjt *nncuui(mva -4b3; of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculat( nja 3;u-in vcum4b*te
(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 agx- +lqe dy is3z*z(+hgu 8*eqt constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total+q+(uie3 yzz*l sqhd8e- g* gx.
(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 p+*1 m.mwiasef oint objects shown in Fig. 8–43 aba .+wme im1s*fout
(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 bbxt ubb1va /16 5moo*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 satelc:- wlgznzlr2d4e/*qz2.hj s lite spinning at the correct rate, engineers fire four tangential rockets as2zzdz: e. 2jl*lsq/ cn whr-4g shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radiuc9jxtz al0y88igb ebzf:/ e2.s of 8.50 cm and a mass of 0.58ijae b c0lt2egb. z/9z:x88y f0 kg. 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 7tfj*l cdwr06 9aya.(on q/y sa 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 hanroy9qcp i 8acc:zd9q 0t*(ln:d-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (eatr:oc *ca(9 zpn: l8qdy9qi0 cch 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 rotatiq1u1ccch 2g3v ng at 10,300 rpm is shut off and is eventually brought uniformly to cg 2cvq31 1churest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelp(kc8r+zepy iprx4aa+ *t5l) erates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the actia ,d(,,uoh elgbsj.9c on of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The bj,.euscb9( loa hdg,,all 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, as .b;acb6 g;oit shown in Fig. 8–46. t.igcb;6 ob;a
(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 twq3dg0g44ioft z *zs:wo 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 jx2 ()wsyr i655: pytz.ywnnp the hammer from rest within four full turns (revolutions) and releases it at a speed ofjtpyrxp6ny 5ziws(5 2 :nw.)y 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 mome+k+ ; zlzddb b8ammf dp,1e+y/nt 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 torqup:m t2rp-z*we e 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 sli1zu.56chaws7 ylz.n wpping down a lan l zh.us675zcwny.w a1e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth w/gx qfyz sh.7)ith respect to the Sun as the sum of two terms7g zsf/qh. xy),
(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 vs/vw is8/:a rr tuz8,;cc bg/and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder./w:b/ 8;t /cgvur,i8s sarvc z    J

  A sphere of radius 20.0 cm and mass 1)(si+.r kgz07tonhe s .80 kg starts from rest and rolls without slipping dnseokr7zt0( )+ .gsh iown a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on itci4l v0dins4a+ dt8 w/s tip. It starts to fall and its lower end does not slip. What will be the speed8dd av/cl0wt4ins i 4+ 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-kt9p6c-xwo+n xkf (ju;y 0anoqk1w k )3g ball rotating on the end of a thin string in a cirn(69kk j 1x-)u n wwxt fcy3pk0+a;oqocle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wmre)po v7z0,j heel of radius 18 cm when rotating at 1500ze ) p0vjrm,7o 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 hi yqql kc4ptfepa*:8j) qc z2+e;-gye 3s side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases t+2)z efqq -gk4 l ea;cpqcp:*8 yy3jeto 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Figuw6f)h zbzxk 55f6 9om w-7zjj. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight w)-z5zxjf96umhbo 5w z j6 k7fposition 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 rate olez.afn 2dn(c zy b;rd e/+2e.f 1.0 rev every 2.0 2;d bln+.e yz/e (r2.decfnz as 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 center at a freqr0ee33o caz-ljg- 6 tluency 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 octle3 3g-e 6razjl-0of 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 motnvfu j h8xu-3jbrv;i;.g(y* mentum 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 ) s 9mg6cwvv 63tytc xfr-3lm8the 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 identic 5fw,x mmjtl 22 he*6bg.ysxm)al disk rotating at angular speed ,tsmxhg).mjwb6 y2fe2mx 5l *$\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsyc5u)- i.y9(m3 te tn)uce noz 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 st .tquqee6,vntc12 4ciands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia. necq uqt62ce,v 4ti1 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-roundp0148yd tfb vn is rotating freely with an angular velocity of 0.t0n8 y 4fbvd1p8 $rad/s$ 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 collaps(+ fmi(pi ,oxmes into a white dwarf, losing about half its mass 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 thei+,moxf(( pm i 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 excesrh+( : cekvt od(.8d;p dwr0x eqoc)/ys 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 n1d)1y:dp7nrxf zr) y $ 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 rotate freelzu) ab6vitp.5-cr qi6y without friction. The moment of ineirtpu5 -qaz.6bc)6i vrtia 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 diameter merry-go-round ll rl0(a s24zpe:nh, utur pz:s lur4(l 0lnh2ea,ntable that is 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 ropeavx) 3 lk (9yl3wfdg;p rolls on the 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 tgyk 9 wlaf)v3x;(dp3lhe spool’s center of mass move?

  The Moon orbits the Earth such that the same side-o3 rtcuk3d,n ib 6-uh 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, d3ho -3ri-n ,ct u6kubtreat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frfn-o 6pd(u g6som 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 c p- kki;v8 2 yv;h)l;csvysut1ylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acce;t s12h-v yvu8; kvy);pkcl sileration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid;ng3 q vqb5k5z* (zjlc cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a*ln ckb5 g(5jz3z qv;q (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, ho6k6ugq hlfr; r;omx( 8w is the angular speed 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 4 )iyhaoh*d 21ter0rsSun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the 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 an 4oae y0*r )t2hsidh1rgular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a tki.4l3vfgv6p:n29shwo *myofdhlcf2 ;/g :low-pollution automobile is for it to use energy stored in a heavy rotag2fv 4 i:dn;*9gf 3hscly2mvt:.okl/ fw6ph oting 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 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:yha orzlp:u*2 0as x6vyx2z.s 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 spee,m1, fk slw(ukd 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 . ts x: 6jiiy zc1ya640cy6mxwcan pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in a4i6 6sz:t1c0mw xix6jy.c yyFig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. 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 staorig .+ y3my,bnding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it3g.rbi y, o+my rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s uycf/v) bhxtcr53)hk 96 ):z (scfr xuon a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal fortx cx)hsz)5h9b rc:kvf/c y(u6)rf3 u ce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 lengthjzligd1-o,) 3n 0w2 t b07 lnrxplj5eq 1.5 m and begins whirling the rock in a nearly horizontal circle above his head7r)bw e1jd2 pxlni3ln, 0j5tq0l -g oz, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and rypw s1o5(mxc1k x;n 6z l0ml*nh;+oqher arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of 61w zxkym5scqr +mxho l0n nl*(; ;op1the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assemblw.u791 par;vb6pt9q 5fpru v/6yvkfz y which consists of two cylindrical plates, of m vav/p6k.;quptvz5fw61 rpr9 uybf 97ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a /:2*iqjjzm7g+ xgypx ,jrx1mlong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the mxgp2rm +j/j zx *gimjqx,y:17arble 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 as; 7nz (l77txy:bol ihtqm0kr+sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions :h5cntnbnknzqs: g(qm / r-7j)gn: h7as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire?nnq :)qjbcshh/ (nr-77t zn g::mk n5g $\approx$    $rad/s^2$(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