A bicycle odometer (which measures distance traveled) is atl9ux7zkmmbue 0 /7wx4j 7 /mrptached near the wheel hub and is designed for 27-7 uw plj0/uxm7 9zkx me7/mrb4inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the/k;8bp6rq *t *a5kxd ura lw+e rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleratir8dbr ae+k 5w *6kqx /ua*lpt;on? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a8 t usw/wap: a4,b5dh5crsg 8f single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.t4;vrb) (g sqi7 l zb4x2rh5xa

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 hax el:z 2t)u,s7twe 0vknds behind your head than when your arms are stretched out in front of you? A diagram may help you to x0,kte:e l2 v tzu)s7wanswer this.

A 21-speed bicycle has seven spr c8c 6jd/aci)cockets 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 laac6 i jcdc)/8crge front sprocket? Why?

Mammals that depend on being able to run fast have sp)z ) c yacwugyg+t:-:lender 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 - gau+cwt)zg:cp)y y: mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lolqa/t t4 +f9uy 2n j(1r+hplzmng, narrow beam?

If the net force on a system is zero, is the net torque a h t.jre5 (5(iye)u.d xz-txodlso zero? If the net torque on ah)e5j xeu-zt( x. i.dyr5o(td system is zero, is the net force zero?

Two inclines have the same height but make different angles withw /as/nscp)dcpu;- wz4p, 5xi the horizontal. The same steel ball-/ispcu wp,p/ 5zc;ndas)w 4x is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simcvrb ,o7.o4( o0fbdxcultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bo rox.do(7bc,c4 fovb0ttom 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 same mass. They start fro5azo5q ;lj-g r-pc,ham rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has taj5 5p-;-hcl q gzo,rahe greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mova06vvtx d)s*aing or rotating objects eventually slow down an06a)dvs *tavx d stop. Explain.

If there were a great migratnft k0jf+;1bh ion of people toward the Earth’s equator, how would this affect the length of the daynh 0t fb+1j;fk?

Can the diver of Fig. 8–29 do a somersault without having any initial rotacd fa++;rcfo+gkh r)2tion w kfo) crac rd+2;+f+ghhen she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its fi8awcqydnok+8* +9j center +cyd 8i 9a8kojqfw*+nof 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 r *lb,sjd0 z8shotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explaihj,s*bszd 80ln.

Two spheres look identice 8ylgf 7o;737vpj ixkal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to d;fil8eyj7 gp7k3xv7o etermine which is which.

The angular velocity of a wheel rotatingt7co9oo)t duw7kf) 9 y 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 points east, describe the tangential linear acceleration of this poind7f9tot) kucy 9o) 7owt at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the ed cybolq8 +ghhua ,/*c68.r xwcge of a large freely rotating turntable. What happens if you walk toward the centbr86c .cy/w cg ox,aq8u+*hlher?

A shortstop may leap into the air to catch a * 6tiiptn2pv, hh-ssgw( vr;e3:au4o ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notog , :i*p(i6sw rsathpv3;hve2-4nt uice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss whyn1vvakpeu:q9s--/mx a helicop-su ep -1k:anx 9vmqv/ter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angle-cjn.lt y6;t dy*hr0 es 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 amaziwryj ,yg-:x.- ci) ucnng coincidence. Calculate, using the information inside the Front Cover, the a,gy.jc )-yrn ucxw:- ingular 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 from Earth. The beam diverges rqg4x *etdfcpp)d ha,(q*9q 1at q*rq,ddqpt f4 (*1)a9hge pxcan 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 iu6g 3x yaqt+:off during operation, the blades slow to a qyi+:6x tgu3rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. us 0sby(88u5ahp pu3a If the ball makes ppu8u0 ssy58 bha(3ua 15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 caq *59ah1,lgqn 23i 6eyuipe hm in diameter travels 8.0 km. How many revolutions do the wheelsuqhy51ipe a,e6i lnqhg2 a*93 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its a7x/vtywls9w0- gf (tdz 21l.uuh1 mawngular vu t xfg7wwl9yd .2(s11m/thwz0uv -laelocity 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 in 4.0 s (Fig-aut5yjw/ h ,f. 8–38). (afj ,huy/w-5at) What is 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 pxic:6brhks b*b: ,h/ velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pokjd7e100qdf hint
(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 particluqc; p t,h a*u /14eb,yvaosa)e 7.0 cm from the axis of rotation is v1,)eatbapy*;u acouq sh /,4to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 282hs qkfm m wzg2+: ;u8uh 0y4rsopw0o10 rpm in 41kr+ h0 f4 ws2mo0g; 2uhsu8pw oyq:mz.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius q ,/, kcv/omhy$R_1$ 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 Apr/1iqo t 0zsg7azu,ly sm /.9gollo 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 minutss 7y/ai.m, t1ggq uzzol9 r0/e 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 0d4xoz)2poh8q .x vkg+h .l rsuniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in th)sv. hx q8ok4rzhp +0lgo.x2dis time?    $rev$

  An automobile engine slows dowqk76hul p: r0cic1 9cyt 1kel1n 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 ie+cd l*si271ub. nzdfor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speedlci.+dz* 7ui1 e2bns d.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly froscw/, :z46yadk 6 ebsvm 240 rpm to 360 rpm in 6.5 s. How far will a point vzd:we 6ssk /y,64acbon the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/as5il y/u ,01j k w:(wu.tddlkmin It turns 1500 revolutions before itd :ls w 0i.d5lytukawuj1/(,k 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 revoluc0 x6ors4f q(bz e3r/ctions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 o rq/ 6rfx04e3ccb (zsm.
(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 uniform6:zda( *j;mmww-( rwj2nfk flly from 95km/h to 45km/h The ti-6jfaj:; r2 kdwz(wmml*( fnwres have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight onm h3,nlw 5klqmdkj v(1lp(/)e each pedal when climbing a hill. The pedals rotate in a cirw(jv /l),hklmeq(3kpmnd1 5lcle 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 djc9l 9fg 6(wqN on the end of a door 74 cm wide. What is the magnitude of the torque if the force is e6l dcq(wf9 9jgxerted
(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 tor.n j 7o8e1hkso;eivg6/ qqzr( que about the axle of the wheel shown in Fig. 8–39. Assume that a fric;jo/vq srn(6 o 8hk.i7gzeq 1etion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass mxa3 yql (/)cvd, are attached to the ends of a massless rod which pivots as shown in F(3)lqc xvd/ya ig. 8–40. Initially the rod 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 cylinder head of an engine require tib-eeo aqy0g9(ou( g-ppbvt y 3 rq82p4ghtening to a torque of 38b ev98a 0u4 -tyq(ogp(-3pqerb2y go p $m \cdot N$ 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 yurl7 9mjql.n; n44yyn l2vo6-kg sphere of radius 0.648 m when the axis omr2jynynu46ll9v7. lq ;y4n of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whg2tzbk )g* h*ka*-kg heel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the h hg2z *b*hk)kag*t-gk ub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hormxg2x7 lz9)bdc3y at2y/wm +cg/lxu: izontal circle of radius 1.2 m. C) 3mx7acz/db l gxc lmy+x/9uw2:tyg2 alculate
(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 gar6 d,s5ja0k’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N totalra ka6j0gsd5 ,.
(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 the5 ,f n- sa2yckz:a6i*;yfi7e ;rrnrb v array of point objects shown in Fig. 8–43 ab,vaby ze5a- 7 ysrrr6nfi ;nk f;2*:icout
(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 wgs1sbtpo l(,i+e +h jx,;w-dshose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinnin+yi bw9i.a4p ba40y vvg at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the i4bw +. ypva049iba yvsatellite 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 un.x;cr yu x1xm5iform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. xm y.cr5x1x; uCalculate
(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 from rest0ubmr.fv a .*h 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.oyiqkd8a+h *wr v: blp 4d9e bty+8z8-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite e y*8e4:y.blah+ v tdi wp8zbqk9o+8 drach 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 *6v+kl,m7 jgrlwatu1and is eventually brought uniformly t7l*urmajg+,1 vk 6wl to rest 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 accelerates a 3.6-kg ball a dzyvye:hgke 35 y7k,;l96owsau6( eyt 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 the fortnf1 i0oa3 6/gy-qnks earm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to gsa1k0q i- t3onnf6/y10 $m/s$ 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 shown ic4; gbmhv vm*h+ k7e6un Fig. 8–4*khu vg7mh6c4; m+ veb6.
(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 ma*)kvvj q.;qogsses, $m_1$ 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 wpf4txeia gl 5vyb1,zeu ;b 88( 0l+ncpithin four full turns (revolutilebgy+u;5nlp vaz (8 81tc,0f eb4i pxons) 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 inhgdx) 8a6-r-magh9(u4f m elbp;a1rzertia 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 deveuy7vv.s 42k tziyxu y9(1(slzlops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0tv:v2 dyqu,x m.b(gdpdb01q*c)bi t 1 cm rolls without slipping down a lane atvqbcxt,1*ddi10m:bv (q tg.pd )2buy 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with re9ks56ptmi ls+(a 5bpispect to the Sun as the sum of two termsms5tl pbas5ip 9i k(6+,
(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 m1rm wbi).7 y2,vfjw 0+lxhuhuass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest towbj,r. 7mlvu21y+)f h hui0xw 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 szxk:7fp9b v f 41ehi,ntarts from rest and rolls without slipping d1ebkfvf:np7 zhx ,i 49own a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starx4:3lxpc fb g)ts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use c bl:x xp4)f3cgonservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball ro-goptn/ (h2-q)q hfgts* wo 4atating on the end of a thin string in a circle of radius 1.10 2-s4*wn/fqogop )- tgthq(h a m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momh pg1o,/ egq2 6rdks)ooxr2 6uentum of a 2.8-kg uniform cylindrical grinding wheel of radius o 2 r2o)dhr ,gq/eu6 gxkop61s18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating atw -mj) 0hdbsz7 a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the-jmsb0 7 )zhwd speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inz5 (8(+n byp5jz3s6bbbfa) b vk1jccqertia 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, what is her angular 8b)zs5 c6p fkbjbz5j+3(ayv1qcb n (bspeed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotyouip 1r1i a5s )1yru*5 u:tmhation rate from an initial rate of 1.0 mt5p1)r o hua y*5:sri 1iu1uyrev 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 clz.9 sjgj( 9kmenter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg anl9g mj9k(s .zjd diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skat34mmq b:j1; v2gge.yl erxmr7er spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earthk - vaxbw*m+5yn8l h/g
(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 dropmivn0 e;pnx2,,t-ns 6ka u b4iped onto an identical disk rotating at angu, i,n-mn xep4ki2;06btsn vaular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 u3ff 8 7*coy9uqd:elr)8kfld $rev/s$ 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 ce2v 7eh1 uqxj+cnter of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 92 hvque7jc12+x0 $kg \cdot m^2$ 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 velocity da9is3w-6,fl fg(v2akl -p nhof 0.lsf96f (wd2,-avk np-gh 3lia 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 )oeshc+y fhpfr4) ; j6a white dwarf, losing about half its mass in the pc)y6 ph4 j+;f)resofh rocess, 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 exh p:bs:9titliq4h 9z) cess 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 y uq lo191psf4$ 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 c(u42kxmfw3 : ,scanfmms) 1aban rotate freely without friction. The moment of inertia a wnfk43u ma()2msm:1b, cfxsof 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 mtq)5k 1vbtg6h erry-go-round turntable that is mounted on frictionless bearings and has a mo6gqt)b15t k hvment 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 or; p50kvhl)nl n 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 )0 5;pkhrnvll does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Eare gjltj*g)(r2th. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular g 2t*ej(lg)jrmomentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a r87ir fn;ptr+u ;h.w-o(3he 0jlkubrvate 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 of radj 1eaf3e8fn h1z6b nqzs,/cp. ius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at consta8a fe6z snqj3 c fz1be/h,.1pnnt angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and a,*i7 p dmfj2jjao07-9l *ic e encu(tdiameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is re*j9iac-uja7cm 7*j 0 ln(pe2, eftidoleased from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of * h(ega)ayha1the 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 ofif2+hj c/x u*2 8ary,kuxeyp) our Sun, 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 rotatioc yu8+ pi fku/axxrh,j 2*)2yen speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it ty5 v4kx ct5fd kx;u1g)o use energy stored in a heavy rotating flywheel. Su)k kvg4d;5cyu f51x xtppose 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 illustrak so.bog)w yi5- :jmd9tes 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 rolwd y *nt6 vibe;8.9uwuling 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 maspy:c0 7 .vx(pnn,p,qws 0(c 3vnmwnp vs M and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration vyw7sn ,:n.qppwn3, n p( vvc0m(x0pc 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 standio/8(gtp lx4 tv s1v1ning vertically on the floor, and we want to exert a p1tv o8glnv41s it(x/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/s on a flat road is makingib2wb0 ( *0r/fvi vkch a turn with a crbb0k 2vv(iih0 w*/ fradius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a .j vs(xto g8pnt:.(dksling of length 1.5 m and begins whirling the rock in a nearlygt8.(x:(n o.p sjtkvd horizontal circle above his head, 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 5b2 hky1my)yb 6j-bu qa solid cylinder 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 o yub1q2h5by mky6jb)- utstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly whi5ywo;e * kkionav xv41py7c76ch consists of two cylindrical plates, of nvopkae5y*ico7w4v 7 ;y1 6 xkmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 xvt zvk:u3qm 8u+on*,long the looped rough track of Fig. 8–58. What is the minimum value of the vertict *xo8 vu3 uvm+z,kn:qal 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 nitjyyc0v,/ nz5 i8zc+ot assume $r\ll R$ h =    (R-r)

  The tires of a car makealh3s,-np0i k- yl.fx 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 k0 --ahsp3. fn x,llyim. (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