A bicycle odometer (which measures distance traveled) is attached near the wheekrr :kjgh2m 25l hub and is designed for 27-inch wheels. What happens if you use ij2gmkkh r:r2 5t on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point oqkp09 (1ejxrs n the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear accelerak1qs0 r9p(x ejtion change?

Could a nonrigid body be described by a singg 6 2cl5ln/bm0ti2 nos.o lun4le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger foru+a8ocoyt r*9n1bp 6 hce? 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 yourb2jx x - : uh9r(r8nne.n;uskt hands behind your head than when your arms are stretched out in fro:;r-8rn hnux(esu nx92.kb j tnt of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three aosc4/r2xrn +v t 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 frontv x rsrn/4+co2 sprocket? Why?

Mammals that depend on being able to run fast have slend,ma 0s00eqaln er lower legs with flesh andq0ea0 aln, ms0 muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Feu+w*cv ;. egdb-ci t.9yzl4 pig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is tdfhb,4oey t,8* u q opgnr:c5l/b3z)phe net torque also zero? If the net torque on a system is zero, is the net forcepgdyo5r c:b)4ohn ,u *tlbz83p, q/fe zero?

Two inclines have the same heighuu8) lxnzsj 3;t but make different angles with the horizontal. The same steel ball is rolled down each inxj)zs nl u8u;3cline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from r8(5vr* uyrrv .utrg9t est) down an incline. One sphere has twice the radius and twice the mass of the other. Which reach*9rtg u vr8 tuy5.rrv(es 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 f v-p0 sd-8jlythe same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed al8dfp0y- s -jvt the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentuas(7 9ywrdi0 )dks jj,m and angular momentum are conserved. Yet most moving or rotating objects evenaj rkw,0d 97jisys )d(tually slow down and stop. Explain.

If there were a great migram/x t1fr-f;vcse5 5.gvyi h8btion of people toward the Earth’s equator, how would this affect the length of the da xvtb;c/ih8 g e-.ymf55r1s vfy?

Can the diver of Fig. 8–29 do a somersault witlkq :;s(k 2qva.y/pbmhout having any initial rotation when she leaves tskml ; vp.y/ab:(kq2qhe board?

The moment of inertia of a rotating solid disk about an ax c)xe2):xlk p6 e8agipis through its center of mas:8gkl)aep )2ci6x epx s 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 lduhn7 ;vfvcq 10e. x02-kg mass in each outstretched hand. If you sq1n;h vxceuf70dl 0. vuddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and /w3mawpoj5v; bw0tx9: fnj 9h the ojo:ww05vt w fjxm9/a nh ;9pb3ther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel biq(w(b 8ov4jrotating 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 point at the top of the wheel. Is the angular speed increasing or dejbi(vb84qw o(creasing?

Suppose you are standing on the edge of a large freely rotating turntabluwkf +2e5ndfv7d-1fq b.d n a(e. What happens if you w75a(2uqf ed+v bkdf.w1n d nf-alk toward the center?

A shortstop may leap a c+o1 ,i+7tt:oygfrtinto the air to catch a ball and throw it quickly. As he throws the ball, the upper part of +toy:oa7g,tr +cf1i this body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatioscn w,aup;06 (bc gd1xn of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable( u s,gc;cx 0npdbw6a1.

  Express the following angle-cpp: 5f bta6cs in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coinmyc h76 op):b70 i8)abo )rxp op8dwmtcidence. Calculate, using the information inside the Front Cover, the t 8pc)mry 7bo:w)m6odpiabx 8)o 7ph0angular 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 Ea *hsaw;g vd0 (r,b-mlurth. The beam diverges at am-,suwl rb*dh0(avg ;n 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 of0 xzshtf -.0qrr ;yp8p8 wss*f 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades p;s* ffz0rx 8q.s yhsrp-8 tw0slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 k3 qsxrw3 z/y*gx0x*km to another child. If the ball makes 15.0 revolutions, wh3*0 x *kr 3ks/gqzyxwxat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km3ceng3ehhbp3 w.:/62csdgi2o . hzwjvrf5d/. How many revolutions do the wheels2 .gh3b/rgsi. vh5/eno:j3d 3dzw e wpf6hc 2c make?    $rev$

  (a) A grinding wheel 0.3noi +4jfej5h )nc 7qs55 m in diameter rotates at 2500 rpm. Calculate its angular ve45s5hci njnf)jo7 e q+locity 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 (Fi;6 y0ldhns3k balx8w92g- d ytg. 8–38). (a) What is the lin2tdlwhs 0-;96l 8bk3 xagyyn dear 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) in its orbit around thlb1gz: cec9 j)e Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poinymlr(h8 vgk(e2u6 c 9dt
(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 centr;.dfihx 7ut*gifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100i*xfg udh.;t7,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c tn-hnaw7z* b5enter from 130 rpm to 280 rpmbanntwhz5- 7 * 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 radius)cp0*,, d wkcltpv a*h $R_1$ 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 themseliqdfvys12z( n pmb zc6(g)0:oves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diamcbz2sqyiz(vo f dgn pm6:) (10eter 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 unifoosh9 z/qt pf3jt+8s 3krmly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this ti8 +z jssfo3 tk9h/pq3tme?    $rev$

  An automobile engineai:m quklbj 45y-4 iw6 slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspexuwt04rg *twq,w6 bkv8 .)1fhcs n /vbed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 co.gfs*hw0r1c,vb xwk64 qb w8/u)tvtn mplete 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 accelerata 6rh /-+bodqqes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a/h6bad+qq ro- point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 8507 cyd n54m5fqrrev/min It turns 1500 revolutions bedc 4fn75rq5ymfore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reg . g 5t6ufo(buu 0)k),ge+g+.cvteh+cr msoqduces its speed uniformly from 95km/h to ughvm60t gg .tkq r.cceo ou )u+b+ ,+)efs(g545km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uc0 xd vvfla12:9qzwm;5fv;e9ujqi1 r niformly from 95km/h to 45km/h The tirea5 vf9qij;w1rm zdeq 2 1 lf9:;ucxv0vs 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 bikg+9ii.s l0e l xga;ua-.k3;oze-s won e puts all her weight on each pedal when climbing a hill. The pedalo kx;gga-0 l- ess.ua +9ilew;.oinz3s 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 end7rmr:b5c n 5ab allp4) of a door 74 cm wide. What is the magnitude of the torquen rbml45r5apb)7 alc : if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assumj/xb 9+a( jrdve that a friction torque+dx( 9jjrva/b of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod which 3a )n)2n;dlemdm uxvejca1,8zj ;c0vpivots as shown in Figavd n)v;n c dmje;e ,l)ac8xzu20j1m3. 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 tightening to a torque oly0 .ca-ey771osa1 sr u:sccxf 387x:c 1yyse.c07 crs a o-aus1l $m \cdot N$ 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.l, 0-uv3aq8b.a iut)lr ne iu when the axis of rotation is thro luq,u3 vi- u an)ra.tb0i.8elugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of)ouk/qruhqbyw 4z8 qm+,n (l 2 a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored lr qqbzq(mh)u+ ywu28 onk/4,(why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotatedp;55wgzyoxh *e*.eay in a horizontal cie *;yyag x5z p*ohw.5ercle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant an hv5h r-wa8a0sgular speed (F8s0hvaw r5a h-ig. 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 Fi4t: x yr;gvk*pg. 8–43 axv * y4t;r:kpgbout
(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 mass is d/om)eker j 79y)il.uqxn f-2$5.3 \times10^{ -26}$ 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 cylindre vseo6dp , ade2/oy11ical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reaco2eo ,avdy6psd 1 e1/eh 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a masrk17h pa a((ops of 0.580 kg. h(rkapao7 1p( Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a d cuo5 g*,zl r/p5e.a8 cdmv(t4ugt k+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 tangentiall4l +j5tu5ty q) g4;8poou zomzy on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 76zt5op mgj +8y4 z4uo5uol);tq0 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventua; .v mnj8alc52 .ciofclly brought uniformly to rest by a frictional torque of 1.cj.im.2n cola 8fv5;c2 $m \cdot N$ 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–s lk8*rkx+-g0 dp)oq f45 accelerates 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 solel1tzi1bmrc :1c748y/qav *oysb j(pjoy by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated ua7yc1oto q8z b* v irj(:4jc/psm1b1yniformly 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 considerejyqj8l a5c f6cl*wyew;e4dzk0rv ck 4t)h5/8d a long thin rod, as shown in Fig. 8–4a8/r cel5c 5*;kdeh4z4ly8kqw vw c jy0t6)fj6.
(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 consioxty dkrz4 .53sts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full tury23amxz. + wowa9tsu5ns (revolu93oay+ 5sz2 .umwaxtwtions) 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 mvfw*u.0y g ;byoment 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 develoc6y.f s4vw1b jps a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls wl fa,jb/6ec-q)xg,2z mdy;b0fgsd m 5ithout slipping down a lane at d,szc g m- j5fydbx,)m0 gb6lf e/2aq;3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun aq;56 /cxkmb2e y1fqhh6 sswp1s the sum of two termyh1h15w6/ c es fx62b pkmqqs;s,
(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 r(ei ,8 ppidn7dadius of 7.50 m. How much net work is required to accelerate it from r inpdpd8(7i, eest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg startkkmipe16h cza d- m9u */v2s4qs from rest and rolls without slippingmh*ci69emk/4 1 pukd- avq zs2 down 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 i26yi tqaxw /6sts tip. It starts 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 groa26 wtxiqys/6 und? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mh/t :(4aemrzy omentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at anme: zty4arh/( angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg ugc sd5(p jv+6fniform cylindrical grinding wheel of radius 18 cm (csvgp 6+5djfwhen 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.ftaqn 1n6mafai w 6d6qd6:n) is rotating at a rate of 1.3rev/s If he raises ha.t6n66i dnn1qa) m:ffa6qd wis arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in hlxwad s7kr56ch+h06s, 6mb mFig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If m+6 skhrb6l c5 hmh6sd0 7,axwshe 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 wjg 6u w6bm8z9spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofzg98b6wju 6mw 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 vertica+(2q bedazcn. l axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk 2zq+.dacne(b 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 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 mx /5.l:e jh p69ndxmkd8ke5vh omentum 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 ofkjfm27m4+im,wh)jva-dsv e3txn/ r c.0y x p1 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 identicxcg ftouoq6c00g,q(j dlnb jp-3( 1)yal disk rotatyg(-60)1d qcjpnx blo qfg3c( ujo0t,ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 cd3qvcdv f b/;,;en5 m$rev/s$ 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-go2jhe +(5,y n sg1) ckitg;qovi-round platform of radius 3.0 m and momei(+ niv5gt1 2c)h, k;qosjygent of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely witha2.m paa9:k dz4 ah tq.olu5i; an angular velocity of 0.8 .4t;oa.h am q2:pl5ka i d9uza$rad/s$ 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 collap.lf2g, ku -fo-s omr 55dcibhc,cbu2+ses 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 c5oc f2dug shlm,c--.i 5 +ucfbbok, 2rarries 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 wifffcc c, h-)*snds in 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 uayb :c+;2qrx$ 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 resh)1aqh1a1o sc/6e: gb wh(r smt, that can rotate freely without fricti1m:h(e)/osc b1qg wa r ash16hon. The 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 diameten 9h29r.9et kyjh; rdcr merry-go-round turntable that is mounted on frictionless bearings ae2; n9yk.th hjcrd99 rnd has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the bp64wl5qc: dmrope 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 witcm 4qpl6 d5wb:hout slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same spyf)) ong35 raqov-+jide always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbitalg f)ajp5vn3yrq -o)o+ angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratk -u/4ocq/9nd ksqi9x e 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 cylin0u)(3dr8ex.e -nfp r2 buqw bjder of radius 0.20 m acquires a rotational rate of from rest over e0rrue-nq3.u2bxf (p bdw)j8 a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.05ile:(3kc dj7 q0 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050c7:ld3 qiekj( 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, homcxzzf;iz;2u:8 fcfq9mvw0r z z2y4kwk 8i;,w 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 Sun, but with mass 8.0 times as great,o2huxz8i)q;k:5: donti 4 dwo 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 that2o5i8h ui xd o)nd4 ot:k;:zqw 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-pu: fm::7gt p3h3qxlvid/ ; ;p cl/geprollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a /h/pguf3igl ptdlc; p7:: r:3eq;v mxcar 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 illustrates av9xe0(sdd al *n $H_2O$ 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 o5f qja3. ukmxi (+u6qa horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (w:*8a6 vzw6i:ta bwrsi.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 of thirw:wwtv8 asb66 a: z*e 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 standing verticallm2k ,) ocy*yt)lbggt ab* 2r yc4.x8pky on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55)xy) g *gtpc.y*2m4yb),bkr2c tao l8k. The step has height h, where h

  A bicyclist traveling with speedueqqx; vozt-/ +.8tje4di7 eu1sp cm+ v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cy-+o1;q ume48+etvd/ pqu.sxt 7zcij eclist 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-kgzt :s81g irxs8 rock into a sling of length 1.5 m and begins whirling the ro8:rgzt 8 xsi1sck 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 torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body1)tksu uppza r942* qi as a 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 outstretched arms, and with arms held tightly against her bodspu2 4p)9rq zk a1tiu*y.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofrqpomvht(i1 rx+)y./l y q8i 7 tvly1qqori +x(7 ri m)8. pyh/mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro u(qh/+i.fph2c .tobjugh track of Fig. 8–58. What is the minimum valfq.c p/h+o(i utbh. 2jue of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume zu8por, o,*p kle:a x +l-u9ig$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car re5;yuw 21,m(q/ grz1drtfrm og duces 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 tiy/f(qo w1zgr d;r r,mgtm51u2re? $\approx$    $rad/s^2$(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