A bicycle odometer (whi+uf 54xcsg2 bjch measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyclexsu5 +bcg fj42 with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on6pxuoxx w34ty;( 6lcoxj) wt / the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/xuw(x)tc6y 6;opwt x xjo/3 4lor tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sing7vw ne2 x +ow9vpsk/v6le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forc y5wx,1 :g.jcobtt l6ke? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head thk0w;zkr *fhx41dlt,ih q 4 rn8an when your arms are stretched out in front or8* zdh k,q 01n4tl;ihf4x rwkf you? A diagram may help you to answer this.

A 21-speed bicycle h),qzqr q57p,xu5ycpqas seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to )55 cqqru zq,y7,pxpqpedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being abw-4b+4zb7ntbj hdkb1 le to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of r4b-b1jb k h+wb7 dzt4notational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walket,b:cdbr w17f 3 .owutrs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net it63 m5 vq u gxiq,sgb)q(rst+;i//zl torque also zero? If the net torque on a system is zs// l ,rv ) xmq5qtgui(i;i3bs6qtg+ zero, is the net force zero?

Two inclines have the same height but make differenem2d),rj g9 h kpd8m+yt angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explainy+ pm9khrg2)d,d 8j em.

Two solid spheres simultaneously starmkqp 3p 1y)y2ft rolling (from rest) down an incline. One sphere has 2 q kpf)3y1myptwice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the sam:r(der a+l ;kqe mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotatia(k:q; r+rle donal KE?

We claim that momentum and angular momentum are conserved. Yet most moving14bx,vt5( xvs94xp juvd27bj q c9k ig or rotating objects v9qug42jdxx jbvstk c94i 1( bp5v,7x eventually slow down and stop. Explain.

If there were a great migration of people toward the Eartfi8 bnt sa2mc:odw45(a/-xv gn twp 7:h’s equator, how would this affect the length of the dayf:p oat w:s8wn/a4bx m-cigtn5v(d 27?

Can the diver of Fig. 8–29 do a somersault without havin 6wuc.voe8v:c 8k0z my+uc3fr3dp .ou g any initial rotation when she leaves t.v3 om ov6u puf8+cwcu3czd kr0ey8:.he board?

The moment of inertia of a rotating solid disk about an axis throu )crm: jph*j 3);gsirbgh its center of mas 3pbjij))r ;hr m:cg*ss 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 rotatingj/( y7nhjd 9 nk0lsx erpn-.wo7 fwf:+ stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the 0e+ o lnp-nf(kndy7:r9wxf/ jh w.js 7masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same massdxjyq, ;) ou)a. However, one is hollow and the other is solid. Describe an experiment to determine which ; doyj)u)qxa ,is which.

The angular velocity of a wheel rotating on a horizontal axle points wesm8nn0bu wsj vrywm m,5t;37;m t. 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 obw70s j;n8 r53nmvy;mw ,um mtf the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large frek 5g.f;l.r6 udg:zujfely rotating turntable. What happens igfl.jk5 ;6udfrg.z:u f you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he th 11hai*b q,occrows the ball, the upper part of his body rotates. If you look quickly you will noticec,bco1 qi1h*a 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 wh . hrl)t5rg3bz rzvj+*y a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to rzrt .5)*v+ gbl3hzrj keep the helicopter stable.

  Express the following angles in radians: g:* oam. uom4e(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 a; frqj3qp0mvjc+f(a0xs12vj 2a 1prvn amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radvxrq;220a a fsf1jq vr0 p1vj c(3pmj+ians) 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 fro6e, .rxrknn77 fq;o pt0i)uz6n+jxyom Earth. The beam diverges at an ok6 .x nf r p77jq)eyorx6t0n;ni ,z+uangle $\theta$ (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 tu(ai dphpy2;q. rned off during operation, the baq yp(;2phd. ilades slow to rest 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. aq(hkq/0-qo2k+m2lp*nszv(7sr whfh+q 3nxIf the ball makes 15.0 revolutions, what is its diameter? 2h*mxr w+f0pqk(hql s o+3 nnq2s/ak-zhq(7v   m

  A bicycle with tires 68 cm in diameter1y boisrqj *.6 x;cf)e travels 8.0 km. How many revolutions do the wheels m6 qyc.1i;esr)j ob *xfake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 25y wxfm-fisae -)-o 4w;qi*qm ,00 rpm. Calculate its angular velocity in-es q*xw-i;oqyi4,)w -m fa fm $rad/s$ $\omega$ =    $rad/sec$
(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 rrwk-y3b9 jlx.1ta5f9 m 6s2l0 hsqrqin 4.0 s (Fig. 8–38). (a) 1w 9. - kb 06mh5 xjlrtsfqylaqr9s32rWhat 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 velocitrpb1te2kuf 3 /y 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 speedw2.(pikltar4p .( t gqe+ti8h of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axisn) tlg bdesv wam,lqkt02w. ;;;9 k+ty of rotation i k ;0dvwl;tnst ybqge),+9 ka lt;w.2ms to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm tonk5; i i8jbvjb9izz3+ 280 rp5vii +398nzjj;bikz bm 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 radiusd:sq 0u-1vdnm77vnquakrx+ 0 $R_1$ 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 spacecrsppxr0 7yxd.9 aft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they p7yr.sx0 xp9 daccelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uhbvb2.*.+ j oxi 4.dzslf3zih niformly from rest to 15,000 rpm in 220 s. Through how many rev.z*hi3l+hd2xv s ibb4of.z j. olutions did it turn in this time?    $rev$

  An automobile engine slows down from 450d9gfs7 /j4shs0 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jxly7 9h7 nco7mr2l8anets in a whirling “human centrifuge,” which takes 1.0 min to turn tn 9 8x7llo7ny2rah7cmhrough 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 accelerates unif qomyr1 jq9*cay.k2p1 ormly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the eapc m9jyo qkq.r1y1* 2dge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it i) icmd*5snax+c)mp *ns running at 850rev/min It turns 1500 revolutions before it comes to a stos mi n5*)nacd*mpx )c+p.
(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 reeu0v;-uy5bbggg s 9e /duces its speed uniformly fr-eu/ y5 sgg9;ubvgb 0eom 95km/h to 45km/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 )jz 2em.8.r dcx1wf04o aq2eahaaag0 65 revolutions as the car reduces its speed uniformly from 95km/h to 4d2.a8 e jfxmh2oara4q10 e)0azc g.aw5km/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 bike3 20;wpug pflv,csf-t puts all her weight on each pedal when climbing a hill. The f,2t0l upw sc-gp3 ;vfpedals 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 tfca zk* .bmyj(o2 u h:j(0uaf5he end of a door 74 cm wide. What is the magnitude of the torque if the force uazf j.((m*a 5c2:bhu y jkof0is 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 torqu-tno+.ehg46naoocp.;xsy jiz 1-ep-kd ,6q ge about the axle of the wheel shown in Fig. 8–39. Assume th-;onnap 4c6,.-q1jgx - tzgy+p keo o.si 6dehat 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 attachedskr ka2e:jmh d+7a:o 2 to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction e+2 2 :s 7ajh:kamrodkof the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to(mpg ,, h+dq:cho jc-b a torque of 38,:h( cmqc,hjb p +og-d $m \cdot N$ 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 inertian2);c8vr *f h4mkgieby*x2j k of a 10.8-kg sphere of radius 0.648 m when the axis of ronijf**kbx2gc)8 ym2 r4 vhk; etation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The; kz oan3 y j64g 2zl0a2gio35xs+h)2h xxkyox rim and tire have a combined mass of +oh ox n3lgsaixz6g2 0ykzoh4j )2 xx2a 5k3;y1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizonta p/34-rvv+ ,eic q p/ugli/kqnmngo8;l circle of radius 1.2 m.kg;qin/e ngv/ m/, op i3rpu4v+clq8- 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 angular gecqx/hg0w h0s)gh:8cy15h q speed (Fig. 8–42). The friction for 5gh1 )yhhchg0qex80:qcw/sg ce 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 obj5tmnh,fw,tkt z+ lj. 6z0s/waects shown in Fig. 8–43 az0st5km,,/h6j n l zf .+wtwatbout
(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 oxy3r:n4x )2teyvibf/ shgen atoms whose 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 spiape.llt)/ggdm7 w4 ;znning 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 ea; dg .zpl7)lema4tgw/ ch 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 (ttady5bx /2luk3.fe radius of 8.50 cm and a mass of 0.580 k (5al etx3bfktud /2y.g. 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 bat, accelerating it from rest26at f4gk 7uog 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 tange bztw:qthh .2w.1q ia8ntially 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 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to pro..hwbqht1 z28t :aqwiduce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rota,8:dcu8 t kmhvting at 10,300 rpm is shut off and is eventually brought uniformly v:8 dkthu8 m,cto 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 accel)b xuu x ;)gju*2vwcc-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 action ofbo-(.i4k9ch gj6rd /ej hh:mk the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniforc khhj9jdg6b-ek(/4i: mh o.rmly 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 t;) fc bmp k7w*6hk6iwmhin rod, as shown in Fig. 8–46.;mkp wi76b c )wf6hkm*
(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 con + 1d xmjuak97bha sq8-ntr55rcr0z6nsists 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 acc bmr(fxnrez,64m4zd *elerates the hammer from rest within four full turns (revolutions) and releases it at a s6,(zx n mz4*f rdebmr4peed 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 hf7ovh/nwcdk-1 z/pu1as a moment 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 torlaosxh l,u i. :u;)xtt:lff8.que 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 w6kro/;h. (b fvrjgu )without slipping down a lane at 3rw)f/(o kgvbujr;h6 ..3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun aqr5*v em*tkfnq/y/m 2 a 2zrb4s the sum of twoae4t f/vmzqr*n yq22/bk 5r*m terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1rl0if1e 7 z9c( jldj*x640 kg 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 revolution1* ejfcid(z xrl9j7l0 per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass f6 tg4:la+hu(o)xamf 6 8qfdu1.80 kg starts from rest and rolls without slipping 4+o m f6u: gf6aqh(u t)axd8fldown 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 verticak0+etp ,nabfc /rr5.u *kja3d lly on its 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 ground? [Hint:3n*d+u5ep.0t krjac/, fr bka Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotac.1a-0q)ed oh, pbxypes t1z 5ting on the end of a thin string in a circle of radius 1.10 m at an angular spe)xb .0ydecz-5qtsea1,o1h p ped of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricalv 1kfwpb:h dr 751hz-x grinding wheel of r 5 vhx1wprbz:f- d71hkadius 18 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, han ,75d6tqjv m hwnq(,yjds at his side, on a platform that is rotating at a rate of 1.y dqjm h(,q6w5t,v jn73rev/s If he raises his 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 F: :qben bag twn,2x0 ine0u s1-+t1eywig. 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 she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular spnq wgyt-eeu ,wb:0 at1x1n:nse i+b2 0eed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increayv,xtm v crvd3dr 5-:6se her spin rotation rate from an initial rate of 1.0 rev e v63:-vv yc5rmxdtd, rvery 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 i0xh0t:4qvrm epc50 a t mf2no/ts center at a frequency of pmtx/45 v2 n :ca qe0rhot0m0f1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of 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 skater spid/b 4 8ok /snpsfdwpn/ykq9 0-nning 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 angula kmmubbwfz;hx3 ) 4b6,d5z7of r momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dn8k;urqnq3 r(w)ba cv*;lt *dropped onto an identical disk rotating at angu at8;r q**)kuvw(cqd3nr ;nlblar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsgk* o c64d1 i mcd7h.mku22 )zqdxk7nb at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pladi6l, ;ao b.wcm)guo.tform of radius 3.0 m and moment of inertia ud,og .c bim .a)low6;920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocit5cdb od kw0 0 oprnjg9thp558,y of 0.8 pwn 85gobhd05kj p9t ,5d0ocr $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about hamybjt79 ctr kxmime;e:1j/bt8( 1+oi lf 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 woul tei;7k (/+j 1b8mit1b9xc eor mtjym:d the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess ofu+z a87 gr p;ibctw 163.fobhj 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 -h1r0ajbfu c5wnd/,o $ 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, n)yh4a 9w7oa vthat can rotate freely without friction. The moment of inertia of the person plus the platfo oh9 7awa)nyv4rm 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 teyo g;+9d8/+1do / oihyblb khurntable +y9y/bblo1d/ookige d8+ h;h 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 rope rolls on the groundiz7del7;a11f7 u rtnm with the end of the rope lying on the utl17 n7fm z17rdeai;top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such t i-,i of(.gtdvhat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat -fvgit.,d i(othe Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest uh81diuuu(vjqc, 9.e 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 uniformnklag 9n 6j3c0 cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration36j k lnn0ca9g. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0u0ma 1i9r fwe..050 kg and diameter 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, ie. w1uaf r9mi0f it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular sp xg q3(o1aet4:3gc+*n yrequk;kq b1j eed 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, werezomy j63vr:4 p-g4dwg 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?gd:zgpo6- w4vr jm 43y 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 automob .(mw5k4ghn tkile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a utm4.(wkhg 5n kniform 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 an 60um*p,yacb v $H_2O$ 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 on5+u r-kqh1 hicm 4 jhu*ctym30 a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass.gp j;mnl 1 bbn1pe-/w M and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in F -/wen;plb1b gj.pm 1nig. 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 istr.l49gak 1u8 6 uhzgr standing vertically on the floor, and we want to exert a horizontal force F g1 z rrh a8.k6ulgt4u9at 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 b+8ghl71/msk vh8bwh/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are thsb187 +/mb v8hhwlgkhe 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 intr2gp- x( o)+ p(krvknu//itiao a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rtv+2 oi/r)(gian/k- kpux(p 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 her arms as t o:qkwh 80ob+a5yrm9whin rods, making reasonable estimates for the dimensions. Then calculate 5mo:w9q 0 8hob kayr+wthe ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consz6cw-sozs1 o:tr f zzz+2 )p u6au8+gdlg2 nh2ists of two cylindrical plates, of zorgot+ 2 2 z8zcfu 2wpsdaszlnh)zg6-+1u6: 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 r0 suvft4 nxgif;5 t3tttw(ay/-r,z)b rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the lo5ant0-rg u;ty f,x 3v tt/bw4)(itfszop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do no7vny 6+k3nvjht assume $r\ll R$ h =    (R-r)

  The tires of a car makd /seb7i*qn j67/xxyze 85 revolutions as 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 tin bd6xxz/es*qji7/7 y re? $\approx$    $rad/s^2$(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