A bicycle odometer (which measur x/0o8dkc:zmk.qj x-h es distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wmoqkkzx: 8d h.x-c/ 0jheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rz4x3s kog/ol1z 9jj 7oim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acjjo7 oo49zxk 1/g s3lzceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the mvenz 5;+yx d,ch)h+yangular velocity $\omega$ Explain.

Can a small force ever exert a grea8*l-h6zg m) beg( oygb 9vok1zter torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands in3 /b2 t,sqwmbehind your head than when your arms are stretched out in front of you? A diagram may help you to answer thi2m3/qnb wi ts,s.

A 21-speed bicycle has seven bu5 tv3xd78+ie imfq* sprockets 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 to3u+q*bv xi 7ftide5m8 pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being ablo+)l9pe2f .iw:ws i voe to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational 9e+pl2v o.fi )i:o wswdynamics, explain why this distribution of mass is advantageous.

Why do tightrope walo6nx f 1.he.mafxc *, ds.v(i04oujo fuw*q v9kers (Fig. 8–35) carry a long, narrow beam?

If the net force on a syste:soodo7.d hkc 6dug9*m is zero, is the net torque also zero? If the net torque on a system is zero, is the netod*7 g.k ou6 cdo:ds9h force zero?

Two inclines have the s4mvj7tx2sb fud :t5hyr x6w14 ame height but make different angles with the horizontal. The same steel ball is r h bft6t51vs44 r2wd yuxmj:7xolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down9d8bb t -/5bvc nr/zup an incline. One sphere has twice the radius and twice the ct-9 z8 vdbrbpbnu5/ /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 tgz 1bg/5s1 :ciyo 8wsohe same mass. They start from rest at the top of an incline. Which reaches o 1o:wgb5s1sy/gz i8 cthe bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movin rtfyrnp84 :d 2jqh,twum4gm0b+-c +gg or rotating objects eventbhp+yr82f+: r m qm,c ttj-0wgud g44nually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equath. wzqrw8e. l9or, how would t .ql9wwr zh8e.his affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatioruives:)g (5qdnwi. )n when she le )iudir.g (5wnsv qe:)aves the board?

The moment of inertia of aox o,+bor,gq/1 k0yhe rotating solid disk about an axis through its center of qexo,yb 0gho/1 ro+ ,kmass 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 roxuq5pq3/w14 rmj +vkg tating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreasu4gk xq3qrw jvm5p+/ 1e, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeveo+:y lgq9ax o1hmk; 6 2uzt4iwr, one is hollow and the other is solid. Describe an exper1m wa+: 4z ihu;oxygt29 kloq6iment to determine which is which.

The angular velocity of a wheel rotating on a horizontar,nhmh0e13s nns6w()zybt7x l axle points west. In what direction is ther ne6n ( zshy sm,h)wn0b137xt 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 decreasing?

Suppose you are standing on the edge of a large freely rotaor))ktd 9clg +y vky07ting turntable. What happens if9r yg + ldc)vtk0oyk)7 you walk toward the center?

A shortstop may leap into the air to catch a ball/ hbhx:zm2mdgkl.- ,l and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig.h hlml,gd/ k-bx .zm2: 8–36). Explain.

On the basis of the law of conservation of angular momentum, discussyb() 2.y :lu6 wkz,jrj neheq7 why a helicopter must have mohby(ej:k 6zr7y j2)eqwu n,l.re than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (f-2kc-tqkhra13jd8)l5 d 0jf mad r/ba) 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 Eardj+5)vo;5t p ynolpu nl9squ-2nk i4;(da 2fpth because of an amazing coincidence. Calculate, using the information insldon;pd9yk4p5- l5vp2ns qot nu)f (a2 jiu+;ide the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from 9rl aa owsx2zy 0ll338Earth. The beam diverges at an a2ralsx3y8l9ao 03 wlzngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender ro3o + .paqsbmnlyb;f: s:6z.zqtate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acc nm:ba +sz;yf3.s. b6qlqzop: eleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anotherey1 b/w.s2ic m bb/4vy child. If the ball makes 15.0 revolutions, what is its diameter? ysi4vbb /yb2w.m1 ce/   m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mancp6+bu/n-ec(atv vbio4n- m7m /+ gfp y revolutions do thp+evt+n -covg476bm(na iuc-/ /pbf me wheels make?    $rev$

  (a) A grinding wheel 0.35 m i6vpx41n1 ielz n diameter rotates at 2500 rpm. Calculate its angular velocity 1x6 1ivn4zlpein $rad/s$ $\omega$ =    $rad/sec$
(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 come a5: s*kosn zahck23g5mlm.*plete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1h*g n5s3o*zka m5m.:scl ka2 e.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 arc 9w5/wihd.uhg4 eo,2 kez: 2ye(g+pcfmv3yxound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po /,dk ura5kd9 fyg)zixl)*j. (zxc+jpint
(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 centri m0trd,jbo7j *fuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration,d jo 7bmtrj0* of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel aca76 c, oep0v/ig)i yc+ivp,bt celerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. De6a,,/iotbe+y 7igvpc)pc vi 0termine
(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 radiuop,m)b) (aqpps $R_1$ 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, astronaufu+d+w mg9e-v;ch:lrbx; ; zkts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from;;vcb++mg-lu: fh kr9zwd x;e 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 uqpel *lpa0 67sniformly from rest to 15,000 rpm in 220 s. Through how many revolutilqas07p le p*6ons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpt: 2kgx ,hk/ux e/lml2jcln83m 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 jets incshxmg k7r- 4py65 .m, pftm*y a whirling “human centrifuge,” which takes 1m,srpm75yg.6fp-h x4c tk my *.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 ggyd * )3y*j3*rex gvaps2t,9fkc+lrrpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel ha*jfk3y3* geadrtl,cv rgxys9)*p +g 2ve traveled in this time?    m

  A cooling fan is tur:y ,cz *apw x)jzuew c7i7r81 ;lgzr)zned off when it is running at 850rev/min It turns 1500 revolutions before it comes jzz8 leayc)* w)wuzpzr7r; 7,:c i 1xgto 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 cd . u(xl-nf,ecar reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter e,c-fx.u(l nd 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 thexr3l3.2p 5pjl fwi/z7 viz) hu car reduces its speed uniformly from 95km/h to 45km.)j72zu3/3ipwvrif 5hl zl xp/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 b)k+a5ngym oc +ike puts all her weight on each pedal when climbing a hill. The pedaa+5 )mgo+cnkyls rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is ; u g+*2ubxsgwthe magnitude of the torque if the force ixg+b2u ;usg*w s 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 F )xbd7sru g6d 8zr +ctw+-zeq*ig. 8–39. Assume that a fr*q8+ -+) 7btru sr6gedzc wdxziction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mgzf g p(181d jys: )x20ht*jcy*awrv sass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod i21gatcpz*d1hswy: yfv(s8gr j)*0xj s held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylid6ykg+vu n4 .gnder head of an engine require tightening to a torque of 38vk4g. g6d n+uy $m \cdot N$ 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 when th9jmw),6pds dgjx mf+ 4e a6jdmgw s)9f4, xm j+dpxis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a ee9ibz 0wah29tr9z k0vbq1-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 cv199 tai w0 2h9ea-z0bzbek rqan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, l mfx/ww:7e+vf ight rod is rotated in a horizontal circle :wx 7fe wfmv+/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 rotating3 pap fyw:w52i(gk4p6w: nao d at constant angular speed (Fig. 8–4d::2pf 5k3 4ap yow(gwpi 6naw2). 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 iqm,em/6n; ) 7 wylb+mnmzg ql-nertia of the array of point objects shown in Fig. 8–43 about6n/ bm);, qm+ezglm 7qyn-lmw
(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 ln2,v zll h-6qis $5.3 \times10^{ -26}$ 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 9ve8;cgz yle.;nwr0t g at the correct rate, engineers fire four tangential rockets as shown iv;z ne c;tgr.908wyeln Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder witd.rc/so8bz-v h a radius of 8.50 cm and a mass of 0.580c8zd b/v .sr-o kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player sw3-nt3r: i2 yg kc(/ pbqaij.csings a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven9u 8 b70tvtw8y ti(ecx merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 8yt(v8 e7w0ttub9xi c 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 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 orn7(6; 8lmzy jbpx-hnz .m 6nvff and is eventually brought unifn7hpjbyr ;z .-mn 6z8xn (6lvmormly 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 acc f/ 7(pkvide9 3jh x/qzq9.t jj*mc8vbelerates 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 swb.gxzbke c g0 g/11zr.b)d +dolely by the action of the forearm, which rotates about thc dwbex.b g)z.r1g1kbzgd /0 +e elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shov zagh3:-mp:b wn in Fig. 8–46. v- ma3hgzp b::
(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 cozk9 j,- ypv 2y2ix9r8noc ,qicnsists 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 acceleratx4h1y w 57anghes the hammer from rest within four full turns (revolutions) and releases it at a speed of 25xw7a h14n ygh8 $m/s$ 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 hv;1evtug+)pklljr y -8/5d gz as 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 toajzt0nq1bw rr77 ph0.rque 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*a,xf izo hl0 cm rolls without slipping down a lane at 3 x0hlfoi*a,,z.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Subn52b3koa t 8goz tv-n-p0b 9tn as the sum of two ter0ogt2 ttp bv5nb-oa 8n-k3zb9ms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.5457d+ fg xa4eh*9 z ii*vt/rchgpgut60 m. How much net workd9p he 5+cg4 *i ga4uzv6rtg xi/hf7*t is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts6pt*vt7nw;fjm (m+ w h from rest and rolls without slipping down a 30mj7(+mtn pwftw 6*;vh.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 balanvm*omffx. kz.0 yp5b) +0mgn,h;uooaced vertically 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: Use conservatioo,mo 5y;f) pm .+z0 nxbkvamofh0.ug*n of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg balw)-m /q7f*d (g,gwcoyou t o.ml rotating on the end of a thin string in a circle of radius 1.10 o/w-( gg ,tudom cf7 *.yo)qwmm at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding x;ojqhg pfv, -.qz, rg b:pr(q.x8b:d wheel 8:q ovxf.jh;- q rzpq.rgbbpdx: , g(,of radius 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, hands atz/sll;y s6lk ;.gtkn 5q.vh:x his side, on a platform that is rotating at a rate of 1.3rev/s .x:v 6qz s;g;.k 5kll ythnl/sIf 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 Fig. 8–29) can reduce heqr-v hq)yq: g2r moment of inertia by a factor of about 3.5 when changing from the straight pyqr2-q ):ghv qosition to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fro-c)jzwfe0va ar *b()vgvi/wk-3v wn6 m an initial rate of 1.0 rev every 2.0 s tonrgvi36*k-z(w/wwfv)v-e v0a b c )ja 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 ipat 1di2:h4qjfv :98eud.oe around a vertical axis through its center at a frequency of 1.5rev/s The wheel can bi e:dqp8:. 2dvj9eihfoua41 te 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 nv /bt-ey2w.g 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 angulag0kc s;yki6 iy /qe.ixt2,wa8r 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 ae/m,q7+u wmiof moment of inertia I is dropped onto an identical di /iqw7ea ,m+musk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns :jmg0v9;on*kkun0 xlt; g2gs 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 platja;.l a.lm:*tzxpa-,o ,g*s fpob p-yform of radius 3 oj,tyal p:-..pgpmal*zsx-ab;o*,f .0 m and moment 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 frecwyet) r,/n2:k4qwbvuw +u h4 ely with an angular velocity of 0.8 nweubw2:4h cvktyw 4q/ur),+$rad/s$ 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 itu;-q uhq6k5bb7o5ca9*axiw nto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, whata wb- ; 7tkx uhiabu559qoc*q6 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 wind 58 +) yit6mrs k;np5s*xkvy)r.iz ubyj* jcp6s 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 d738ug 7 lbcod$ 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 pvns ad q2b77owovq +.s2k.7g jlatform, initially at rest, that can rotate freely without friction. The moment of inertia of the pk d .n q72sj7w.ao2v q+sgvo7berson 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 6.52sz 5jo/ /tmb+fnd )lo-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia ofbsz+5/ ot/ )jdol2nmf 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 qkr iqxdzdkvcd5,7f* q)+ c597vg n4e the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What gze 4)cx77i fnqd d5,v*kcv+rk5q9qdlength 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 sideyt4eu4q 6fpb5 o i4,0fzpios+ 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 the Moon as a particle orbio+epuyt4 40 q 6boi,sp 5f4ifzting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f60fxq ejik/ 8mrom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform f ciw+p7f2pfa)8mij 8cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate wai+7c pf28 8j)imff pthe torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two saz wz tmeacg,d j-,9m 1/f5m.d e+di2golid cylindrical disks, each of mass 0.050 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 gd-zeia cewfm+g2 ,t,da9j5z /mm.1d reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear;)iz/fjqxi xqqk, 6 r1 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, were195/qharlk,b2j ,,h+7glyy nituy bu 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 th1rkuyb7ilb/hyt 5yj,+9qh, 2a , unlgat 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 ayguip z- bk8f(/ 4jwp0 low-pollution automobile is for it to use energy stored in a heavy rota j-/z(gfy0pbuw4ik p8 ting flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates x9;zvx(rce-c an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on aoak ux b1o(7n* 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 nf9,wagw+2m+ am+ zbscrx +p.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 mmswn bfza+ gawc+. ,29 rpx++released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on/ nx elcuwww9r,uy9)5 the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against whlrwxcy)5uw/e9u, 9n w ich 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 mx k2 k i(koo4o8.w3ggfaking a turn with a radius The forces acting on the cyclist and cycle are the no (figx2 k4o8okgk3. wormal 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 sling of gsykqqt e was;;fyjv/80( ;;alength 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the gaqtsk; ;(ejv8;0s y/yqwaf ;torque come from?    $m \cdot N$

  Model a figure skater’s body as a s 4jh .1npyyeyh*nl/ -rolid cylinder and her arms as thin rods, making reasonable l/4 nhrpj y.-y1*hnyeestimates 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 body.   

  You are designing a clutch ass te( nkxuf tlps /60ukbx9819f ydy41sembly which consists of two cylindrical plates, of mass u9ysxt8k xfse1 d9utkp6( ynl14/0bf$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped4b8d/zwz/ypu c 3p u2n rough track of Fig. 8–58. What is the minimum value of the vertic3 8u ndzyup/p/cbw4z2al 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 assiw l0,w -xcd(ocbl dm. p;o28fume $r\ll R$ h =    (R-r)

  The tires of a car make 87y8 . 1 ,4vnxgbmg-o7n z b;fjzm)0qrti1npkx5 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have 0 47gyrn1;1fgqtn -)k8mjv, xn7ioz bzpbx.ma diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s