A bicycle odometer (which measures dig:7ejp; -u+h i:e dytostance traveled) is attached near the wheel hub and is designed for 27-inch whe; y::eu 7et+iod- phjgels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Do*jf h-ceku;;2 zjr obt: .px.ges a point on the rim have radial anxc.f*;r jbe:;hj 2go t z-.pkud/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be 5wbh7uga;w/;jy j :fmdescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fp3t,* s)ml4f bja2nabju5 y t+orce? 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 handsy h jwbd572uf)5ap4ee behind your head than when your arm524)eeafd hw 7byujp5 s are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at z2fhhkd80u9/utzt l 4ke)gr1the 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 sprocdzg8k/u f)krth 9 l1tz20euh4ket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower lesx .fu:0j, n ocqy2pf5lbn. :bgs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotationa 5..sluobp : cq02ff,ny nx:bjl dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow )ap/qwcysri1p5a:vze, c 8j ) beam?

If the net force on a system is zero, is the net torqul ocy.e/c yy4uo8p/ 9fe also zero? If the net torque on a syste.o8pccl9/yufe y/yo 4m is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontaly3;pg pq7d nzmj49 dp1. The same steel ball is rolled down each incline. On which incline will the sppnmjdz9; gyq7pp3 14d eed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously staqftz5uvgzbex 0k, 5uauj qs k(:345e/rt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total 4 q30,5zqk au/jbftug(5k5s:xue z vekinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from 5p(hfdg bcs 9)a.e:cq rest at the top of an incline. Which reaches the .fcd ch:9 bpes) qa(g5bottom 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 mok)rbspncp5umnl38 dx6b,u/;w w6 sh)st moving or rotating objects eventually slo)d6cn3pmu ,; srkl5s)/nu hbpw6 xwb8w down and stop. Explain.

If there were a great mi:m)l:1g*c,ez+i/ynb) diyi p3ft nxc gration of people toward the Earth’s equator, how would this affecbinxl y:n:,mi)1yct i3 p+cfegz d)* /t the length of the day?

Can the diver of Fig. 8–29 do a somersault without having 0-*8(syjwmju pdqrw67wl c8u any initial rotation when she leaves thelw *s r8q-mjuywj(uc687 wpd 0 board?

The moment of inertia of a rotating solid disk about an axis through i gp* w 70)jvrcyej,bs:ts center ofbv*:)egr 0c,ys w7p jj mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each f7pgs/g5alcdm -/2( ju1nhcwe: v8uioutstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or c /jm-ngvued pi:8 1fc5(luh72gw as/stay the same? Explain.

Two spheres look identical and have the same massyj/;n. 2vevkc /f9d vwi,ro.p. However, one is hollow and the other is solid. Describe an experimnof.vivjd,c;/wk / y9rv2e p .ent to determine which is which.

The angular velocity of a wheel rotating on a horizontal ai:6afvu(u u zljr5 *4rxle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points ru 4l6 j az*i5:rvf(uueast, 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 nyy0c /3pt ki0of a large freely rotating turntable. What hat/ cy0k30yp nippens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he t dw.(y 9m6fcop6wkpn;hrows the ball, the upper part( k9po;p6ywcdnw .mf 6 of his 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 conservation of angular momentum, dis,)z;i wh9m a m(x-jwckcuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the heli ;9ciwm(-)j,ah mkzwxcopter stable.

  Express the following angles in radians: (a) i,75xev q*np /s ,oyyt30 $^{\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 coincidence. 1,iyj kb7 xee).ebkz6)oupw8Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Eabkjwiy ,8 67eu1)x.)o e zkbperth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon,db9e*s)j qa *2/egob jp pk-7g,k7ocw 380,000 km from Earth. The beam diverges at an angekwbpbq 9oc -)gk* s7 /2,jgpeojd* a7le $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender roaentb+c:zwj: nc .: ahud8i 2xn4.3 futate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slonthfaz j:3u.bacc +2e.i :4nun :dw8xw 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. If the ball mu- h 6yjbha.;6qzsjb2: i8mtsakes 15.0 revolutions, wh-j;u thyq6s6j ma.2ibb s8hz:at is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionsnt56t yorj (ja/8g f0yla,aq5 do tn5/0q8l yf6jay t,a(a rto5jghe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates; e-rb;eo:cf ) ijc8 *ub(a m0n2iowei at 2500 rpm. Calculate its angulbijn08wao* uic)f e(2r;me o;:b c ie-ar velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38). (r*2b 572d1ohvxnv e oza) What is the linear speed of a child seated 1drze5b *12vo2vxhn7 o .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 or ,/czd/5vmnut 74ky-uv:l s/ cjfb 5qobit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp -em7ilbkh 07vl uu5-eeed 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 centrifug,bzo+cbh yw2y:u *.fk e rotate if a particle 7.0 cm from the axis of rotation is to experience an accyuw,:y2chfbz*b +. koeleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 28t,mx/tuqw i9,0 rpm in 4.0 s qxt9,,utim/w. 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 4lq+st 9emht3 $R_1$ 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 s*p q:n mnzsv2/pacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At th*qp:s/zvn nm 2e 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 diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 9w f (k v:9c5 xgz7o/(,tf(xrj nijmku220 s. Through how many revolutions did it txkj(v7 mt( 9ko/zicwfu9r(j5g: fxn ,urn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.8b67o8x3ax kdy p2l q7whuu2 t.lq+gp 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 in a whirling/s33oj: x+or siq,jfse2sxk 5 “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reac ,j o q2+xsfx s33ksejo/sir:5hing 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 rpm to 360 rpm in 6.5oozdxr6 so;a8gabo w xb604// s. How far will a point on the o0a6o/ x6b8o ozgd;/xwas4rbedge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It+ jo-7;sb)x9f5vpwt hvly 50n/qce rt turns 1500 revolutions before it comes to a stop. vo)hjn 95+ cfeq t05vtsprlyb7; x/-w
(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 69v bz(+mr vv0hjj8- ie5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have azbvrmv+ v09h e j8i(-j 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 uniformly f gvae 241nr8uorom 95km/h to 45km/h Thvn2e1 4auogr 8e 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 hcn6/m65 m(op aej mr:+y.ukt x,1xzua bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 mejxp5r6u(m,+.uxany/t 1k :hm z6o ccm.
(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 oevabn(d37hfv(m 3y a ci;qt(;x4z 1a ef a door 74 cm wide. What is the magnitude of the torque if the force is exerted a37daze(n eb(vai mv;(hy 431 qtx;fc
(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 Fi6:b84 uh58vrmtzhb hog. 8–39. Assume that a friction torque of 0.4 uzhm: 8 v4bohr5 hbt68$m \cdot N$ 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 whic+j:wm 4bf0nnw h pivots as shown in Fig. 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. 0n4mwfbw n: j+

  The bolts on the cylinder head of an engine require tightening to a torqud5 (s jk,8skhte of 38 ts85j hk(k, sd$m \cdot N$ 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 o qoyr* ulif9f(kxi(z(n)b5 -xf a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its cen yqozfk u5rnx* f9-)x(li( b(iter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wh5slhhnz7p d*qgdhl-9 *t,xg4 eel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igns4g9-d*l7h5nzp ,hqhg*dl x tored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a ho:d(hj*v* k o)w8nt vuzrizontal cik *jth)odz*n8 u (v:wvrcle 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 constan5 0xte wo9-cybt angular speed (Fig. 8–42). The frictiow 9e ob05cyxt-n 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 p q kt7a bt.y,:p*/qhcthe array of point objects shown in Fig. 8–43hty*t bpc 7q ak/.:qp, about
(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 totai ltm7 l +v:rm9t8cw4 (schyf8l 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 spinning at the correct rate, eng.6d3f0 vesenagua. t .ineers 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 r afe..t6d uevgs 3an.0equired steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radiusw:p3lgn3x/ ju of 8.50 cm and a mass of 0./nj :gu x33lwp580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating itb7 m ; 7z7ibl+gtf r+p2akj5co 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 :ty4ez7vz, t+zwvak1 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 o kz1wze 4 tv:yzt+7v,ather 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 rotdhc*5 5(mwamd ating at 10,300 rpm is shut off and is eventually brought uni mdwmahd*5(c5formly 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 acl btdry 4s;.p)celerates 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 of the forearmn-:gkn.wh s8 b, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerw sngnk.b-:h8ated 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 thinecj8h2a9bx6: acs ;i+ r tizn5 rod, as shown in Fig. 8–4ti6r:j;bca+z8acs 5ix2h ne96.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists ofbry0;n5;9q 0nnf nryv 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 f2u rmd8x:7e; ak):w4aa cbjraull turns (revolutions) w dmr2aer)8 kx;jca :: au7b4aand releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment,brpf//tlukb58 j 7zlqtcc77 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 :rg1e*l.q( 2b:mrclgd i)wkn yod 0e :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 rolnugrb on) d ;zp95hb4p7sf: x.ls without slipping down a lane at pubg.bnod; n )fx:hr7zs49p5 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as tm( y bk+ xlz7 s(-q-qxyvhp.h*he sum of two lm+(s xhzhp-y-q*vx b7.q(yk 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 1640 kg ao.r1e*5sille.svhpm 8gd z;*kcjy7 :nd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it isd:;oi87e*jsgp s5cemy.*z .1h vlrkl a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.8ye d )p/+ojoz.+6be vs0 kg starts from rest and rolls without slipping down a 30. z/ j+e.pode6yv+osb)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 / 9jffbecm0 dw*1t9wc balanced 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 th0 9w*cmc1bwjdeff9/ t e ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a q z2af i+x.e1nk )a((ygcw fz.thin string in a circle of radius 1.10 m at an angular speed of 10 a1 zwfeyk.i cgq2z+n.f()(x a.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whe-egpj, f(gokqsi( :tee0deq1 c*:at )el of raotfa1cs*gq ):gj:p(i-keqe ,et( d e0 dius 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, hand*q o/07yvun0 bnf 93ipzm ymq3s at his side, on a platform that is rotating at a rate of 1.3rev/s If he pvoy3mqf* 9nb7/ ui3q0nyzm0 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 pvt+a3 e xb bbyd;sr :-i7bw(a30n*jxshown in Fig. 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 b+wa- dsxbn(v:bx i7e0*j; y3rba 3tpin 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 rotatiop8ypr/ 6ix0 mon rate from an initial rate of 1.0 rev every mpyxp6 o0/i8r 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 ro h9 )1p2 owqmql8fczr;tating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diamqlz; p 9fr182coqmw h)eter 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 momeuic( dp m 1of//ywcs98ntum 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 angularxae-eo*n5oyv6)3 k cc)u yf 9k 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 of2(20z/tt pa tyjgo e17uh9a vz inertia I is dropped onto an identical disk rotating aotp0hzgty22t /z9a1a(v7uje t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ahl0fg7:zm.hq lf7 l7kt 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-roundby 8uez 3g9kp;i7uo / ihxfg/xv3:h:q platform of radius 3.0 9k/ oxi/u bxvh 83fy;:zpue hqg:g7 i3m 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 freely with an angular vb*u75x nni5 dbwh7(kjelocity of 0.8 nhb5b(xj *u 7i7k d5nw$rad/s$ 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 collsnp)u (7ow,l1ff4 dg lapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest ildf(7plnsg uf ow) 1,4nteger)$\approx$    $rad/s$ (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 exces ytrsa;6o o;p0fngp+6s 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 *8 fgx/qvnh;d$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withoutw rn t6dbovt33p /t.d: friction. The moment of inertia of the person plus the platfov3. p/ttt:ron ddb6 3wrm 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 avtaluv3gk; qo0 eeo,2 m )pv3:t the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a mlo0: vqv 2vt;egkao,3 up)em 3oment 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 endp 4 :2etzp43.f*trq 5m rkbwyl of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of .frt:lt253qp w*4mzbrpek 4ymass move?

  The Moon orbits the Earth such that the same side always faces t hlik ;ehu/2,phe 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 orbiting the Eau2ik/ h;p,lhe rth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a r :a. p.q(p62zvwlg posate 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 cylindcn xlh56ryw-(mjb(t;xb s:c 6er of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliveret6m bhj-cyb;(rxn5lw (6s: cxd by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of m)se pz-x:2uxeass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 e)eus :-x2pxz 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, how i)*y wcpf(ies .s 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 mqyk 66ks0 +zxpass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what wou6xqy0p +zs kk6ld its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy st8dzv ,6cizs r9ored in a heavy rotating flywheel. vzdrz6 9is8 c,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 illustrats xadut ;58c b/-evyogsp7 :fqic. l16es 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 -;ju2cjp uzg+rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely4jys7q *1hyd t (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is helyqty 7 4*1dhjsd horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is szv 1fc. 5mh3y p8.2+exccd ikxtanding vertically on the floor, and we want to exert a horizontal force F at its ckx zc xy.h cfd8pe15m2.+ 3viaxle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a42bxip sgyk1 ) nzkx28 turn with a radius The forces acting on th) 224y sxzkgn8bki xp1e cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg ro.mjqc/zwjru4r5ys*, ck into a sling of length 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 t4jyz/j*q c m. r5rwu,so achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder anj. 3 krn2 ukiic,gx9c;d her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outsgcrx 2;. k,ni93kuc ijtretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, of/o:bis)j hr)j jhvh43 mas3rhhi jbo) /hj)jsv 4:s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough track o qdkb61dx da o;.gea.6f Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the hig6bo.dd xade6;1 kg a.qhest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dj1(lflui ,p /a,vpme x 08a-rgo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spei,t 3w ld 1i w ,b7xlh+-,ch:rslvc,tfed uniformly from 9 t7xd3 l,,wf,+c h ,irwvb1tcs:li -hl0km/h to 60km/h The tires have a 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