A bicycle odometer (which measures distance traveled) is attached):dqlx9 ru2.lhi 32b lqzh+ww near the wheel hub and is designed for 27-inch wheels. What happez.2wlqlirdh h9 32 w:u)lb qx+ns if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a po4 (7c,8yokxkc6 v:uvhoz2 yt mint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly,m64 zt7(,kkc2c8x uvv ho:yy o 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 described by a single value of the angular velocity g1 4l.jqld2 lsg6bem6$\omega$ Explain.

Can a small force ever exert a greater torfma tpc om613i/52q0bcqk5w xque 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 with41tk2hp+ xf wz your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer hwk+z 2t4fx1p this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pjqcr ci2r.: *1vvyvw9 edal cranks. In which gear is it harder to pedal, a small rear sc:r wijv2v v .r1qc*9yprocket 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 able/:b v-eznx9xn:zg +ww to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On th:zbwnw+v xx/ -g9 zen:e basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a dgr*xoc/9/7wx8qm.9f+u daqwjc q4f long, narrow beam?

If the net force on a system is zero, is the net torque also zero?sf*dqf8da92azk, pbd4 6mm0 t If the net torque on a system is zero, is the net fotdk6 zsbp a 489m2a,*fddmfq0 rce zero?

Two inclines have the same height but make different angles with the horizonttas1gmva3) 5 g8fw4h gal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explai8g1twa f)a43h 5mgsgv n.

Two solid spheres simultaneously stj :gwf* e 5x3abp5toy7h1 ogc+art rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Whi:p5o fyeoga*c b3t+7 hx1w5gjch 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 same mass. They 1axk26sajv 6ft(z el4 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 1 s4tkaa(l 2xej6v6 zfkinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and ang vsh9az93k ou -f)tow72ky/+fsqi( x oular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Ex-xfsv qf 2o9wh3 (oykza 7tou+/ ks)9iplain.

If there were a great migration of people toward the Earth’s etkm-/irhl0rf*g f76l mxo. l: quator, how would this affect the length of the dar0lgkm fh:li*mf6.-lx r ot/7y?

Can the diver of Fig. 8–29 do a sombbna+g 4 1h/wo7yn6tu ersault without having any initial rotation when she leaves the board?/ aoghb4n1 7wt+uny 6b

The moment of inertia of a rotating solid disk about an axis through its c0yuhg: 8x8zsj enter of mas 8xs0hg8u zjy:s is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outr*zil 4*zykj 4stretched hand. Ifzk r 4z4jli**y you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one s4aati4i6l8c is hollow and the other is solid. Describe an experiment to t6as48 4cil iadetermine which is which.

The angular velocity of a wheel rota.am.c ,t9y cr :insqb;ting on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. :;tmic9.cy,bnsa r q. Is the angular speed increasing or decreasing?

Suppose you are standingig a 3t,piu jz(b;l+fb/l1* rc on the edge of a large freely rotating turntable. What happ r clizg1 t/b+p (ubi;a,jl*3fens if you walk toward the center?

A shortstop may leap into the air to catch a bacc/a;ju8,b djr8grin2* 1pb g ll and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quick ,d8i8r /; uajpjbc*gcr2b ng1ly 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 momentxj;k0q8/jny+iwvs 2q um, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the s;2 jws8q jn+ yv0/iqkxecond propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30h7m m8wes).jh $^{\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. Calculate, dd k ))vax2m6ak oz7 b dfm.r0hlo5*+vusing the information inside the Front Cover, the angular diameters (in radians) of the Sun and tho x07 k6zla5rf+m vh k*ad.)dbd )mv2oe Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at thm7 ru/3s aw0zke Moon, 380,000 km from Earth. The beam diverges at an angleu mwar/k370sz $\theta$ (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 mozgvao88+i o 1utor is turned off during operation, the blades slow to rest in 3.0 s. What 18uvgzoi8o+ ais the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 oc54j;(v n; g7(sxkz/ dktkdum to another child. If the ball makes 15.0 revoljuddoktkx4z ; (sn( kc7;5gv/utions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions dyly.8mbds0 / pp2qt k+o the8pmtkp+ d s.0/l2byyq wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its as(/nnj ; v rkcmkm0f;7ngular velocity in 7jnvc;0/kfn(rsmkm; $rad/s$ $\omega$ =    $rad/sec$
(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 comv,e u. h g(3h8kovjb *jtbp7u0plete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a chpjko 3j7h8ebbutug.*hv(v ,0 ild seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit ar s4k:4qk-aozcound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point xc frq ptu88g 2f vk -)r/7e:8+sixbxsjz1bm8
(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 axiewjwp)) h.,k hs of rotation is to experience an acceleratiw h .e,jkpwh))on of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aeuhdl t5/m p2cc+t:g2b w i;w(bout its center from 130 rpm to 280 rp5u+lw:/ egtmbi2dc;2 c(pht wm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 6zwqs i7(ye *vj v;l50a5a(k qp:nwbw$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put +z-f3ohrpcg ; themselves into a slow rz ;-ch 3+ogfprotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a 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 15,04:hepmro 8p2j00 rpm in 220 s. Through how many revolutrej 2o4pp :mh8ions did it turn in this time?    $rev$

  An automobile engine slqm m*xz6o8:dkows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flzdw jgaknfw2kt8w w :7e4hej0 95q -hl.7mou3ying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachim0e4 fkj: hw8k au.t73jd7 w2wh-w9lnqz5o egng 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 68f+ufjrn qm 8yq2*m b(.5 s. How far will a point on the edge of the wheel have tq8*b fmn2yr(uj+m f8qraveled in this time?    m

  A cooling fan is turned off when it:y kqu1 j 7.+llpgu,qf is running at 850rev/min It turns 1500 revolutions before it comes to a stl,+uyp gfqjq lk :.u17op.
(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 reduces it q:eyquw0a f))s speed uniformly from 95km/h to 45km/h The tires )fqae u)y0qw: 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 max 6pxx 3c-4wnu/ j,h6no8sobjv lt;x.ke 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter onjn o 3wxj;. -l ,v8 b64ho/x6xtucsxpf 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight o *(g o3fislym(n each pedal when climbing a hill. The pedals rotate in a sfo*i(l my3(gcircle 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 doat1w/z s5 pt07ende :qor 74 cm wide. What is the magnitude of the wdt atq:n5 7s1peze/ 0torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. As;js/c+ ;lx7. 0 5jifadvpn hpdsume that a friction torque of 0.4fd/+; c vijx.;5nhalps 7dj 0p $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of - j* b4yn- ui7x5wewpfmass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal 4p7xfw*5ubw- ie jy n-position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tiggn ki8 -ddbc2-htening to a torque of 38 c2b-8idn-d gk $m \cdot N$ 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:ve0zwt+ r:x9k4 o otf-kg sphere of radius 0.648 m when the axis of rotation is throutkfwv4o9t:x:+o z0e r gh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a zzh b *0m zqxc/2hhfl/ ;+lh(mbicycle wheel 66.7 cm in diameter. The rim and tire hal* hb(+ ; zc0mzz//h 2hmfhxqlve a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram bal x9 -0+v.w*v9tmk8 e r0h(knifgxkb8zfj ocp0l on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 * w9h0nm(c0v9 -kgo trfefx0j pvz88kki.bx+ 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 1tsd 9- 6)9bbokupkhu a bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tot)d-o 6bhb tu9k1k 9pusal.
(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 objects8.k1x qfahrb 3sbnv0 t s1i34- w6cegb shown in Fig. 8–43 ab 1-bnb63tb814fgh.0ec qrais x3vwksout
(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 oxrs:wc t44g9okveoit:sdp 1*9ygen 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 spinning at tm0 -6jkcu+, yb ee5tt vc9y-wahe 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 y5ac+jv-9,-bttye e kcwmu60is 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 with a radius of 8.50 cm and tvs )(8cgmmh0we 8as* a mass of 0.580 kg. Calculate 0mavhsgm8(st*ew8c )
(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, accelerating35 ewuvln5v+y 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 tan;. wcx:pn + lol2r2c* 1lbpieegentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a f: *lb2.pw1xoe+ric2ln elp;c requency 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 produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor row/1:epz/zw/uzj.8u - jbei vbtating at 10,300 rpm is shut off and is eventually brought uniformly to rest .zw1 j/ 8vzwbpb /ue-:iz/e ujby a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a dx+ .tlh+a0k h+mp mpre9 e+u83.6-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-kxaosflw:a .6*g ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the tricep :f6lo.swx aa*s 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 shown in Fig;y h)vft )tw5r/2sfdn . 8–462yfr/t; s)5 dhfwn )tv.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of twou/6x-l t7.eu baotis3 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 hzc1 6(hh .ix/mvk ur;tammer from rest within four full turns (revolutions) and releases itk tzm xh6/u1 (rhivc;. 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 momfo5esq7-77xyzb)cqc g m4 fe 5j(p pe*ent 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 ps;4ua mxvxhs8l9 d8h -ug ).la 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 9.07e (p:ud9 lcyi cm rolls without slipping down a laneyeiuc:l 7d p9( at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resp+gb mt(pnvr db+:92cnect to the Sun as the sum of two termsgndr:mptvbn +2+ 9 (cb,
(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 1640f p/1l+( ;yz/jawxb cn 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 revolutio/; z(lpwn 1abfyj+xc/n per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest antk4b d+f; ip8) aql(god rolls without s pk8 tl; f4ib+od(a)gqlipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. k)dm,w2gi:r k It starts to fall and its lowerr)kg i w2,dm:k end does not slip. What will be the speed of the upper end of the pole just before it hits the 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 th+3x61 keevtqcg5a:qyot ,(ieg3cl,w in string in a circle of radius 1.10 m atwok5cqgvieg1q l6ce, t 3etyx,( :+3a an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mom e;4y6h8ljpr vcgj+ .mentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm wh rl4 e8mc ;jgj6pyv.+hen 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 w ,l(od,g* f9kqfwm4ms at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his qw(mk g9o* f, f4wmdl,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 herk0vgkq+d).hpk46r stt9zq 0x moment of inertia by a factor of about 3.5 when changing pqv tz 9ht+)x sq 0dkr0gkk4.6from 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 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increaxt/-uuf91uuc m gw) c)se her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofx)-ct fc)/ uumu9 uw1g 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 vertick9rjn yrs (;b(al 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 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 (rr9y; jnks( bthe clay sticks to it?    $rev/s$

  (a) What is the angular movbmsz 11ws8 m*mentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum oxr-ypml m0(d;hw;x c/ f the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an r*roij s,ne) ;identicier;s , *r)nojal disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 0+ :)muvc8x40y shq u(u :vrjtu ulzy;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 t:pt -x6tdjxv ;he center of a rotating merry-go-round platform of: dp -t6;jtxxv radius 3.0 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-roun7l(6p cx4 vqtod is rotating freely with an angular velocity of 0.8v6 o4 (lqtxp7c $rad/s$ 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 dwarforh87 xrrq8iny2hza */(ugz), losing about half its mass in the process, and winding uo8r(ayh*z7qr /x r2 8nu ih)gzp with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds i/fnmy- j+ fxv:a1:kqmn 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 lj vzy tgylr3;2qm+f8d6 r0 2s$ 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 cas7bp* 2jgsj8 c mw,nj+i5 d uamq5o+4hn rotate freely without friction. The momm +c qm sjs8n4,o57u2dhw g *5b+pjaijent of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person h*ncp ajnu:uk2z wxb1mva0 y2q2;-a0stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia ofx b0aaz2upwmn2*c u:2-j1n0 aqvkh ;y 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope oydjr q8 uc+o:(z/ax+,fbnn 9lying on the top edge of the spool. A person grabs the end of the rope and walks a distance+fu czojd/ob:a,y (n9xqr+n8 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 that the same side always faces the Earth. Dete7 : qtl i88 dcbp4qm s2o1sch-6fkcjz:rmine 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 aib84 hskc od-j:q: 12csqct p8lmz67f particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/q) .o0inj 2c k,3clffo$s^2$ 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 unifor, h 8gukfof;z6m cylinder of radius 0.20 m acquires a rotational rate of from , 8fhzkuf;6og rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, ec49ue-yypc641exu o qzi w(y 8ach 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 enerq ey czwxp44i(6 yc89uyu- 1oegy 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 is the angular s+e1hg84) cnyg gm, jcbpeed 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 v ;t l3oyd-7:lq,zdpnas great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergol ;o:tz,v -n37dlpqyd 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 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 storedcw* wvon1w 3,9zedag) in a heavy rotating 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 withe)3a* z1,wwon9vdcwgout 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 illustra o9()raznoud/ey.f gtr46+px tes 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 a horizontal surfac),h sc/ci/tqg+b er b:e 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 le3s tj++dtpn6y/ kn5wlngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then relepslnt y 6 k+5w/tdn+3jased. 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 rwbz86 qljis*p .)ud ,oadius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it restoq)8 l.sbi,zdwuj* p6 s (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2mz+timp n(. b:h/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force(pznh+i :t.mb $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 l989e cvp7fc jjength 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 t79cjfjcev89 phis feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body arjt78b :3dfj9pm kak59 ,lhhvs a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her 3 9:89v j dftk jbhr,7k5mplhabody.   

  You are designing a clutch assembly which consists of two cylie 0f8bfs4j4qcr,qisld s gr l -/1-wu,ndrical plates, of4b8ir,,1 q rss0w dcfgse-/fu -4j qll mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls aldjt2mv+1f 3a gong the looped rough track of Fig. 8–58. What is the minigf2j 3v+d1m tamum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, b+:tf,u0n e ykwut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces i q)xy7 rpo3(p0tiv jk+ts speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wp7q)(pkj3 vo x t0iy+ras 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