A bicycle odometer (which measures distance traveled) isxr n;nkd1nzm v qm t*12hf0j:4 attached near the wheel hub and is designed for 27-inch wheev jmnq14xn ;trf h0:nzd1k2* mls. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rimwfi o+m(ozo9/ have radial and/or tangential acceleration? If the disk’s aoo o9 wm/f(zi+ngular 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 described by a single value of tnhv 8 lj*zwj00he angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a lardkw06mfp3) f- c.tsua fl0dc)zhow: (ger 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 behind o6 13zxcz2d,4 ap )ntk+iygx wyour head than when your kyw a x4 3ztgo,iz+c1)62pndxarms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle hap7.,t53(9ftkg -qww8ys ceycixj ki5 s seven 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 5t g, ix.wice5qykp js 3t cf97y8-kw(to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run dd6 .95 f)u,, nrrpqayhdri.ofast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the urodr.9,5pad yni,hd6rfq. )basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry .-zbxw nk*ltz+wr +g 8z, a0pda long, narrow beam?

If the net force on a system is zero, is the net torqgk5 +e8p8t;/qnqety r ue also zero? If the net torque on a y+ e k; /tgqpnet58q8rsystem is zero, is the net force zero?

Two inclines have the same height but make diffke/pcm*k6d0ta :/lf xerent angles with the horizontal. The same steel ball is rolled down each incline. On which incline willextp/kald0: / f *kmc6 the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultanxsvqbk8o46x ; eously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which ;x q4oksxvb86reaches 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 wo fdpxuuu2o/ qch9hb3(;.m 6kjyc 7hmd .i)-same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater toujbmou 9 hu .) .;(6dyo73hifp/cx d2km qh-wctal kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conse d45z :pv/sycvp:9zmerved. Yet most moving or rot/ 4zd vcp:9mp5 :svzeyating objects eventually slow down and stop. Explain.

If there were a great migration s qtl .3ahq doaer254z b9yo.+of people toward the Earth’s equator, how would this affect the lengthoyr. l 3+bq4 e52sthoazdq.a9 of the day?

Can the diver of Fig. 8–29 do a somersault wi1jkdt-:u17 vhcj2a a agwpn )5thout having any initial rotation when she -kjahavnt1 uc7:g1wd) 25a pj leaves the board?

The moment of inertia of a ro hxgv 846cz0dhtating solid disk about an axis through its center of mass isxd6 4hhg c08vz $\frac{1}{2}WR^2$ (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-k 5p2yhzeytj+nk0m( 6-4 gqair g mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, de en5264mp0i+ -r(jy qk hztagycrease, or stay the same? Explain.

Two spheres look identical and have :4oq gczgi+b o*o xp1:the same mass. However, one is hollow and the other is solid. De qog1gxzc+ p:b*i:oo4 scribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle hnw 0+3y52r fupnx 83zjwuy89 p j,hkppoints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or 0n3hhj 3 8ywp,y8w5f2uk +zn9 prjxupdecreasing?

Suppose you are standing on the edge of a large freely rotating turnwkvs0 e lvi qgndw29nz/3 *j9,table. What happens if you wzsgnv 0i/knlqvwj*299w3ed, alk toward the center?

A shortstop may leap into the air to catch a ball and throw it xsc9 1gh0m)e bquickly. As he throws the ball, the upper part of his body rotatesx)mh 91c bsge0. 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 conservaby 9j (3l1zzgz oxe;4etion of angular momentum, discuss why a helicopter must have more than one r 1ozjbzx( ge zl9;3y4eotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: muvz 4htbre 9(8kn/(c (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincijy:,,bxba8;;myqt 8 jqcfion 4; )whsdence. Calculate, using the information inside the Front Cover, the angular diameters (in t ; s:qjo,w4bay chnqymjb8x );f;,8i 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 Earth. The beam diverges -z-xalfh;p+ qr,udt iu k 9/cy(aql3li 3ym08at an 3m 80(r3 xap,lil;hizayqcd+y9 qlu u t f-/k-angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate0*rvl zj2 , 6wk/wwxnn at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to restww0/kwv6*2nr, lzjn x in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a lev8h xetux1,j y 4.;l lsqrzbr4c l),sc7el floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter? tjrlhzcs1 784.r4cuqb,y ) ex sll,;x   m

  A bicycle with tires 68 cm in diameti ,b2g niwwa3/er travels 8.0 km. How many revolutions do the wheels make? 3wai,wn2 g/bi    $rev$

  (a) A grinding wheel 0.35 m *ntt :rwk3tg; in diameter rotates at 2500 rpm. Calculate its angular veloci3nkt t*:;grw tty 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 rdtrk4-fz qp2-/ hvaj;evolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from t-hj2dt pv 4qk-fr /;zahe 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 ov0/-t.e.metw/dhkm 9.cymk v rbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 2 1:rsvo(d yhwof 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) must3.7j ezj1xc be a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experienc71xzj.e c3 bjee an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c3syi,7jsuri . enter from 130 rpm to 280 rpm in 4.0 s. Dr3iuj ,sy.7is etermine
(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 radiut+wzj0 g i88 jgot;w.xs $R_1$ 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 spacecraf))wc2 ba9j mnxt put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The sm29na) bxwc)j pacecraft 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 frogy3ahl6+:i upm rest to 15,000 rpm in 220 s. Through how many revoluti:6 p+yh iu3lgaons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 race kt4 ; a./hh:okkj pgf(/h+pm 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 jetqmz j)o fen7/9s in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 oq n9/m7zef)jcomplete 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 rpm to 360 rpm in 6ak.d 6qmijfrw2bs7 t2v-;v6+-qz d ez.5 s. Ho-v;ma fzvq 2 2si7d-t 66r .kzj+wqebdw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns b )-ruhw5w)+(pwlmsyl)oq 8l1500 revolutions before it coyl 5 )wh ol)-+ur8)wlm(qpbswmes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car redu-2w/7w p qm z nauvb8tc2vum o0+6re8oces its speed uniformly from 95km/h to 45km/h The tires have a diametea u+2r o6n0pz- mmv88qoc7u/wtebwv 2r 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 thesgvay:9k5 *g6 bh o*on8dl- tx car reduces its speed uniformly from 95km/h to 45km/h The tires have a d:yl**h an sd6gbvxog-8 ok 5t9iameter 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 bike puts all her weight on each p0hm- *z9ob kjcedal when climbing a hill. The pedals rotate in a circle of radiuzcohj *b k-0m9s 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 w.gaj2y8;c hzvvk.5s. What is the magnitude of the torque izh y.s;cwv2j vg.58a kf 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 the6y5 ,n:z7uzdv m hrg2s wheel shown in Fig. 8–39. Assume that a friction torqu vm z g:d6syrnz25,h7ue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attac4k/fbp,m gm l;hed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the ne ;lpb4/kgmm,f t torque on this system.

  The bolts on the cylinder head of an engine requirxo98 , 6blp.2jzicmg0l up4p re tightening to a torque of 38o2 86c ,0irjpmx4b g.zuplpl9 $m \cdot N$ 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 whenshsv q. ol:k 1.xf 33pfdqvj4b+8:y at the axis of rotation is tfv:3:ldbh1 a3 j4+s8t xqqypof.v ks. hrough its center.    $kg \cdot m^2$

  Calculate the moment pwr e4f9+ fog lx:g ky)e-75c,dc-vepof inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire havglwoc975x4vy f:)c+,rp gep-kfd e e-e a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotats)g4h .yqphv 2ed in a horizontal.ypsh qhg )4v2 circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant ub )zlky/(v 68dsswc3angular speed (Fig. 8–42). The friction force between zbk/ scwvu ys)86(l 3dher hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the ar pp:lp)dp, f.pray of point objects shown in Fig. 8–43 about:dp)lp,p fp.p
(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 whpw+y .eokiyisa lx,vewl)yc2h 3 +3 18ose 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 aqktu p:5sqwd (xbne+tr 8 9+4et the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of q+r8nd: xt p+se9eq(4 5t wkubeach 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 cylindkjl t dr 5qxj+da50-2der with a radius of 8.50 cm and a mass of 0.580 la k52dqdj+ j-xd5t0r 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 swixf;oe)m 8 7tayr1uq *qngs 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-driven me(oicl44 m)qmtamy2 b4s)3k jurry-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 a3mi 44s))(jbqlcyum42 mo tkradius 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 rotatin9t l (mi;pms5x33yl9 .ijdx;uow6awpg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2y 9wo;mla3 jspp5i(u.dxi6xw m9;3 l t $m \cdot N$ 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 3.6-kg ball at ojmudn3 +9/nq 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 forearm, whicx/lq:rz0 xw, qe4qs;mhg z:.ih rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from r; ,qzsi :xxzr w0lg: hm4q./qeest 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. o(emdvvt -k*nab.gas7-ow1 a long thin rod, as shown in Fig. 8–46 g e.wsbvmna-.ov- o7*1a(d tk.
(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 two masses,l,e v f.iatk41 $m_1$ 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 accpx+fh (y1fuft3/) e znelerates the hammer from rest within four full turns (revolutions)u/ f+( tfnezh1x)pfy3 and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia o.sk gvb,( 2d0/nxxmrgf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine devel1l88t+ b7vc5r7l q ukd9 pbrzpw;c)fkops 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 masgr h/m uk*me*+s 7.3 kg and radius 9.0 cm rolls without slipping down a lane mhr*u *g/m+ek at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thef2zaz0kvv p k :a,8,,agqxe:l sum of twvlq8f: ,:aa a 0pk2xgzk,zev ,o 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 and a radius of 7.50 m uwr: 5sm4-cslcpw8 p/. How much net work is required to accelerate it from rest to a rotation ratecsl4 /ws pr:8 mpcu5-w 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 starts gksa2 v.it( 0bkd6pop)*g 5dffrom rest and rolls without sdp(.o )vsikftg 2*5 b 0a6dpkglipping 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. It start1 cblets( 7kh-s to fall and its lower end does not slip. What will be the speed 1l7tk b-hecs(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 856xchpb l uu.end of a thin string in a circle of radius 1.10 8l5cb p6u u.hxm at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular m; o:5udr5 q qv*j1gdkdomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatiqqv dk5orddj5 u:*1;g ng 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 6ds4n jiwmx zi(t:8 6qat his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a hx6nt:siz6(m 4 dqi8 jworizontal 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. 8–7e geu, 5tdsfx;+sxn dg4ex (329) 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 2xn+;st x,ges3xdd4e e u5g 7(f.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 e9mp+zevru-(g (iwcd ,7) ihg/ 8chkespin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate o+im hge i-vu) edk/(gh re(9 wp8zc,c7f 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a f gf(c0d y0o9cs3,vdkn requency 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, aov9 n(ds 3cf,gc0dky0 pproximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnin2k p+t(xtga(o 9gwo:ag 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 of the Eart vomf:ls69qnakkf-,,r 7ws5 mh
(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 mome:;7 p7vm 84cbzbhj ceent of inertia I is dropped onto an identical disk rota :cvm 4b8c7zh 7bje;peting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2wfiuj o.y 6,)b5 9mizc.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 /4zvua7p)(x fgm. jbrthe center of a rotating merry-go-round platform ofr )jv(a.g /mufb7xpz4 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-round is rotating freely wit zuj urzs8;nv8x8h) o1h an angular velocity of 0.8 8; uun8oxr1j8zz )vhs $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing a09 e:b ndj :fi9jfo6;wkb-uumbout half its mass in the process, and winding up with a radius 1.0% of its existi; ewf-nuj96 b 9jid:uk ob0m:fng 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 in excess of 1227rpkv *e b (zc-lg0t4 lmy5gk0 $km/h$ 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 nk0uc ;iogza:4 yxg;5$ 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 fh,ofv9c 6i*5w6 f (wy6b9+qe,jqxb mjq kj pj(reely without friction. The moment of inertia of the person plus t6 jje9b c(i6bmwf5f +yjjq qw ,o9h pxqv6*(k,he platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter me w l god89on9q*3;lbhkrry-go-round turntable that is mounted on frictionless bdn9q*lwo3;hl b 8gko9earings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on n y)(h(4alt4 lqw/hsqthe 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 length of rope unwinds from q) wsq 4(l(4/thalhnythe spool? How far does the spool’s center of mass move?

  The Moon orbits the Earfh(((syf+iv a m/ /ejlth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Eart/vy j(/ml+sfi(ha fe(h.)    $\times10^{ -6}$

  A cyclist accelerates from rest atcuw jquk9g*u *sgg nkfoev-fe8 n22q(9y. n) 8 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 cylinder of radius 0.0y( l: 8p4 (zkxyaktjp*g8arv20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Cy 0(kl ktraz*p8jg y8:p(ax4 valculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dis1nm(i :yqz8z wks, 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 r 1y(:zniz8mqw eaches 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 jpx/ vnlb7fd6lr yka a5(2:+nangular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, /0ntot-x)cb; i6v)qbkrk; rnwere rotating at a speed of 1.0 revolution every 1x rq;0b/iobnv6kt)-nckr; )t2 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 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-pollutvgtd, 9 ggd6;k vjydza4, tt7k6km 20wion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350aj z7 ;vg6kt0kwdyd4k,d 6 g9,tgvmt2 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 angl1q ( k14ovod $H_2O$ 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 ho;a; jbalb iqlj/ 7(u-3pxul:jrizontal 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 freelypwc: ku5 k ;xw*1r5fka (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is heldp*xaf:;uwkw5kc kr1 5 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 dfk8 50hh4mu lis 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 rests (Fig. 8–55). The step has height h, h kfd5h8l0 4umwhere h

  A bicyclist traveling with speed (z2anppv4*: yap ln,5p 9p duwv=4.2m/s on a flat road is making a turn with a radius T 5dpy ap*pn,pa zu 4vl9(2:wpnhe forces acting on the 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 rock into a sling of nzzple6 a7,2ulg t/ib4ixumd05 z2 q,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 to achieve this feat, atb,z md/q,i2elzpn x5uaguz6427 il0nd where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as th7 fv2 tepnl :zcc9yv(es:rz 9cp/7ul3m lj6.ein rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a sp9t sl l2:pzlvcn(e fecz .ej6:7 uv3c9my/r7pinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch asq jqu/yrfc:9hp/7f.1oa (f bdsembly which consists of two cylindrical plates, of maa:rq /d1ujyqb9/.h7 fc p( fofss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tka9g5 1ds/l0o fk.ggf rack of Fig. 8–58. What is th 9gg/ dks5.f1 kfaolg0e minimum 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, but do not assumee;3im p(r*x sxdw8o9 l $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speedk1vhmu+9gv4 s 7x8 bndz:4slb uniformly from 90km/h to 60km/h The tires haves8:slvnb d7z 49+bv gxh4 ukm1 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