A bicycle odometer (which measur7tl4) t8c ez+yd7ti vhes distance traveled) is attached near the wheel hub and is designed for 27-inch wheels.ilh 7y8et4v+)tt c7zd What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poin( w 8do8)teljsgg/bv8t on the rim have radial and/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 acceleratiow)8osbg 8(t gvl 8/djen change?

Could a nonrigid body be described by a single valbds1l.cn bn us9j)zv7.iof / *ue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? lwn hd:dc1b7m74 *plvExplain.

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 to0c9ue 3ibx zda-4jy6m do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help ydx40ye63 - j bm9izcauou to answer this.

A 21-speed bicycle has seven sprockets at the rear w;j3/ kdo w5q9ymn)wdzp r 0m,lheel 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 to pedz;m l0q/)drk5w wnj3py d9,mo al, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fl+ j-w3tqaht6jm h,m w2esh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution o+t tm2hha 6mjjwwq- ,3f mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a l75mq n*qqsng 9ong, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the neoi )l(gf d,6twt torque on a system is zero, is the net force ze( )fo6dlwg,it ro?

Two inclines have the same height but make diffeg+ +u(mnb2q-q (elocdrent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explaqdq-mo 2(+ bgle c+(unin.

Two solid spheres simultaneously start rolling (from rest) dowy3;qdb ly3 z+qlui57dbsluve4 v *91 un an incline. One sphere has twice the radius and twice the mass of the ole33vl b;y lz594quuuydsd i*q1 7b+vther. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. Tkee ;s;b-sxpr b ,qa9.hey start from rest at the topk9; , ;aserpb -ebqs.x of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mo c5x19xl0wxni9e 7yfvqf*.k sst moving or rotating objects eventually slow downkxnxl9 5xi*fwf9y qv7e s1.c0 and stop. Explain.

If there were a great migration of people toward the Earth’cxy/mg apoa8x0l nf6y 3/ 2m0ks equator, how would this affect the lef3/naagc 0/lp0 2 yk8mxm6xyongth of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial r;bdu 8 rl6a7qmotation when she leavr ;a7 dm8b6lques the board?

The moment of inertia of a rotating solid disk about an axis i2hxnru.j:acm1d c; 3through its center of mass i;mudcr j31a:x2. cnih s $\frac{1}{2}WR^2$ (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 rotatingol0.nj po ld40 stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity incrdop nl0l. oj40ease, decrease, or stay the same? Explain.

Two spheres look identic8s krj 9eybpn)m/y, ,urwe5/ qal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which9qe8b/m),ks yru ejwy/ rp n,5.

The angular velocity of a wheel rotating on a horizontal axle points wrin tv*9f5un )est. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points eas u5rv9ntf*)ni t, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a lapt-)d1 2yzhdhe yamywf8kz)4(3 ,u oerge freely rotating turntable. What happens if you walk toward the cente)ywyhya (mf e,d1t-kp24oz zh8de )3u r?

A shortstop may leap into the air to catch a ball and throw it quickwqhh0c i)x zy1 e3/fhs31/jqoly. As he thro zxcq)3iswf yj 0e/1h3/ 1qhohws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angulp2hhh 43 q1:0sn cgvwlar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.l4c2 shhg0:nh3wv pq1

  Express the following angles in radians: pdju4x7 k+8ov(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 coincidence. Calcu.r a4:dv4tjmx x53rbz late, using the information inside the Front Cover, the angular diameters (in radians) of thex.x:rd4br3 zvt a54jm Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earfocmvhl6 5za .8, 9aqz/m st7eth. The beam diverges at an ac8e .hqoavs6 az m ft759/z,lmngle $\theta$ (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 af(h 6j /gi*apmenkf- *ra:xz. rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is th*:jxp- (hie* nr.g6f aakfmz/e 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 qmtr;4q v /oa*9a(3nok1i zax the ball makes 15.0 revolutki4ra(q*oxvznm; 1a3/aot q9 ions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manx*33ym pjnix :te dd9w.p4vb+y revolutions do the wheels make:p n+j 4tv .xxwmyp9i3 e*b3dd?    $rev$

  (a) A grinding wheel 0.35 m ibuhae0w3oq+u1; 5uy .u s/s7ml iyqo1 n diameter rotates at 2500 rpm. Calculate its angularwu q 37+ ioysb 5yu;mauuseh1 /lq01o. 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 iy1rq( ev.. 96taogpmcomplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speedera.p96.tqvmiy1 (go of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of thdvd0 j* s -hl5b(ekr.5sy tz-qe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointq 1 /cf3zlqzpp7zx,z3y4byv1h 0wx;c
(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 centrjrkba( 9) 8c* ,bjxpsnifuge rotate if a particle 7.0 cm from the axis of rota j(bp8j kxscban*9 ,r)tion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about mur 3ox,i;pz ebn;+)sits center from 130 rpm to 28p3) iz+os;r;ebmun ,x0 rpm 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 radiusn oyx86yw7.ox : dm kg:)prec3 $R_1$ 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 a+wo( b2ur (b )-)ls3bjsdz 4fe yvn4qgboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minutgw(eqbujdyvof4 )3s( b+ n) bs-2z r4le 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 frnba0 , .ayunj,om rest to 15,000 rpm in 220 s. Through how many revolutynnj, u ,.0abaions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 12bjgqh w ;5ey2:)lk wbog4,o6f00 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a wh *ng*/pw bp*euirling “human centrifuge,” which tawb *en*gu* pp/kes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 dvh9 pew/gev(mfjd:9f i s/64 rpm in 6.5 s. How far will a point on the edge of thmd spv vhde/4wfe6 /fi:9g(j9e wheel have traveled in this time?    m

  A cooling fan is turnxm,p r*6ir: 3a ippga*v jv12ted off when it is running at 850rev/min It turns 1500 revolutions before itr,v 1ia : 2vr*imxap*36tgj pp comes 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 r x/aoi9u9n:+b36+ap ulpyl hm educes its speed uniformly from 95km/h to 45km/h Thei h pxoyaa+ b63l nulup/9+:9m tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the camdy m 6;t0hwr1r reduces its speed uniformly from 95km/h to 45km/hr 1d6 ;0mhwmyt The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedaljvahqwm cv3sqd+ xk m.piiv06.0o)1 + when climbing a hill. The pedals rotate in a circle63+c +vio)p.sqiw dqvmkax1m0 .0hj v 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 thog,j9,t i ed ycsz.u8:e end of a door 74 cm wide. What is the magnitude of the torque if the for:8jget.,suyi z do9,cce 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 torq:8 zy -xtm+wvvue about the axle of the wheel shown in Fig. 8–39. Assume that a friction tor ytv8x vw+-mz:que of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of massnsz oth6.6w.5*p mq8ugnmd :g 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 position and then released. Calculate the magnitude and direction of the net torque on this sn mqdz:*w6 uo phng6mg8.s. 5tystem.

  The bolts on the cylinder head of an engine jy)tn4rh 7f: .,i;zmjed)vjg require tightening to a torque of 38 fnh.idmt:74;y)gjj),jz r ve$m \cdot N$ 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 awe:ja(iljtqaj1 gz ; 64; ;bhtrbj 1d* 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its ceqzl;atjw t;*jaj b6(;4:edi h1jrb 1gnter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in n.ua4mwezfd79e5u) s diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub cs74due)e5m u fa9wn.z an be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a 0hj/u kk0n .xdh sghv6ouwl0.)eqk ./horizontal circle of rq .0kw60ugkxuo0 kn ls ..hh /e/dj)vhadius 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 cons:t i4, vkkiegb:qjbm58t3j9i tant angular speed (Figqt83, m5:b:kijtvj4i bgkie9 . 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the arrbyp: 3cj91zn say of point objects shown in Fig. 8–43 abo:9bjny1sczp 3ut
(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 cons-3)y0dblx0c nbr o dn2ists of two oxygen 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 cylindrica*139 dyarimn,6amdgtlm4r5 el satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to react1imrd dam,ln 9yrg34a *em65 h 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylind cbwpn1b*: se,eui+z,er with a radius of 8.50 cm and a mass of 0.580 kg. Calbp,1ceb+ z, *isn: euwculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest tolf5c kf)rv5qj ,bq 7f07 xibq* 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 merry-go-rou4y:2x v8yyftu3l f6qxnd and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torqu q:3uxxflt v4yfy8 62ye. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually broug./a,ni h *dfxmht uniformly to rest by a frictional torquxf,ihd m /an.*e 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 accelerate,zkcg*o , 6pois 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 b9www s/ bk0yu(aw-m2wlh; wq ;y the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly f9hw0wlwwum s; /q ;wk(a -b2wyrom 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 long6skta-r;2vj k- mnk( p thin rod, as shown in Fig. 8–4p(n;tk2kvs-mk 6ra-j 6.
(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 a +qiu/i9jdqkr0 5a3bconsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four fulbk m/-b+m1xq9e bd5jhl turns (revolutions) and releases it at a speed of 2e b dxmhm -q+bbj51/9k8 $m/s$ 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 1bkzx.m39ytk qmp 29qa moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a to yv079inl)e1taqy8ej rque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 q+ t0ohgg4j9z7 nk -gxkg and radius 9.0 cm rolls without slipping down a lane at jgt7 9-4q+gzx0gh nko 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of thelk p5+d-y2y :9utzt lw Earth with respect to the Sun as the sum of two termsdkt9z -pyy5+:wtl2lu ,
(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. How much netafq 4oi-/h ze, work is required to accelq fi ,o-/a4ezherate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and r gf81tj2u jx2uolls without slippi j2u82fg u1tjxng 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. Iz:(6w;u fbpquuck / h.mt)cyli6eg 0) t starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Usfwip tuu:6 .gqybc)chek6z/)0l m (u;e conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatim9m (iu bhx+;llu:4du ng on the end of a thin string in a circl :xlu9(md; bil u4um+he of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mocwt4tqgf u +8ahvy)eh ,3om,; mentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cmg,w4t+mha h e8f)3 qvo cy;,ut when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is v oid,9(f/ewv8p.- vm4pymbu rotating at a rate of 1.uemv9 v-fpb y.4vpo(wmdi , /83rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown6vi - cj,i81dej. hh,yey5lrs 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 rotah68vrc1y ylid.5sh,ee -i jj,tions 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 incrg1 fe/0.w7pt nbp*ki pease her spin rotation rate from an initial rate of 1.0 rev everyp fi07pbn1pe w*gk/t. 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its 0 c.ta5ay/kgbcenter 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 fa ac05b /g.ytkrequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spj if 2u 4r7orlqx+uq:;inning 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 o 1lsr0d9;ggn)no6j hm 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 ov i )ma5baym+xp5 0r1kv6ym:of inertia I is dropped onto an identical disk rotating at angular spee51 i):ym +x6pvv 0 5kraybmamod $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2amsm 5)c 0lm)t.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 stand,g ngm)(vwjo9 s at the center of a rotating merry-go-round platform of radiusg,o )n9jv g(wm 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 with an angular velocity of l c:ggy8.xz( (d(uek )w 0j4fuwpx ib40.8(x4 di(bg (: wxu)fuw.p 4z e0gckjy8l $rad/s$ 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 abd8qt;.zl, toa72 hqdrr q*mg 8out half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carriesd88 2a tl.7qrm,rqhqtdgzo*; 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 w ap)7pf4d-k pt3)ttdrinds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass /vkh nhehyo s ,6e*kc7z 17ka9$ 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 r-d6bepb;v9t-0:j p dl)hq 2 ycqe2dm votate freely without friction. The moment of inertia of the perso le -2) v b2qym0d;evchd6pqbdtp-j:9n plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diametefchz +q:ln1 t-cy a+;*6faqhnr merry-go-round turntable that is mounted on frictionless bearings and has a mo z6*ntfca+n-ha fc+y q1q:;l hment 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 ropea3 b47stw. :tdfxrn*( xsw n8tpm gb** rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a diwwtt .:d8p*gsafn3n(4tms x*b * 7rxbstance 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. Detdkanhixw4 )qud, :6n) ermine the ratio of the Moon’s spin angular momentum (about id :h kqxid,6an))4nwuts own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates lir1c*) bzy qa:.i9tg)-i ouhfrom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder offw krr6pv ;ini-yp0.+ radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate -n0ikw6iyv pfr;+r p. the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 k:ohox*l( kx6 o1z,tr zg 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 th x*zoro6k h,zt ol(1x:e 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 speed of dbkp/4ge kr7 f6 2b;nuthe 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,w 2 88.ldxc27q. gkl8h gsjzgg but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it wc.sx7kqg2w ggzj288 h gdll8.ere 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 lypj20. nm+zg c5.7fbeiw3u puow-pollution automobile is for it to use energy stored in a heavy rotating flyw.75micw p+ ynfg.32b0zu epujheel. 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 illustratep+ dzm)x*)az)1u i ddss 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 rollga6nbhjg+(a8a ;l /i:hgh nhm7b.uk 6ing 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 freely (i.e., w q8 sebbhvb/tc+f 9:j+/8n;tzfls*gme ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleratio+c s;f9ls88te+/hj/fgv mzb q n *tb:bn 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 radiusyja/m1 * 436ucoton hm 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 rests (Fig. 8–55). Th mmj63 t ocuyo4/*1anhe step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat ro pi( +li/yq3mlh*dn 8ry 4hsg1ad is making a turn with a radius The forces acting on the cyclist and c hyy1 s3d4l/p8iqln+hg imr*(ycle 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 atg ebx i 2x,d4+j+1edy 0.50-kg rock 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 to achieve1+jde y +xxd,egtb4 i2 this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her ay4;r5at38zeilh)ypemj) x. frms as thin rods, making reasonable estimates for the dimensions. Then calculate the m .z8yafr5pxhie )4;tyej3)lratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of t uzqih*tpr) ) as8)be4wo cylindrical plates, ofir))tu 8z)h*ea 4sbq p 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 along the looped rough tc..3*glsij6jfy p19) nyns iz rack of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of th)s. n1jypyglfzjn6s. i9*i3 c e loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ubbfu ,b5g )gqis:. 9khho(o1zbr65,1irfn t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revo 3jydwc8ne,akac;roj+, i wq3y .t3x :lutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of exj q3a3,wji8 nycew.,r+dot a ; kc3:yach 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