A bicycle odometer (which measures distance travel5idw (vmj9,d10 oiuo med) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use d1d(omj vioi9 uw,50 mit on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pv tzwe*5+(gwroint 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 li e*tz+vg( wrw5near acceleration change?

Could a nonrigid body be descric/uj. gjvh32l0). tdwhfi 6 brbed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forceox+wuop7 tylal1 g(;1? 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 yoddua*7mu6+frs u1f-our head than when o1du-druf7u 6 +fams* your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockjpyhan20 w3s:(fhdf8 ets 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 to pedal, a small front8:pa(jy3nhf d0whf s2 sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lo..u6)qhm qcg4r3 vu kjt;ho.kb -hw8 kwer legs with flesh and muscukm.vtr4k-h8b. qqkj ho);chu 36w g. le concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam7n*f f-dry i0;sck t3y?

If the net force on a system is zero, is the net torque alsohn: w0+k avca,feu5 js:,s(ts-2 manr06qdeb zero? If the net torque on a system is zero, is the net kh 0::0, bnva5ujte6a f m-wncssa+r(2, edsqforce zero?

Two inclines have the same hei/pv* fl wo9/v r;loj;h/rohm*ght but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incli;9*j*/vohl r/ohmrv; pl /fo wne will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollinnpl(o zkk,s*(as p1)p 0n*gma g (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which hppap*0ozags( k s,k(1m*)n nl as 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 massh/er7qg)ya n- . They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater) nhya-r/7geq 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 are8to.y7 : k0a4(g 8ztf1umly1iuy r6 2iyrpj zf conserved. Yet most moving or rotating g 8yrfuu(i4y1y ja1k ry0l.i m8:ot7 tp62f zzobjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Ea2xvma vy- rsvh ba,lp14;c72 orth’s equator, how would this affect the length of thmv-c,b7vsx22p r41v; oa alyhe day?

Can the diver of Fig. 8a )roq5m1y,frcku e,)–29 do a somersault without having any initial rotation when she leaves the boaem fya)1kuo)crr5 q ,,rd?

The moment of inertia of a rotating solid disk about an axis through itvo2 r ,zooz -54webd;fs center zoz-w,oo5 v;2bdf er4 of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a -a bmq4*+ufg s;f t 6x+6gwxmnrotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vel*x+ ff wm-+; 4 unqstg6bgax6mocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mas0:tv* hk -aq6gzh dna4s. However, one is hollow and the other is solid. Describe an experi- kh g0*aqnhtv: d6az4ment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointscw 5mqw043.lw9 r sobx 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 poio xs 9q4w wb3lr.05wmcnt at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing ortr4:sd4 xoj 7aj )juvi,i2 m6n the edge of a large freely rotating turntable. What happens if you walk toward the cenr j rmo 2ij4)av ix4:udt7,6jster?

A shortstop may leap into the air to catch a ball and throw inm, aih62m+s mp ltq6c 5,vk;nt quickly. As he throws the ball, the upper part of his body rotates. If you look quickly5,nmqmsv+ac6 p ni,k;l6mh2t 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 moment k4 (ef ejty.jl-e 3y:y;pvxu2um, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propellex.3-ejey(yule : ;pjyv2kt4 f r can operate to keep the helicopter stable.

  Express the following angofl2 o*(i zb 17x, pad3kwpl(f55q mnsles in radians: (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 amgl0/hm1 xn y5xazing coincidence. Calculate, using the informatio/yn1x5x m gh0ln inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon8ka4fd y- dhnar0u;h -+5xbjl, 380,000 km from Earth. The beam diverges at an angle xjkl8+a05bfh-h-d d4r;yan u $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender r qo7)bxb)hm(uh kitp152r-y totate at a rate of 6500 rpm. When the motor is turned off-i( hbk1xmp tor5hy b27u t))q during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball mnk(zv).d n(rl akes 15.0 revolutnd( (kvnr.)zl ions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travuf xhp lkab4; s1p +w3yqe43c0els 8.0 km. How many revolutions do the wheels make? 3xya1;4 q+ uefh40 sbpk wlcp3   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 25 )krf z p4tgf 5kf9u20pdzl6o)00 rpm. Calculate its angulf5 ko2r zp)f0 4f)6tzkdupg9lar velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution/wzz6 x9i lsd/ in 4.0 s (Fig. 8–38). (a)69 z dslx//wiz What is the linear speed 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 the Earth (a) in its orbit around the j 8ni dsy ;oh3 zrk)fih6kd-8 hgy29l6Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sx907ity eixhxn4yyw*.pzz ) 2peed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 csy xmvq0u /xipa2lx.481;uj dm from the axis of rotation is to experieuu1ds y pq402m/j.8xaxx l;vince an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly8/fei :z7olvg about its center from 130 rpm to 280 rpm in 4.eog ilz:fv/8 70 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 ct8x ,/,firq5, )qf rtnuked nx6;gbi 4ovf(7$R_1$ 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 spacecraf5xsvz vedv6, -v6*jhst 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 spacecraft can be thought of as a cyzj vdvesx65,s-6 vh* vlinder 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 15,00wg51ohp o q/a3 m2ebv20 rpm in 220 s. Through how ma/mw ahe513bqo g v22pony revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcgg* 68f5e )au.- rbihwieu)nculate
(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 highsp8 dx65h;d;.wgmjpc zpeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn thmwdh gc85z;j .;6x pdprough 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 rpm 1lz*y.k8isj:i n 8fii in 6.5 s. How far wi1sik *znly.if8j:i8ill 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/mj: ruswq-)gx0 in It turns 1500 revolutions before it comes turq x:0w)s j-go 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 r 92kd)t gimcil5p ;5pdevolutions as the car reduces its speed uniformly from 9mpik2 ) ;ddp59cglti5 5km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the c(alx.bag.vp3n(nfji s f4 )ygp*lr6 ;ar reduces its speed uniformly from 95km/h to 45km/h The tiresn6 rfav(pllyfxisg(pn g3).; a4 jb.* 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)zgmh4p)))4 du qdbfi puts all her weight on each pedal when climbing a hill. The pedals rotate h4iu bqf ))dm )dg4z)pin a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm widxx41wcoser g 7x;dbo2o xd:1 )e. What is the magnitude of the torque if the 1xocx4;:oo2 se)gdw 1 d7rxbxforce 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 the6 jh69ytu rl5)ip:qp03lee lg axle of the wheel shown in Fig. 8–39. Assume that a friction torque of qhlrt pg3e9)5lp6y6el0j :i u0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masslessfk2:8ykqt*m5 vvho* e 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 ovket5*hoky*2 m8 v f:qf the net torque on this system.

  The bolts on the cylinder head of an engine requ,ngrh2hj;j(qk6i s6 u ire tightening to a torque of 38 nh srkjg,6 j(h62 iqu;$m \cdot N$ 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 +y fs+fe,np (jbbm9 i :c7; vznnt8w2vm when the axis of rotation is through its cen:,zt7mn+ n ej;(wfy8cnbf9bv2 s v+piter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. vbnw+4ius r-q8zmp u2h*spi9-x x q2+-nmkv2The rim and tire have a combined mass of 1.zi9 sq8 sqmwvp+vk -hx-bun+m2r4n*2i- x2p u25 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 ro0(a -gr0sjuo kd is rotated in a horizontal circle of radius 1.2au0g sokj- r0( 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 pot48a 81,wsygoprc4cs hter’s wheel rotating at constant angular speed (Fig. 8–oc c,rgs4w818sp hy4a42). 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 array of point objects shown in Fig. 8–4ksr8jrc0yagxa795s 9a 9sjz ut. gp;03 gkjj89 s g9uc ;sypat0rz.s7 axr950aabout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose 1o-qs, u+hjt s ay;(latotal 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 q cv/f1 uy,glhh.o7b 9 wage86the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radiuhugfl 8g/ 7,woh 69cbeq1 .vays of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 04d nq0q-7qbzm.580 kg. Cq0mqb7nq- z 4dalculate
(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 to 3 5syzngnzs z36 q8ie-5$rev/s$ 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-driue /p *arhqs*h c+7u3tven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform qu ahc + r7phet*u/*3sdisk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is sh59cnii dpgv5 l*4uig.3tw5t gqpn ;.out off and is eventually brought uniformly to rest by a frictiona ip4ggq unid 95vlto3 5g.*wn pc5t;i.l 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 3.6-kg ball atl 7bjwsxmd grjl8 q 70;7y*3to7k7ofd 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 tgd: +ejg(my.yvi)3uy he action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–4v:i gdyg) mujye(y.3+ 5. 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. 8– c 2kg7,smruohm s7:5bjz2/mm46.m br/m77mm:, 2us25sgzh kcoj
(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 maepm;ij5ubn6 i45z a:isses, $m_1$ 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 full z k csfqe -3v)v1-0 ;ey5jfnpnturns (revolutions) and releases it at a speed o;qn5ee-vn-1 v03pk )czj fs fyf 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 bs6sl7nf.f 3xo tk pr/zx5 v,;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 torque of 2 156)7v xop fk.qjvet)boq ui7w2u z ezxe622u80 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down a sj n5)1ifodra9 b,ti2lane aiob5 1f2,tdns9i rja) t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun am:crjk2 tfq6msg/*3c0f3 g prh *wq4 os the sum of two ter wm3o04r*3gp fcq2cg:/m6s hrtq*fjk ms,
(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 o 1m3awr-ttd9 mass of 1640 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 revolution pe19 mat two-r3dr 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fromv7 7o;7yr lz342izrjqat:ysl9na l4 b rest and rolls without slipping downz7ay:4 7vl93 rz2nlqy l4tb;osa7j ir 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 vertic5y7 l:qz0*bvl i3.hfvvv 6v hzally on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just bey6iz*h3 vvv0:fz57 llv.vqhb fore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rot (ka// e6xax2/ km 2z;rqr5oqkm7iqbyating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.472a2( y ;rrz/ai 5 kqbox /qkmmqexk/6 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular rcq g1st5 ) a4z4ek/4p7jnxjkmomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatinejcn4rpj5a/z447k1gxt sk )qg 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 rotatingz:,f.)p 6dl2hpmv3mlejin e+ at a rate of 1.3rev/s If he raises his arms to a horizontal posiei,2+mlf)j npz:d.mh ve6 l3ption, 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 .-d.s,f d4u us:vat lon+y8msin Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 sdvmo s t+ 8f.4nusdu,asl. :y- when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initialy*i8 0,v7jxqyl ;rwl xrf/eq ( rate of 1.0 rev every 2.0 s to a fin fx;/yevjlx,wyqi 0(l87r* rq al 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 center 6kne tklcvv;:fb nvgz y)o0.9o xz +(1at 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 the vtx0nk1)l bo (6.n9k z+:zyfevgovc;clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning aat/vy)xw+ z8 4;w tgigt 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 Eartpc imgaao/f80fya/ . k.tu fe+fj;i5 3h
(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 dropp, nd44dadku x lyw pf 7evh-+yw)+x :8i7ahp8ced onto an identical disk rotating at ang4fi xp+8,hwk)d lpavd4 cuydn7e x+ 7:w8ah-yular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a kvjae; iko-e155xu u: (oe0jde xs/3ut 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating me-4fnl+ o- 3pd mpy/7eiycuma 7rry-go-round platform of rad/m7 y-c4nuodf 3+al -yie7pm pius 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 frefj;p.nol0 an4/a cs c1ely with an angular velocity of 0.8 apco n4l/1afsc j0.n;$rad/s$ 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:p;re(niuq/0tl t oqla g6n+4 white dwarf, losing about half its mass in the process, an;it4n/rl:lqaueog n (q p6t0+d winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest 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 windak+hqy y is0lr)8ci;wi4)m a ep kew:tol;-;(s 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 rhf -w n(tvn2 7c411pne4 pz5bgo5buh$ 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 ab:t/x e ro(jq5o,wqi ,t rest, that can rotate freely without friction. The moment of inertia of the person plus the platf:jot,(b5q ioex qwr/,orm 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 edhs ae+ng7m6* mge of a 6.5-m diameter merry-go-round turntable that is moue6 am* 7ghms+nnted on frictionless bearings 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 the ground with the end of th 0 p1t8oht6kffxuyattp 7b r1 16ui c4t,(0oupe 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, Fito,p6uh7 to6t8u1ty1a4k fupbp1 t0cr (0ixfg. 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 saztfyio9 r i54ps+hvf+t8 /4clme side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentumop5 /fi+yr9t4z v8flsc i+4th . (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratesit d062)0 syq j*kgwdu from 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 cyle2dl 5dyr-cl, inder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Crlle dy-d52,c alculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid 9 ;foodgv:n6 ijh 47pmcylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it rv9:d hmpjfogo7 6;ni4eaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the r jac92ssujj .9 8,tt7ighuv*i ear 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 masof ;y1t ei;)yu*5bo6*og ky ols 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no at i6oue kolyf *1yb;;)oy5go* ngular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile iv6.p+b2oj rvkg) we2s fa.m2is 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 cylind.afbj2mr ie2 sk2)gwovp +6.vrical 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 illustrat9jo 3r p5len6a7,wunwes 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 surface at sp) r4u9, rtdj9v+lusjbeed 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., we ignoreh1gfb/io05nti( f mf/ i,hj8i 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 acceleration of the tip of the rod. Assume that the force of gravity acts at t0/j g8/ bifhh,5fii tfo1n(imhe center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically r+5xn(hvy w wbvs *;/y-ehgh fqx93d 4on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step agaxqe; +h rdb(f hw4xy9/vsn3v-5g h*wyinst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wif/pw :j o7h-2mhgw5z:1jm m2 kjc0v7zduf nn *th a radius The forces acting on the cyclist and cyd7ou kmcj np gh2 mjw vf5z7w*nz2f:-h:/j1m0cle 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 roc r *cril j.eisl,0y6x7rp ,jd1k into a sling of length 1.5 m and begins whirling the rock in a nearly horizontael i0 sirl6yp1d*x,c.j ,7rjrl circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylind u aoc qh7gc2d79ba9-8zw2f.bq rmka4er 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 ti2-k azq acud cm2ghbb 9rf.74qwo98a7ghtly against her body.   

  You are designing a clutch assembly which consists of tw0o)rzd j 7lmv:o cylindrical plates, of mavd)r:0mz l7oj ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alo* ;nk fd5 u2ztkevnv7:ng the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach t vzneu:dkfn;t 27*v5khe 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 assume2i/y- t) olg3a0o *r hbyrrw.q $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spe ut y(bqf),xxq+c26 de3jwg:ded uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angx e:dxd b 2) gt3(6qc,ufq+jywular 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