A bicycle odometer (which measures dg, mr 1vr7chwe.33f . r ii-) qs(ardmtm5aq5sistance traveled) is attached near the wheel hub and is designed for 27-incr.dqm 5.)h7t(w fssearr a3vqm igr3 ,c-5im 1h wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant+ql,x:nsr ikmadibk (da) up,r .0f (9 angular velocity. Does a point on the rim have radial and/or tangentsq rux.9dmakkir da( p+:nfl,0, )i (bial acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be des z ,w(3k-pr+.iv4bem.ibgissdpnm* 3 cribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever7.r;0hgn sj wd exert a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up wit3 a4 jzim i8,1fpkern-h your hands behind your head than when your arms are stretched out in front of you? A diagram may help you4i m -k1nrz8eip3j,a f to answer this.

A 21-speed bicycle has seven sprockets at the rear wheekxh5jxw/j0r + l and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocketrk jx /j5x0+hw or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with3bzih0r(u (vg0jgw. j flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advan0ig bhr wgvzju0 3(.j(tageous.

Why do tightrope walkerskz dp7bgq5w :b81c77 byk4pin (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the netd3di:e x(6 lnu torque on a system is zero, is dl:di3(6 xenuthe net force zero?

Two inclines have the same height but make different angles with the horizontalj nw;4 fuyi(5;vkbe m4. The same steel ball is rolybu5 k4i;j m4ne(v ;fwled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inc g/p 12(lvqdzf8ig ov:2: xllzline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kl /8 pliz(z:o:v x1lqfgd 22vginetic energy at the bottom?

A sphere and a cylinder have the 8s56f zc rovi/d7p)rdsame radius and the same mass. They start from rest at c 5/fi6v8rdr7d)zs pothe top 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 j q-x rh*gt/jv5oa4y 9km(+b gmomentum are conserved. Yet most moving or rotating objectk9tr b-gg*a(q/5j+ov x4hjy ms eventually slow down and stop. Explain.

If there were a great migration of people towz0wk 7 vi(+nenpgiu8 +ard the Earth’s equator, how would this affect thek7n + 80+v(gwnieizpu length of the day?

Can the diver of Fig. 8–29 do)(/4bdkd5oug)abnl 83 2 q ap zbybfo+ a somersault without having any initial rotation when she leaves the boardq bd 5l23)o p4(a)bbg/un8yfbd o+ zka?

The moment of inertia o9wzw5n/nl 2nv8yo6f y kaw:rm;r f.z: f a rotating solid disk about an axis through its center of mass y;nf .z na8n2/ v :wmkr6wfo wyl95:zris $\frac{1}{2}WR^2$ (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 roprsq(hl g.a0*r x h/m+tating stool holding a 2-kg mass in each outstretchedashrqx /+g *(mhp 0l.r hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical apyb3i*te+ ++bboes4 ind have the same mass. However, one is hollow and the other is solid. De so+4i eibp+ t3bb*y+escribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west.q(*odl0 yg 8 zam)i; w,jmxj)cauj5v. 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 decreasinwm j)u;vo mjc5a*0zq,(j xdigl)ay .8g?

Suppose you are standing on the edge of a large freely rotating tu-2.clkdd.44 beduf,cqo2b 98pu yokrrntable. What happens if you walk towardod,2p b4-u.8kke9oy cl dqcdbfu2r 4. the center?

A shortstop may leap into97yb+3xv,6w5 qio5udom *xr h.yjkqy the air to catch a ball and throw it quickly. As he throws 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–uj7hvwikqqo 36 5x.y xy+m5rd b9, o*y36). Explain.

On the basis of the law of conservation of angular momentum, discuss why au.cl0o ,drm ,rj mk15m helicopter must have more than o,mr o0ku1m5dc ,ml.rj ne rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglsd2kwx r28t,h es 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 amazing coincidence. Calculate, us-p )5il q d(xoict2a1iing the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seeotp25iicdq() a i-x1l n on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 kmh0;xz hsj 9(yz from Earth. The beam diverges a0h;sjz(x zh y9t an 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 blendesslu 3iy45kr dwi.09rh 1 .-utfviih7r rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? i9iv s.s1hf -ylh 3.ui0rtw4u ikr5d7    $rad/s^2$

  A child rolls a ball on a x+/c nl fhb5d,1,f vnylevel floor 3.5 m to another child. If the ball makes 15.0 revhfb+ y/,15cx,v f dnnlolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions53 4uocjxaift902 1tz(mspca do the wheels m3c i faxtaztp5ouj2 0smc(194 ake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rc/x d 3bnx9.z .zmhkf+c,rf;whjs 3vxt.d)g ,pm. Calculate its angular velocity x.+cf kxbvxr,f)hzj9 zh.3tm. /ng dw3,;cdsin $rad/s$ $\omega$ =    $rad/sec$
(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 comjghw *je5i,1 0 4mubhhplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centeb0m4 h h1h,uje5 jwi*gr?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angula v6+ ht8dq3-,b fhmaxqr velocity of the 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 o p)zr4.umeoa) b6bt 5f 08lbl/zvckp6 f 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 cm from the axis x znh 0e7.bor*ikl/)sof rotation is to experience an acceleration*0 b7rslz/)eh x.n oki of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centwu0( +h b2ar iwnm )y;wtj,8y-o tyg7oer from 130 rpm to 280 rpm in 4.0 s. Determ(7itnyh0 w+- taybo,gjm28wy;) r wuoine
(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 6, fyvati1g 0 yaxp+)c$R_1$ 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 Mo gip0+j5 yqnw,oq oo*qu t1;:lon, astronauts aboard 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 minute during a 12-min time interval. The spacecraft can be thought of as a cylinder wi ,io1on0j q :ol5+;ugp*twqyq th 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 3,qkt;p7: :s gairvv erest to 15,000 rpm in 220 s. Through how many revolutions3ve ivk,;q agt:p 7:rs did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 15an )dz wy4f3efr7 lp;200 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 stres d*r6ha70nc rsses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tc6*0radsnrh 7urn 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 fk ti c8bns.. 6t/h8syto 360 rpm in 6.5 s. How far will a point on the edge of thets.68 f8ibhnys.ck t/ wheel have traveled in this time?    m

  A cooling fan is turned off whevq.:*a b s,w6r xcfq)ln it is running at 850rev/min It turns 1500 revolutbq)la,:xf*6 r sqcv w.ions before it 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 reduces its speed uniformlykt1+ 74.t hirptof2bc from 95km/h to 45km/h The tires have a diameter of 0.80 m.pto7fk1i.r t+2 tbhc4
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its sfef1tx -n;rt)peed uniformly from 95km/h to 45km/h The tiresf;ex)f 1ttn- r 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 eahdo 5t yz-0xrg)*s2s ach pedal when climbing a hill. The pedals rotate in a5 yhx-dts 2rgo0 *)zsa 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 /fo f -o1.zsfrr9/*se,ik l zxon the end of a door 74 cm wide. What is the magnitude of the torque if the forcf.//-zfr1lexk rosf sz,*oi 9e is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39 o84 2ejifayj5ufjld2g7r- d /. Assume that a fricti ro7j2djldguijf5e4a - 2f y/8on torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mz 2 .1bm*csg iet9noh7assless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal 29.c*zhtgne s 17iobm position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an e)vweb m 8z,k9fu pk4fcxpsj2y6e 1u /1ngine require tightening to a torque of 38 w4ysz) x 8,fkj 26me1ve9fp/up1kb cu $m \cdot N$ 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 of6 ozty n6gik03 radius 0.648 m when the axis of rotation is thro6n60i3zotkg yugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyc3*n: c(m.8qq(cf yig 1mknbi+q0oi uple wheel 66.7 cm in diameter. The rim and tiriiq1f(0kpcumncoy3min+g ( *:.b 8q qe have 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 rov5l p nnw)f*qpv;s1)oyp 4l e6tated in a horizontal circle of radius 1.2 m1p; f l* yo64)svvp)p5lwqnne . 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 jaiqfeq a/bnha3 )v)9 0f1g+y angular speed (Fig. 8–42). Ta qnjg90))ev/ +b3qih faa f1yhe 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 sh 9cn( 1dwvoyx 8t)i: )ik;sfgnown in Fig. 8–43ciy twvfns(x )kn9gi :do1)8 ; about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total68)q6 qmqt ga x -dmkgq-.;rbr mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct ratwcumsc kj d-a c,1to //(fb5c 1mfw./te, 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 satemkf(c1b /uw to1 /af 5t cc/,s.jcm-wdllite 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 j,kk 3 ylwm 5(dj2et(zof 0.580 kg. Calculate ywd3( kze,kt2( jj5l m
(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, aqymcgo nh* 8;: g;bwb8ccelerating 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-d+67g txpbigc5rpo xiw.t- /p6riven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other onr+t 75ptox cb/pg-6 gi.6 wixp 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 rotaox(11 4z zxyn4 8fumoce(qe(nting at 10,300 rpm is shut off and is eventually brought un 4 m1nexuzexozqo( (fc41ny 8(iformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–fqfw/7:dz m:i yifu eg;+6so745 accelerates 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 thrcrt 31kw -kg.hown solely by 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 frg 3wr-tk.h1 ckom 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 w29z0qz tknj6long thin rod, as shown in Fig. 8–46 zq2nwj609zt k.
(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 consis7aqek 1:-amgdqc qi :2ts 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 accelerates2nywreh+n 1txu6 f e(r.nh8h+ the hammer from rest within four full turns (revolutions) and relehf+whn e.(6u1n2+r8h ny exrt ases 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 att0g8s f2c qz4+f l8nr 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 t0klij-1c;) aohwly; develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass bo8g,mp.d8 4 ub:fkki7.3 kg and radius 9.0 cm rolls without slipping down a lao dikp b8b.f4g,ku: 8mne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of t5s5 j2c(. yxh.zxzjrjsl.y a9wo termsrjs..cy z9 y2jx5ah5 s(. lzjx,
(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 radv g q63qs:aas*5m,)xj-sxa glr.qw z(ius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate6v,a sxm (ss* zgl:.j qarw)gqx53-aq 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 gsp42*egv/9gmrs.rh rolls without slipping down a 29e /v4hm* pgsrrgs g.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 ic 9ny,, wsxm9fs balanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground?xwmycf9 ,9s,n [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on tk;14 na i2 lqpu.cvvb;h)ft9v he end of a thin string in a circle oui vvvqa;)4h;b9t2 np .k1cf lf radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg u8o rykhu*9zhk q-qq f(5fx)m9 niform cylindrical grinding wheel of radik-9hy9rkq(oq* x5q 8 fm)zuhfus 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at9: giecc b..ox a rate of 1.3rev/s Ifc gei9 .c:.oxb 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 shown in Fig. 8–29) can reduce her moment of i9 hi 2i-h3hf5v/rwon vnertia by a factor of a2r -oviw f9hi3 n5vh/hbout 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can inc,)2vc)rqjsyx0ns7 -pwel+gk rease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rapqs7x-+j)e yl )n2cskvgw , 0rte 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 arnw6)ytz /o*p/ c-r7x m) cknrmound a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and 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, o7royzkncn6 *m-x) r/m /tcw)pnto 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 mome b7+tie ds fm/u.-*oqn5 e0cwo/ 6dkirntum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the E agaz;-nwb35 9b.fjis g) h(vdarth
(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 mo0l1bj2er n dbbs04o3vment of inertia I is dropped onto an identical disbve3bj0s l1240obdn rk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.r 1yoy azhq37ncm3e xs3p p1l,/3u4nd 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 rotatingwb3e:wy7sq(l merry-go-round platform of radsyl:eq3 7 wb(wius 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 iswol:uk*w k (8a rotating freely with an angular velocity of 0.8 kwwu*k: oal(8 $rad/s$ 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 acl)p/y5kwz 5d *oji3ubout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what wik/uw5c y5j)p l3*odz ould 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 120-3jn re;p:a+s 1favu 82lv j(w4f- tp:kpzjre $km/h$ 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 nmnt6 29g2ny pa78var ghw (h8$ 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, to zg4exju sa/g0;66v rhat can rotate freely without friction. The moment of inertia of the person a/ xsu6g4orz; 6e0jgv 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 diameter merry-gohntay : l5rqg*gq9 1d(-round turntable that qtrqygg95l1hd ( na*:is mounted 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 ens/z-h 87ch5vhg hje (m0xsip.d of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distav8ixg(hh ph5jz7e.h- c0m ss/ nce 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 alzdadxga;s q 485i8 7ek-hy oe9ways faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latte7zige d 9hxy 5a88qoka ;-4edsr case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from remo0n;z-r4 02t bftegwst 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 of radius 0.yvc*7xe2zt s820 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate se t v82yx7z*cthe torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical di80n roq-)cq1hpoaj cc/y6w5 bsks, 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 or/ca8q-y q0 w)1 cb5p6hjo ncof energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed t ,.wfc;i:9tcum 4uphd 86yck 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 witmr u8, g.5mcojrsfhz4;t5(hyu oe50 ih mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 day(g;us 5r m8o5ut .h5ejm0hi y,fz cro4s. 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-pollution automobile is for it to use energy storemgx)j r1dk0 :r2fu1ll d in a heavy rotating flywheel. Suppose such a car has a total mass of 14ld :r u1k2mlx)j10fgr 00 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 illustrates a+ 4dg jw6p68mntal,w 0ag1fifn $H_2O$ 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 surfa(o f+z ohm /.9lakck:2.p7ci of49 +fplldbd ice 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., we ignore friction) e w ; hjfucum11)bd44+e(fkuu 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 the ceu1+c 1fj4ew duh4u( em ufb;k)nter of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has rao k;)txz7q ;-gzmvo 0qdius R. It is standing vertically on the floor, and we want to exer-) gv q;0koz7o qzm;txt 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, where h

  A bicyclist traveling with speed v=4.2m/s on a flat ;h;3f sx9:+mvyna cj rroad is making a turn with a radius The forcr+ ;xajy9 scv:nmf3;h es 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 length 1.5 m bc - kzkk9gh:;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,9kc g;k:bhz-k and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylini/zy.fyx y w2wp+p6y5q i4q: mder and her arms as thin rods, making reasonable estimates for the dimensiofp6 w2+iw4p.5x:mzi/ yqyyq y ns. Then calculate the ratio 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 r)34,fkp 5ayyayxylu*0t/w s two cylindrical plates, of 3s)fy ,pu ryylk a* wxt/a450ymass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 gj n*w0:y p9mn8z xx o3k*y7nzradius r rolls along the looped rough track of Fig. 8–58. What is the minimumpm8y:w*on kg xnnxzzyj 09 3*7 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 assume -wa1.. z j+-nmgt: nzjkh sw(u$r\ll R$ h =    (R-r)

  The tires of a car make 85 aj 14t q4jbkh79y dmh,1 lepjr yer60:revolutions as the car reduces its speed uniformly from 9jymaj7h0 b16hydt1ql e:p ,je9k4 rr40km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s