A bicycle odometer (whichkjkf; dz:f14 t measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on 4f;fjkk:z1 tda bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the ri4w 9ex0 +x0 )4m/ ;bpagpqwztsf tiyfyt7+rb: m have radial and/or tangential acceleration? If the disk’s angular velocity increases uniawzp0fr gs ;74 0mbt q/tp +f+xye 9ytbwi):4xformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of th3ntq s)/ bi0d9h8(9qpwyqr ufe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? E c1hi2mxomse ;-rnq 5;xplain.

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 sibga +h0gbytpo3*t x3-t-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer t+gtopty3g - b3*ah xb0his.

A 21-speed bicycle has seven sb*2fqysdq /sgd 77)t pprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a lyqfd77*gq bs2ds) t/ parge 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 awm.4 a2xs (vxwble to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational2sawxwx.4(mv dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig: r k;bb ywwmlzjj 2)ak0re7:8. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the ndibi1* n y2x2e 9brfg7et torque on a system is zero, is the net force zey2ir ie bgfd97bx *n12ro?

Two inclines have the same height but make different anglesbpv 026f 8mjqr / mpdom0o1btfu4w;e5 with the horizontal. The same steel f mq6fpj8m duwrv451pbem20t /b0o; oball is rolled 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 in6h (ydhq(7jx ,gsonq )whzho+x3 ; dn1cline. 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 kinetic energy at the bo y ,nhxdzn(h ;s+37 (wx )6jhdo1qhqgottom?

A sphere and a cylinder have the same radius and the same massg zpx)( eho ;6gma2ti2. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greatpgg x)h2oa6t2m ( i;zeer rotational KE?

We claim that momentum and angular momentum are obbjmhx, vy3 *7 ccr,(conserved. Yet most moving or rotating objects even(*cx,job y mb37hc,rvtually slow down and stop. Explain.

If there were a great migration of peoqnl5f(qu/ +a qple toward the Earth’s equator, how would this affect the length of the dunl5fq/+ (aq qay?

Can the diver of Fig. 8–29 do a somersaulbim + 6o:;d gpsbh.r,zt without having any initial rotation when she leaves the ,is: ;gop bhrdzm .+b6board?

The moment of inertia of a rotating solid disk about an axiiiu3s*zw snmnl4+*hkk *2)m ds through its center of mass z u3i4*snns+m d m**i)2kkhlw 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 rotatin9zrv17 0 f.vpn4wf lgog stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Exp 47f l1.v90rfgpnw zovlain.

Two spheres look identical and have the same mass. Howevfdvt1 q 95:xa8j-qwc lctu1.wbg ;n8per, one is hollow and the othe t1 ;fqpvwx cg59w.8u-lqajb d8t 1:ncr is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizont.-3o kv2y 9oejx,et/cl x ip*tal axle points west. In what direction is the linear velocity of a point on the ,i*p3 kejox tx v.-coyt2l9e/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 decreasing?

Suppose you are standing on the edge of a large freely r*wx;. rkv) palzqxo6;otating turntable. What happens if yoo.v6;wr l kx;)x*qa zpu walk toward the center?

A shortstop may leap into the air to catch a ball and th ecm*v:*q8-j2ryvlw r z-yug ( pd xg-*:/auqnrow it quickly. As he throws the ball, the uv wc 8** e-qyv g(nrq-azd:grj* y: u2u-xp/lmpper 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 /ofs (1z0gpa d d)pe+w1h)jj cof conservation of angular momentum, discuss why a helicopter must have more than one )p (ddj+hps1)ca/1wjf o 0ezgrotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radizh2ds6t7u or0.e wgfz 8rdn6) ans: (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 w qddt:7 2ptczsk5/s 0amazing coincidence. Calculate, using the in:p2/ swc k7z5dt td0qsformation 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 Moon, 380kfhak/mq/f:e( 66eya ,000 km from Earth. The beam diverges at an angle q6feykk6/m/ea :fh a($\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6 aipgly(p2 c28500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as t a ppy8(2clgi2he blades slow down?    $rad/s^2$

  A child rolls a ball on a level flop6ee;ck s., soor 3.5 m to another child. If the ball makes 15.0,e s o;k6scpe. revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many reg5 un4 jp4jo0lzjej8(w 9k8xjvolutions do the (j5p4jxw zuj8g8ke9 l0j4n jowheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm.o x 6/istk-ox;ywi:g 4 Calculate its angular velocii /wy4x6xtok:ogs -; ity 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 n,f(/ lsk5da min 4.0 s (Fig. 8–38). (a) What is the linear speed of as, na(/kdf5l m 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) inv94 xy; -e6 qudupuat6prmp1. its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofmw 3(z+pij+a y 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 axe2 ym;g -mmse.is of rotation is to experience an em;m -2ym .egsacceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its ce cls-+vg)vq 2wrpysn/ ;f 8ywxf1449pfoizh-nter from 130 rpm to 280 rpm inxfw4;/ i8p -+2hlf)ns -pf91vq rcygvozys4w 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 1.yee;d/u8zcw 0 lpo z$R_1$ 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 Apollb2z gl -n70psno spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the 27 ns0nlz bp-gstart of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uwra-yyv,o7k (2m2 gri niformly from rest to 15,000 rpm in 220 s. Through how many72,ykoy(g2m w-virar revolutions did it turn in this time?    $rev$

  An automobile engine slows00e6/vfbu72 szecq xl5 9dsb y down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested f(3 mvn4cjbmqilg* 5pc:l;n b(or the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 mi4 q c cgm:n*jl(3bp5vl(nb;m in 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 rpm in 6.z wm)mcf659k o5 s. How far will a point on the edge of the wheel have travemo9cw6mk z f5)led in this time?    m

  A cooling fan is turned off when it is runn vdw rpwr);2x.b3 hgu16xzs n0ing at 850rev/min It turns 1500 revolutions before it comes to a st 0hwnsp26g rx ;zd.1x wvb)3urop.
(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 uniformly frg/l0 lyj l7b8yom 95km/h to 45km/h The tires have a diameter of 0.80 m 07l8gylyjbl/ .
(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 t.6.rvqb aag f:he car reduces its speed uniformly from 95km/h to 45km/h The tigb fa: av.r.q6res 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 pedal when cla.ae.zga0resx 7 f *p8xxyw/1imbing a hill. The pedals rot7a1xx*0 gye.ezf pr ax s8a./wate in 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 endjj:))pkg5 u8 z:ip amt of a door 74 cm wide. What is the magnitude of the torque if the force is m)ij)pazj gpu5t 8k: :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 th agld2g7 1e*lpe wheel shown in Fig. 8–39. Assume that a fri e27 a1gldg*plction 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 3)h6etyh w0it a massless rod which pivots as shown in Fig. 8–40. Initially the he tth3wy 6)0irod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening t5dj-ed6qj5 lh*l *cebo a torque of 38 j-ddl e5 e6b *c*5ljhq$m \cdot N$ 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 radmf;hhvmtb:g1 7vj;3 fcbc1q9 ius 0.648 m when the aj cc3v1 1b:m ;tbfvm9qh7;gf hxis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whez(syo ez7(gdvsi+ y9 )w3gy a6el 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (3zi (6g+yyasswyeoz g79 vd)( why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod isb j9 r64benq+h rotated in a horizontal circle of radius 1.2 brnb9eh+q6 4j 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 constant6 *mu(byfipsgx mu2-; angular speed (Fig. 8–42). The friction f*26gx (-mu fb;impusy orce 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 ofy:auz y 067yvk(: br *3iksn3 gvdb(py inertia of the array of point objects shown in Fig. 8–43 abzigyp:yb s 36dbkn(yrk7:v 3 au(*v0yout
(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 tnm. s(l) /i 07frhrogaotal 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 rate, e k.ap(xzm t zj3mmp1ho(2a62 6gc*mwq ngineers 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 reach 32 jw(kz6xc zm*m3a ( 6q 2thpg2.ompam1 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius 2i,;qqh2f/ se6/nihqhve .cs of 8.50 cm and a mass of 0.580 kg. qh226fseq ,h /siveq nh i.c/;Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to 3 q kb87cyq(jo f*y1,ibgu 41hl $rev/s$ 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-ak7 8/izosbx* 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 ao7zkx8 s/* iab uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at c0 7ie15td*zdlo,ob f10,300 rpm is shut off and is eventually brought uniformly to rest by 0t1lbi odd7o *ze5 ,fca frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball an 0j +.: kmipe7lmyen*t 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 isb)xf w6f5p*,uwq 4ngwfb hwy7,+ og: u thrown 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 from, x+b w6y4)fo,:ffw gq5 *bpn guhww7u 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 i416svp+- v cwuctmga7 n Fig. 8–46.7+ -6c4 sv pcu1gmawtv
(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 ma6iwz(s51esip8m6 vz r fpe 32asses, $m_1$ 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 fucl 1j;et9l2zzp 61hyzll turns (revolutions) and releasz; l6zl2 1ecz1py9j thes 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 ha1z9vyz 7h xx g43ln1xws a 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 ze d 7s6gr5iac11iwb880 $m \cdot N$ 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 1gm4vtyqp3e;.7 zks ywithout slipping down a lane at7e3. kzmqs yt1v4p gy; 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 +7q)t() gdb.jr, /nazlrozso of two ter grjbl)rdt /sz., )(anz+oq7oms,
(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 a1/-gq 7lslpvlh g,(vj0jtv(r radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 rev 1tp-(r 7lvsljgh ,(jqlvg 0/volution 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 ro djw0.mq1-v jx y8q*lmlls without slipping jlv 0y.8q *dq-xj1m wmdown a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It stary)+(h( v8 n sgyu/txzofs 09lits to fall and its +nsos9ytli( 8yxf)g( hz/v0u lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a3dvf q6f 9o.w-msp a(kigbp3; thin string i; 9pq 6 ibkd-fvaf(m3.psg3won a circle of 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 unifoa4(t7 yaphnx.uu9 nr5rm cylindrical grinding wheel of radius 18 cm when rotatin9ah.5xn atrp(u 7 nyu4g 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 at a ajd0tiu/ yeg0)x, z/* azkct ,rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, thezai0 zuxdta, yt0/k/gc, )je* 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. 8ivgd ,a gn8lra44.ws65 kiv,+;f wt ry–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 s when in the tuck position, +rlingwf;6r4 tdv,i4,a vg8y5.a kswwhat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increasehcua me4 rz4,e: 5vj*m her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of h am v*:e e5zcumr,j443 $rev/s$ 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 s+ k0w,eerp7(v .r 2h j,9k*yls/cpc iesum x(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 3.1wsk9xcespi2e r,vj *ky0+s/.hr ((mp7ecu ,l -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 clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figuc3hhi( 7 bg7chuf1s j6re 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 mo1 lt fdj.+kz3*1 zrifqmentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertihd)rt4r o)b2y70(swzm*gxs r a I is dropped onto an identical disk rotating at angular speed*2) 7y 4s r)b0rdotwzxmgr(sh $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4xhv, ;lxn vi4s()fa)i -dfsl1 $rev/s$ 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 rotatin. pkv3hldczj( jr;3m (g merry-go-round platform of jpjlr(3z d .;(mvc3hkradius 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 4q7gp rvjp7 8c0c8q47 7jvr pgp.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 eventuallw m+ z*ve*i1zyy collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radiusmw zz* 1+e*yiv. 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 wiov7.m8 zetabg9gl -l4nds 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 hc)5g ((beiu7 3ehc1mj.c zrx$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely wit 0+55r lmblk*r+8rkdk t6wbue hout friction. The mte b0b+wurr56m k+*dk 8llr5koment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m di:vvehc-*:bbq gj , wg1ameter merry-go-round turntabg:j-eg1c qw b*v ,hv:ble that 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 end of the rop y6ffmrwep9 0e ld4rvk: 4m8*we lying on the top edge of the spool. A person grabs thrfe 408e v4y6lmmrwf k*9 :wdpe end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same ojp r8lpqs*4any **h 5qhpp6o l2sd+)side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own a j+p)hor8sh n4yla ** qld5*2osqp p6pxis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratea iz0y c5kf(.g 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 jnq-7dbg9z za)qd s38 yi j;i0in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration.-jqdnis9 )gdbq 0a8y;3i7z jz Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cys0z zeir:/dsrc0c. 0kybc d3 s+5)dkylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.005ckcd3 ibc0sz+0drry )0sz:yk5/ sd.e 0 kg and diameter 0.010 m. Use conservation of 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 of the gimb2 z ng 69hiy+s++ ;v;mpnnrear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8v7a1 ; o or l-6()5kq6wwv*qluc qlgid.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, w io)( u; 1vwqr6ql ck6v* lqd-l5agow7hat 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 ipctsnlps.p 1z2fh;/ ze-+2qh /j t6l stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical f/1j .ezp +-2n p lpttss c;ql/hfh6iz2lywheel 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 illustrate2 (4gdq wghei6s 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 g 02oe0 w f gb;)ncr83es6bshgrolling 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., we ignore o9oh+ro lh +s+ - ydo:bl:vimp/vt;y8friction) 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 accelera:b;ovi+s:v+8lo/yp -9l todm hr+ho ytion of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has y5ugry2;r aj0;j s+iw qyr*7 cradius 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;a * cj7 ;qsuir r5rwy2yyg+0j which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist travelina3z.lx3lxn k 8g with speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are thea8n3ll zx x.k3 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 1.5h8(dr 4 f54k loe6fzki m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a ef56dirkkz fh4( l48o 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’7.9yh)r m. qks :. cromfkn*lqs body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angulary.9 )*qmofcrnm7s h l.:q .kkr speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch asse 45cw;ob*xn kombly which consists of two cylindrical plates, of mascowbx no*4; 5ks $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ) +q.cq)dcjling 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 the highest point of the loop c)+idq cj)q.l without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do6v/q2v u5j our not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car d8 j 6ahc5na aj6m1o)breduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of m56c6jad h ao1bn8j a)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