A bicycle odometer (wh9-l -y uo2r8ys hcdw+wich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use i l+hdu89ys-yo -cr w2wt on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity.g2ypholt6yn 7v. ( sw1lqu t11 Does a point on the rim haveh12ls.6 un qyogyw7(vl ptt11 radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describvp 20t:xs;it. kc:fbe ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grr fj+9 cqw cg6iw:k:19 ry+nuyei:/dhj ckl,, eater 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 with ;) 5py j)7wbgdu/wq nt-jy+sy your hands behind your head than when +yqw-jydju7 ;b/t pgn)5y )w syour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spr)lpubx 8.dfhs3 4ld.vockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, lbx8h3d)f 4 ls.vdp.ua small rear sprocket 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 havexdc yiksa0n2r-j3: +t3k;n rl slender lower legs with 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 advantageo i3c rk3 2ld;:rjykn-ta 0s+nxus.

Why do tightrope walkers (Fig) l1m0 qnbbk7*ixc nq,. 8–35) carry a long, narrow beam?

If the net force on a w pw 7f8t6ut;lsystem is zero, is the net torque also zero? If the net torque on a system is zero,wt;7f8l6wpu t is the net force zero?

Two inclines have the s1isxtg;w. ntu xi9n- (ame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Exptx-ngi w;i (ux .n1st9lain.

Two solid spheres simultaneously start rolling (from rest) dm7 2g d 3k,+r,ap xzn9/eugvolown an incline. One sphere has twice the rad u ae/3gx7,k29om+,z n rlgpvdius 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 bottom?

A sphere and a cylinder have the same radius and the same may71bq ; wbk2guss. They start from rest at the top of an incline. Which reaches the bot1; wub2 7ygkbqtom 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 mom.f0(m/w/f )m iuzaopuv z-i amiv(u;+entum are conserved. Yet most moving or rotating objects eveni mvauf(ozwmvi .m+/upz a-(u;0 if /)tually slow down and stop. Explain.

If there were a great migrati-jdh1ge y 6)bton of people toward the Earth’s equator, how would this affect tybt eg)-hj 61dhe length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotaw b4pzd7r :1xation when shexwpr1z 7db: 4a leaves the board?

The moment of inertia of a2ggo) j4jn) t stdd46 typ56q*tlib )y rotating solid disk about an axis through its center of mat*)ng5 p2yb6tq4d tgt l))j 4o6jd siyss 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 rotating stool ,irisy)um)er*qw v-d /tuc*4 holding a 2-kg mass in each outstretched hand. If you suddenly ds/*wuiy*rm)) r-4d cu,viq et rop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same ygwwn:q0 r2x*mass. However, one is hollow and the other :*w qnyr0w2g xis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rot 5oebxs29p; t;uqw8wm ating on a horizontal axle points west. In what directioo uqw8p;xtbw2em;s59 n 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 decreasing?

Suppose you are standing on the edge of a large frejdis34/v;ncolq(0 z.be mghk,f8 +xm ely rotating turntable. What i xej 8ods3qf +g,;/lh0 mvm4b.(kcnzhappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw kvftd04z ,* nnclx(, pit quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you wil c4(p,zxtvnk f*dln0 ,l 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 6o1h ;6 ytx3tb/ ymsuejuq* w /2u1azxmomentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways thxwy* yt/ x;osj eubuh1/zumt1 632qa6e second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 yi )vl; em9*b/i:,l lfvuc3u x$^{\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 coincidencesi8fe pk:t,n +. Calculate, using the information inside the: st8ke+pn, if 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, 380,000 km from Earth. The beam )0*si*:c ry0xw 9dn lbt6aia sdiverges at an ani ts6 :*xc)w0l*nsrb a0ia y9dgle $\theta$ (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 6500 rpm. When the motor iec g9b6 54txbgs turned off during operation, the blades slow to rest in 3.0 s. What is b5g egc4xt 96bthe angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3stzl:+(( ,wd l slpr1s.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter(lw(llsz+stprs, : d 1?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many we4 c r;kxeajm2ew25jv, jj1 :d r37lwrevolutions do t;k2aj7wjece3 5mwrx ,jrv :ledw421 jhe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 r8.iu (k 9zpnq; fx/jfdpm. Calculate its angulaxpzf;ndk/ if.9ujq8 (r 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 tpy //9ev0prkv c:hc- makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2c9rp: h0kvtcy/p v/-e 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 ar:8y 7r 6smxotsound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pn x-- eve(h 96ai5st* ckquz mnb-h+a9oint
(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 rotatkllnouy k+ 3 f 6oj4se5nom)yg w1i9*,e if a particle 7.0 cm from the axis of rotation is to experience an acceleration of ky)3u jgl6osl,fmi *1nknye9woo+45 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboutg5( f)eyt 1 vzhkv,: ppi99f(qynj py+ its center from 130 rpm to 280 rpm in 4.0 s. Determin(9ivpkf1 efp yh9y tjy nvq(,5)zp+:ge
(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 radius2gz00 yhb /9imvnk1ib $R_1$ 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 sp1zorbko2:fxq,ub4 z i.eo ;tc35e(vc acecraft 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 euzo 2x3qt,( koferc;v5zbb: io.c41every 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 uniformly from rest to 15,000 rpm in 220 s. Through l) d1 bnt 2zsve,h68nhhow many revolut)8,hvnht16 lb ze2sd nions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpypa6rd t8)q;* nda )btm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling as:5lp p0t5je “human centrifuge,” which takes 1.0 mipap lt0e:55j sn 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 achn 9xl-mfm*1 0i zrpj;ws) (0qds1hakcelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this tim wn9mzhfa*l k sx1;pi0(r qjm1h s0d-)e?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revolsxvz) sim32r 4uti) z x3s42irsvmons 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 itstvmceff /hv,;k(x1xt; z d7.a speed uniformly from 95km/h to 45km/h The; tfezxc.,1dftv;k x am/(vh7 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 car reduces its sv s2l+p7l nar7peed uniformly from 95km/h to 45km/hpa7l+ lvr72ns The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbv,7iu qc19d ge6nxr z.ing a hill. The pedals rotate in a circle of r enz6 xr,q7ud9iv1.gcadius 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 8 mi1w w ;ajo-yzbgo93of a door 74 cm wide. What is the magnitude of the torw9y1z3 ;jo-wi o8mb gaque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the zo4ei2b n.l0mn- g7); vzma bdwheel shown in Fig. 8–39. Assume th.l; i 4b)n zangbo72ve m0-zdmat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of majxs+i f.3 n9juss m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position andxu fn ji+9.3js 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 to a torq*v zxvb5,g *o1b-lg adue of 38 gb5zov*x,d*a1- lbvg $m \cdot N$ 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 radiugbxt dx .3fcm+30 ou1ws 0.648 m when the axis of rotatg0wb+x.xt um3d o3 fc1ion is through its center.    $kg \cdot m^2$

  Calculate the moment og.;nzy)i8fsmxe 4 0hnf inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can nsh)0 ;zm84ngeix yf .be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated v- 0akvwf+)nu in a horizontal circle of radius 1.2 m. -v nakwfv)0+uCalculate
(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*)tltx8j l: tsisty si8l;3- a wheel rotating at constant angular speed (Fig. 8–42). The friction force betw8j-ys38x;i:*t)l sials tltteen 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 ij6mxb v6ny97fv s/: yr,pzt1c4-vjmhnertia of the array of point objects shown in Fig. 8–43 abovhv497f/ jyzpx6:mt -6bmvr sj 1c,yn ut
(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 twohdd j((,zc4*i qsx9 +xliajt3 oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylif pof18fl ,v/00gfm,li1ous78a3vlt. q pfg sndrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 361ftugql fa7g,pvp1lf08o vfl ,im. fs/8so3000 kg and a radius 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 7xu( pcgwn+z* w(x( -y7vb rtgcm and a mass of 0.580 kg. w (n+g ztvcw7xy7-xp g(u*br( 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 fsy2(olus ; f9grom rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-gopeaxoiqln*8 k4 gu81 y79i;nm -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, and7*qu4o l8nkpiyexg im n 8;19a 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 isulo8tw + iw9m+ shut off and is eventually brought uniformly to rest by a frictional ou+t wm+l9iw8 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 3.6-2gknbmd1xif m :/ 3x+skg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whipcjrxwob pl ++: s2rs 6(1qrj6ch rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is +ssr(1 r:jwcbq6p+ p2rlx6joaccelerated 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 longqup(gpj81+h n 1e;nsy27 ynhr thin rod, as shown in Fig. 8–46hyyj rsug ;(21ep8qhnp1n+ 7n.
(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 masi246olp)4qm+gz /0 8 qndnq)oxcwhah- 1fy jrses, $m_1$ 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 re p.pp :pycol6(h 0pbg5st within four full turns (revolutions)0:gpp pp.l chb 6yop5( and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inert x28n k9/omvr/ v)lzazia 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 li 4skrsmtx*3:6 /n yka 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 7.3 kg and radius 9.0 cm rolls withou/q iaw;x2qbp+d5ni;no1 bll 9t slipping down a lane ata2;i p9x ib n oq+;llbwdn/51q 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun a*ynpbdk gr-a+m1(pc3u. 3wig s the sum of two terms1( yc-u pma+b.3wrg3ipk*gdn,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7 30:(e1. k vdnur,yt kxlgwve-6w2eeu.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution pe e01ken2yw ve .ex (3vtu:dlkwugr,-6r 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg sta ab5h(()wdr jbie3*c g*kv2vs rts from rest and rolls without slipping down a 30.0h2dsv(ab c ri(5gwk )3vj*eb* $^{\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 rc,i2xqcq v,-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? [Hint: Use conservation of energ,riqqc,2- cv xy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rot7e:.d si)bsf + gm xnejcqk;n,o)80gl 4uw ,gdating on the end of a thin string ine+ m odd;:x4nsc, wei kg,)g7 n8.)0 ubgfsjql 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 unifortto9x-)s 3ua.r+ t ,f htabu6rm cylindrical grinding wheel of radius 18 cm when rotating au tf3r,ab 6ut9rtt-+o.ax sh)t 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 4.m y uo ao8lzbs1nn.y,)jtn,his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizono)jut m1 la4, ,sb8nnyn y.z.otal 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. 8–23jchbzo (c5dt9qh )) b9) 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 p q5)(bzhjt 3) cboc9dhosition, 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 initial rate of 1. bv5b7ah- 50ahwuzkz )0 rev every 2.0 s to a final rate of 3 a5bh )zw7h b-u50zkva $rev/s$ 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 vertic c vu myysm;3,:tthj,3al 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 po3s,cmm3j h: uttyy;v ,tter 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 clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.d- -qewyb* viuv71.5j d9j. drnjb(tr5 $rev/s$ 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 momeab0f ):hi/jq tntum 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 didy g*+pry 5lq(up1n.n eb3mnve6u-/-i gy)cpsk of moment of inertia I is dropped onto an identical disk rotating at angular speed nl+ -cbuen d er6.5/ny1ygpg3 (ipymv-)pu*q$\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsg /u ;po fh;eml)vp/c- at 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 merry-go-round pk. kvo3.lxd6 u ,zhzl+latform of radius 3.0 m and momendo .v,+.6zl uklzxk h3t 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 mer) ) mkuexdi4gdx6u)5zv v4v3f ry-go-round is rotating freely with an angular velocity of 0.8 exk zu 3d54um4d))fgvv)x vi 6$rad/s$ 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 as)d+n(ka:uk 0bb t etp d0-a/cbout half its mass in the pro/k-+:aatdu)s0c k netb0d(pb cess, and 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 winds in excess-t wyvfxk92lzr:x0umjg j) pa;4 e a,0 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 yc 5woolm18 3hq r*,uy$ 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 sqvd2ufr 6oc)c(so vvg3*8u*hout friction. The moment of inertia of the persqv rvc) o df(ug 8svou2*cs*36on 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 merrq( ywqy/( rkb8y-go-round turntable that is (b(rq8yy k/wqmounted 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 ro(:r q3h sctmm0/+wv ugpe lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, hold:mqr/gcmwv+ uh( 0s3 ting 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 *8 c4(n8hpk s zmz1sevsame side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the se 81svzhzn* mkp48c( latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fro9or qr au;;4vz4s1e.vdkwx6 wm rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m a dams5cup8 q +hbs3u(:(c z;rhcquires a rotational rate of uh ;s+p:au3cq bz(m5schdr(8 from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricx(qyvvuer3d19n7, n zal disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub1rz(9nxnve y7uvd, q3 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 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 thegrpav-84 (0zpjfli tbct845d angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the si78o;s nky ,a/lyttb/r8mh1g cze of our Sun, but with mass 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 anom c7t8y1h/; lg,srky/8btstar 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 p c*.t1y j(deouse energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flyw*1 otd.p j(ecyheel “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/2qdhz s/x gjglz4 b4j,0eh7an $H_2O$ 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 r,o. jjqcsyzd2ero*igzn ;6+ 2 olling 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 ignore2b1m9w37:jldcbl 88 cxt+ek mrnxry3 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 angulaj:dbxm32 9b k+ry1nl ctxl8 r7emc3w8 r acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically onw93m1(;qo7nmeolb yk 8h1nbh the floor, and we want to exert a horizontal force F at its axle so that it will climb a step a yohw9qn;lb7 b(om1 ek3nm18hgainst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/kmb3pwpiig21 834 vhj-k)nx rs on a flat road is making a turn with a radius The forces acting onijpwk31ikbr23m4pv x n)- 8hg 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 3-xen,adwb4 p a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, x-en apwd34b, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as ; k9.tjr;( fg+prc lgothin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with armcr kfl;r+go. ;gjt(9 ps held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platesg.qyc ns6 ue 6aldg1apo;i347 , of e 61q4luopg7ny .ci aag6d;s3mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radi5n3 4v8)cc :x saawe pmtp,;ohus r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble muspwo nep c);5xa s mh4va8t3c,:t 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 assu8s(fo6 acof+fme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly frddsmk3do9 vl,0 gp3m8 om 90ks098,d3l3dg d mopmvkm/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