A bicycle odometer (which measures distance trav)y *h. aovie2eeled) is attached near the wheel hub and is*yah.)oe vei2 designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angl+ /j -zy:)lf1n-elof1suklx ular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitolf l +j :-x/u)n1ye-llz1fskude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angrp)+ *yg-x qxnular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? E56;p n ts7w e599edbpu+drncgxplain.

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 5 *baljv c41ijwith your hands behind your head than when your arms are stretched out in front of you? A diagram j lva b4j*c5i1may help you to answer this.

A 21-speed bicycle has seven sprockets at the v;in39gmu+13snjp acdr g9p 5 rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small re3ir1vm jpcn993p; a nsgd+ug5ar 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 have s jtm6atjm 0)3pygn9 +b*ixkz 6lender lower legs with flesh and muscle concentrated high, cmx*pk3jj9b n 6t+ z )tgm0iya6lose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8yju 4 8yluyowtnv x,3l:i 46.f–35) carry a long, narrow beam?

If the net force on a system is zero, is the net 4 eba4)5 uvxt)9up1 ()f9wyskthdqiw torque also zero? If the net torque oni5x1uphwt(dev4)quf9 wt) a4y) ksb 9 a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the bp p7z .7 pxbss*e*vr(horizontal. The sambp*xrz ps7p*sv7b.e ( e steel ball 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 rolli2t,yvc yg; py av 0xqi.0jj04/ l1xrxb(p;iv mng (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has thxbp02r4y; , y/al;qvxv0 cgi jpi . j0(vxym1te greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start froa4mr e1o5nrj)./z vj *kqdb3n m rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greda*4. rkn)3bj5z1rn/ eqjmvo ater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum ar+-bsq4skw5k 7u ( zm-zdm*ag ee conserved. Yet most moving or rotating objects eventually slow down b -az(5gsk* zk-sm+ uw47demqand stop. Explain.

If there were a greaqo/ iik+3c- 9h9.yzzim . lswct migration of people toward the Earth’s equator, how would this affect the lengt.lz/iz-+3im co.q kyswh9ic 9h of the day?

Can the diver of Fig. 8–29 do a sok+nvd krtp7n cy+37::c hfyo;-jp w(t*e0 nojmersault without having any initial rotation when she leaves the nv nkjerd(7y*cn+3t:+o: k7wh fp0jocy; pt-board?

The moment of inertiac;-so5x rky1f of a rotating solid disk about an axis through its center of fxy5-srok ;1cmass 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 holding a 2-kg mass in e0 g)(vtas +bbt jx.)mlkhx.* each outstretched hand. If)svxk.g(* tjabl0 m+b t) xeh. you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeveypk fhgq 8- ,vf-ai(i;c0+ ziws*isq2r, one is hollow and the other is solid. Describe an experiment to determine whysif-;(8 a kq q-i0zhcws*vp2, i +fgiich is which.

The angular velocity of a wheel rotating on a horizontal axle poi: m-u vwkz4pi*z-heq5w7hz3ints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or de -7h z *kizmwv hp:53wu-zeq4icreasing?

Suppose you are standing xkg.goi);2nm7 y1t0c + jy bwo3lg6rson the edge of a large freely rotating turntable. What happens if you walk toward the ckn6)+ xtg gomy1oj; .iy 2sg7bwl0r3center?

A shortstop may leap into the ou)xrha b ;va +c(-(orair to catch a ball and throw it quickly. As he throws the ball, the upp x r+;a(obc(h )ra-uover part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discu/ita 48 h lwk(t(abfd;ss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep t a8/;lh4tftdwai k(b (he helicopter stable.

  Express the following angles in radiab 5(a++km r.kh zacu8mshl4f9ns: (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 coin*a,w 3fbr p .k0feolntk .y;+scidence. Calculate, using the information inside the Front Cover, th. ;0sr 3,bf nop*atkl+y.efwke 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+;clow, ,mc3rbk* j cl diverges at an angle;3 mb, *cc+rwl j,klco $\theta$ (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 650,znfkxc, )b 7g0 rpm. When the motor is turned off during op) 7, fzck,bngxeration, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to amim0 f:; ; s39ml;v/vcza lkxbnother child. If the ball makes 15.0 revaszcxb 3fl ;l:m0mmi/9;k vv; olutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolm2hc)c (grks3kkg;) z utions do the wheels ()k s;r g)2 hgmzckc3kmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate gi7ysdd7i/l ,d.uo p)its angular velypu7 gds odii l/d,7.)ocity 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 rejoa5;b 7xxol/volution in 4.0 s (Fig. 8–38). (a) What is the linear sx;jo 5o7 labx/peed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit aroilnr4-p) p0bu3sfnve ;g*g -aund the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed a9u zkd5 lj.r(of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a cent*oa vf85utm03vfopou w:3b *w 6qdm 9mrifuge rotate if a particle 7.0 cm from the axis of rotati63:* mv o3uwuofm vpbdt9qf058 maw o*on is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 2* f+ohki45 trt80 rpit+ f5 h4kor*tm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiug 5d;;uq7tba*kiu 2gz.a(.w6 e u kxfcs $R_1$ 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 j1 ( ho y;9ob0a2ajhwxthe Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s 2 j0(xwy;ohh 9 a1ojabenergy 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 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 th0tge3t3i15n9gpza. agi*xjau+ g 8 o o 15,000 rpm in 220 s. Through how many revolutions did it tur1 gi+.* i33hoz gup90xta8 jaagetng5 n in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 ; e+uz,4 utydsem pedvg)z +/(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 fl m:+3xk mu0zmwying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its f+m0mkxmw 3: zuinal 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 accelerat (2 mh heh3pa-plwx.kr6pg74 des uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of thh6pead(3g mp2w.7ph-l 4 r xkhe wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mix i-tc17nj* urfobt3-n It turns 1500 revol*t--cj3i r7xnfb1t uoutions 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 revo:oegl; m diaez7: /ur)lutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires:/r) zdm7lage:o uei ; 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 speed uniformly f3+h+dum wc-y5booc6m rom 95km/h to+y6u+dmo3 hwbm c-co5 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on eachws9c/gzie76z00b w foncmh; , pedal when climbing a hill. The peda/9 fmws0n h70o 6igc; ecz,zwbls rotate 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 end of a doorg6hkzs+)2up : yyc7yl 74 cm wide. What is the magnitude of the torque if the force is exerted:kz pyu+c7gysyh l 62)
(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 axlelb5y,nfpc cv.v(zu0 6 of the wheel shown in Fig. 8–39. Assume that a friction( vbfvcp65nu .y zcl0, torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of massfxc 6:yze.g fb;b-x;h m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. C g;hx ;fcb6z-fb.:ex yalculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head o mn +k 3ub5cdgk2,r -xgdf)l4*dj3 hhef an engine require tightening to a torque of 38 d3en)c-ukbj gkfddl,h+ rxh3g* 45m2$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m io n1g yjr,n8yd8ov((when the axis of rotation io8r8 yn( vj, d(g1nyois through its center.    $kg \cdot m^2$

  Calculate the moment of inertia v 2*ivrm bzy/3t+lrs*of a bicycle wheel 66.7 cm in diameter. The rim zbl 3m*ryv + 2tri*sv/and tire 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 rotated,g8; vgp ouj4 na77lvm in a horizontal circle of radius 1.2 m.gag8pml ,vv7j4 n;7u o 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-zd0 weu u+fy h;hg.6n potter’s wheel rotating at constant angular speedz +.-;nfu uhhwey60gd (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array ofdxzqm k.;*5 wkaj.8s s point objects shown in Fig. 8–43 abo.d8k. awkx;q*jm5 sszut
(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 whosen 97kt:q )xrzunopkm8 m97q9w 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 cylindrical skjj4, p5jo7y 4vmh/k batellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each ro4o kv4jb5m ykj/7h,j pcket 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 cylindep zryou+wc2. tz1 l(t )u2kle:r with a radius of 8.50 cm and a mass of 0.580 kg. Calcr:2lt e( 1l 2 +.zpu)ckzywotuulate
(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, 3r if)o 9b13 iuxqmtp2accelerating 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 tangv -l49bmjbmh9tltmd -l.f3,v 2ip4i v entially on a small hand-driven 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 on the edge. Calculate thei ,.lj mmdv9ttblh fv-4-lmi 4 pv23b9 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, bzl znmp .2.kfg6a0)a300 rpm is shut off and is eventually brought uniformly to rest by a frictional torz lk.2 a0b6)zg .panmfque 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 accelera 3go;6/nyykap 9) eroz 1r/pwvtes a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the a v c71p 7h8x(kcshq+clction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifc qphl(hc7x+ 18vk sc7ormly 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 c54h8 gs-(ils3p(ifw f /4ewsb /h lilfonsidered a long thin rod, as shown in Fig. 8–46e g5 /wi- sbi(84pfhl(3fw lil4s/hfs.
(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 twox b,l)e id:6fb masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer d 4d*196rlewl.rpufy from rest within four full turns (revoluprlf ywud6*le9. r 14dtions) 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 hasa:3pppu+.)bosyp a1 z 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 o sohx8.:oxsco1y/ps8f 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 rol)hzhp89 ag5-bsb ap7lls without slipping down a lane aa) pszalb-98h75 hbpgt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun ae hpv n:a.,v*y 1mtxoplsi ,5d j24qx.s the sum of two5lxtje: 1.x. vyp,n asd 2oi4qv*, pmh terms,
(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 7.5:2iay c1xzjhin53g4f1o p0 o7yf lg4v0 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assumona1i j2zx5vg4cy:0gyifho4f3 p l71e it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 6buasxc le3 ()kg starts from rest and rolls without s( x6be)3csalulipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vert-ai)ye 5l shuh-,72)hcm uthh ically 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 grounhhl,h-h 7uh )ymceu )st 2i5-ad? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kgqdk ./ 6vkri4l-(g qdc ball rotating on the end of a thin string i-k /cd.r4 id6k qqvgl(n 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 unis)sd6+ 4ee9cu4glsb tform cylindrical grinding wheel of radius 18ts9s g)ec64bdel u 4+s 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 atwslbd:a::0m oo/ b3ra a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrw:a/0:a m: osbr dobl3eases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one 9p vt(,-ey*y lo1bhor shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tyy1 *e ,vpohlto-(b9ruck 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 increase her s2yyn:tl;+wz y w3 mmfkj5b-c5h3bipt5( byj6 pin rotation rate from an initial rate of 1.0 rev y h kfww;5jy3n5b3zjmcy(b-mlp: ty62t5 i+ b every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotatingijfadq :t3n b,*5/qp2h n 1vgm around 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, onto the center of the rotating wheel. What is the frequency of the wheel a:*3gndatjqvmf2 /5i 1q,h nbp fter the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure f+sp rfxu. v/z50ewv,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 the8a(sq x)jha3r7 ge iy+ 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 inertia r1)ornqa;2 0tf j/l aiI is dropped onto an identical disk rotating at angular ;0t1f rani2 jr)a/qol speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns n0)fv,pq w7g(0l otpma+m)j y 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-round4/f 9 efcsz.ba platform of radius 3.0 m an /zb49cffas. ed 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 vymo+((xh n.ifreely with an angular velocity of 0.8 +(hxmy(n .v oi$rad/s$ 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 whi(9v/mpiei )-naogo 2 tte dwarf, losing about 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 momentgpi9-/ov m2oat) i(neum, 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 e:- k+f)e 8ifwriut2z6ur j o6 f;ftwc8xcess 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 n/s4m2kt4n e/yg+a)ph i 0cnm$ 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 1n.s3 ( b5hay7f1j ykf9 zprmjwithout frick ap9y5 (bmsrn 7f.jjhy z1f13tion. The moment 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 muum)r9hk.x084y gepstands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings a8. k90mhur4e )ygmpxu nd 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 rope lying on ;jj7y0zw4yhq : tlpm: jjna, .the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spam ln;4j hjtj:pw :,.yyjz0q7ool 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 Egmn4/ j;5kdjj tux4walg,k8 +arth such that the same side always faces the Earth. Determine the rk n;,kw5lg gudj txj/+a448jmatio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest a*p1r9,yxdgn ,aw:qk zt 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 unifor h4epzn.agr f:am :meg49 h*5fses+kx(omd 6:m cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate g g4 9a (ae5:zps.so:nfrdf eh4 *k6emx+m:hm the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twokj n1w4wz1 js9i0:rd u solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energywz:urw n 011ds4j9ijk 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 spee7xr dhc* k5u)qd 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 with mass 8.6:)bq0pt8 rft ggmmt: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 otm ftp bq8t: gmg6r0:)f 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 automobileag4ur v4kr3 lqv9qfxgx(4e: zd4-g2n is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel f2 gl4 4 x3qv4r9uzn e gkx(-avr4q:dg“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 illustratqo7w ef:afg 9:h k f9yp:cw8j2es an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed-m,jhub*1 ak/qt;laq 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 fricyq;nw5 ) zwu9 y30ujtotion) about a hinge attached to a wall, as in Fig. 8–54. uz;0nojqy9t 3 )wuy5wThe 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 center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing verticab 9d(eoas1mc+g)*nkh d),ydw-f 0jzp lly on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, wher*dwj- p)h,9s e g(k)nd+o cmby1 d0azfe h

  A bicyclist traveling with ax :bg8d( n ;zc q6fnvp.mr:toug-- f+speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclistfxo8 :;gudrcg:- 6q- a .(v mtfpn+bnz 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 c.xre by(okl;4u8p 1rsling of length 1.5 m and begins whirling the roe rl8c( y.upbkx1;o 4rck 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, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as1mb e1w 7dygd7 thin rods, making reas1mdbde7w17 gyonable estimates for the dimensions. 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 two cylindrical plates, ofe 44;nhq4px)ml xh,dyn v-ac . mass c4x h am)n4q dx;l4p-en.v,hy$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolqtwah,d92 :ldls along 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 polt,w:hqad29d int of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butc/1 qv40pk jamq7e j7z do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redu vulzppvkgw jq,8/e4r)v -zs q+t5n/; ces its speed uniformly from 90km/h to 60km/h The tires /gv qj+rq /-8),t z5zl;sp4k vvpenuwhave 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