A bicycle odometer (which measures distance traveled) is attached b1 mi*q+g4nu wt+; vqrnear the wheel hub and is designed for 27-inch wheels.1nv rq4gwbu+imtq+*; What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angu +y37+unp-si f gt5pra;oynd1 lar velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’sp-y g+ a3u+5 optrd7nsnyf;i1 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 described by a single valuec+zol6 ef+rs4 of the angular velocity $\omega$ Explain.

Can a small force ev:ovw+y7 k: qtner exert a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind yorrp4 b/c) n1gqur head than when your arms are s) qcr/pbgn 14rtretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the peo 1ec+ ,bg 5owpr0cw-fdal cranks. In which geap bg+or- 5o1wwccf,e0r is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower l4;wuvo v942l-c eqhr jegs with flesh and muscle concentrated high, close to the body (Foc9h-u; v wj4evq2r 4lig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) c2r5 z, ssoh1xk b:0vtvarry a long, narrow beam?

If the net force on a system is zero, is tf +ofr7w,ax 8*x;trxuhe net torque also zero? If the net torque on a system is f+*axwr ,x87urxo t;fzero, is the net force zero?

Two inclines have the same height but make different id f: nfdb)j/idh0zh75q/ pv5angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the bal)5 dzf7/fb nhjvipdihd50q /:l at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rio((atu,rgnu gfcb4pn -vt 34e x s;r4(u)l:gest) down an incline. One spher (u-g(u;nfg (xlp g)4uo ecnt,v 34rst: iba4re 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 bottom?

A sphere and a cylinder have the same rx1h2:wmvv*nmkxdb9 1 5qs yu/adius and the same mass. 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 gre qw1x/nv92d1vu :5mhmb*kyx sater rotational KE?

We claim that momentum and angular momentum are + d/;k:sx dttoconserved. Yet most moving or rotating objects eventtk;od xs:/+dtually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s e0-)j;g7jj x9az pgrnlquator, how would this affe)jn-jgzj9;rl7p axg0 ct the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rwpe(lgk 1 3h ;sgr(2mmgw16 plotation when she leavesp(gsrm wk3 1(w;megllp h216g the board?

The moment of inertia of a rotating solid diskaak hgheol p( p.1)-5y about an axis through its center .)gkhpa(ho- py1 al5 eof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holy5m74xn q+9vu 3p uzv fg8:noymv 2m*zu90mziding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wil z3ugmxvv4zmfpuimz 7n8* 0+5mv9ou y2qn:y9 l your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, o ie06qdlt5k 1ene is hollow and the other is solid. Describe an experi0iel1qt5 ed k6ment to determine which is which.

The angular velocity of a 4y*crzv:t oqx*ee :/r. uxp-6 mt42 /wcqxsaf wheel rotating on a horizontal axle points 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 acceleratfep:o: xs./4tzarmect 6vwy q 4uc 2xr*-*x q/ion 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 rotqsqvx4;uj j;7ating turntable. What hapq j;x4;juv7sq pens if you walk toward the center?

A shortstop may leap into the air to cat2n m *s0l8hshsch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotmh 80s*snsh2 late in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservat5gn*g ryt/ l3fion of angular momentum, discuss why a helicopter g/nt5 y*flr 3gmust have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radi4s qh lh/ vq2j6+ is0.s nmbfdh,4pzw4ans: (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 becau81i -7q/5whoi o.ubm cl:dl3t ei4zmuse of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in :m 7lou1d4z /m wqe ih5t-8l3iibcu.o radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 39zx/k+mg zeg 7h.3myi80,000 km from Earth. The beam diverges at mzxg+hm ek7iz g9.y3/ an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm.g3jm(a,b 5tr4p rjp0p When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acce3g5 rmt0 p(4jbppa,jr leration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the baa+kk- l g dxxnbsj*.e(eb./b7a:do. l ll makes 15.0 revolutlbo-+a.*:bekxbajx e .(n7 /dd g.k slions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manymod ftw2n) l sl8l2q5l pr-*q, revolutions do thetllfp5,sqlo -ln2)m *q82 drw wheels make?    $rev$

  (a) A grinding wheel cael:o ek4g+ zkg/:; r0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in lg+ec ::k4 ao;grek/ z$rad/s$ $\omega$ =    $rad/sec$
(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-rounkd3w ae5ile,p7 ic+,)vzj kn0n9hnp5 f7ka e*d makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m ,pel7k0z+in,depn ek jck)h3 n975i v5awa f*from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular/ghnr-ozqsf*iizoeoq*+ve-i4ns q --*1/ a n velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed o:23a mrcgww /yf 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-5eova v)z to8 vuqq+dz. vb4hmir/4 1 if a particle 7.0 cm from the axis of rotation is to experioqzd utz41 hmi-5rvvve)4qa8 v./ bo+ence an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abo-1lk *an) sqruut its center from 130 rpm to 280 rpm in 4.0 al-s )1nr* uqks. 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 radiuek3o+uc gwwd p043g+ q.4gazu7dm . pws $R_1$ 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 aboa *nyd(n/jw bgxqk)7)ard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At ty njkdbx7)(*a w gq)n/he 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 to ycg1+5 etyk j:qfo xi/ vwky/97ra21z15,000 rpm in 220 s. Through how many revolutions did it turn in this ti2ko1: a xiq+/9we7z r5yjt 1c/vkf yygme?    $rev$

  An automobile engine z)spz2jyh;b+ slows 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 for the9d,) .: wm)qv lkffctd stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throughv df kwc,l9:fqmd)t). 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 py(j(8c7lo+vlg c u *zi70sv,fu/ mak6.5 s. How far will a point onz l/7v pujv,uy*078 s fc agc(l+imk(o the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rkia:bz3vq 7mw ccev e.ap44n; o 4,3bjev/min It turns 1500 revolutions before it comes tm vc vzkq3,ojcn43ebeaai;b: pw44.7 o 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 nzh6w/ 0 lwkt: nlq/;vits speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.n6 /nqw k/w0lhvl :;tz
(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 carq 6l/iip5mup5s ( wr7s reduces its speed uniformly from 95km/w5p/6i 7lsqirm( s5 puh to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her wei.b1kkjt 9vry6ght on each pedal when climbing a hij169yrkk vb.t ll. The pedals 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 da;qi c u7+u.x3mmv2 qwd)ywy2oor 74 cm wide. What is the magnitude of c.vw my2i;qa+wuxy2 )q d3mu7 the torque 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 wheel shohd0 ,*hb p fiqr9n9r,uwn in Fig. 8–39. Assume that a fricd0hfq,bp* n9rih r ,9ution torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attig06k wnh,7wkk 9x 8bzached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially thenwkzg98 k0b kwix h67, rod 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 w+v gxj-ntz00of an engine require tightening to a torque of 38 0 v0x-gn+jzwt $m \cdot N$ 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 v ftp bchf)29+b.vmb ; pt47zhof inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through i+.2bft v;fct) 7vhbbphpm 4z 9ts center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7urwv/ .n q;(o9h:b utc cm in diameter. The rim and tire have a or9;c:/ n t.huvbuwq (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 u,rto.odx b0svrq7)-y) el(ez7q ld 2 is rotated in a horizontal circle of radius 10e lxq,7 sd zy.7qulro (vo)redb-)t2.2 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 po8g1lf2t)xspr (oic -etter’s wheel rotating at constant angular speed (Fig. 8–42). The fr st opc8)elr(i-2g x1fiction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Figl:c 8*z4 mqe3 yx3 qr,qlqynr3. 8–43y rql3,ql4ey:c3qz x n*rqm 83 about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atw9nc) fs :dgqhau4 zt2ah p,68oms 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 cylindrical satellite spinning at the correct ry *03dnn whub 5aq39(lcb)o nnate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite c*nod53aw 3 90yluq(n hbnbn) is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a ma+dvkaxy;il w 64jh-yht l)7:kss of 0.58 ay +7ivjk txy-hklh:;d4 w6l)0 kg. 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 fro5 6eri1 :hw-phvq*q( mz4uivq m 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 tangentiall/ry abt:)fa: sae6s1yy 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 the torque required to produce the acceleration, n:1 6aerys/fsabta :)yeglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brol x-0 )yc 38fr,ck1vio2/r1zpwznt nought uniformly to re8z-1p 13ilw)koc /nx2tr v yf0czr,o nst by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.2(bgn ej /q: -zjgfb:l6-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 action of the forearm,i;rr,np:rkwy;ry +c ie 1(fc+ which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated u y+cpey:r,k w;(c1i;nr+frirniformly 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 kk hcl(z d;q mniym p22:o6(t+considered a long thin rod, as shown in Fig. 8–4p 6 2l;k+tio:qc m kn((2yhdmz6.
(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 consistem i5q*uhha2(.+ k(fxkbki5 v s of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four b k 12vu +70o;z7fcsnhvet4xf full turns (revolutions) and releases it at a speed of 28fctnbs0zxeu27v + 47of v;1h k $m/s$ 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 htke/la t0,, pzas 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 kh( 7rx2iuyma81db-utorque 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 x)- gk*5ita97qhcw rh3 gjf:s9.0 cm rolls without slipping down a lan-j stx7hkri c5*ha):39gqgf we at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respef 9)z3e/gzlar8rgh ,/rd r to/ct to the Sun as the sum of two rz th)lfe8g /gda ro,9zrr/3/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 rayx0d0 g+ytzl1u 7 ;lr2ysp0 ufdius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? pyl7;dr +zgu ly0 10tfyxsu02Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.w0bvmy u g770w;flu7p80 kg starts from rest and rolls without sl lug7w0my ubpv7f w7;0ipping 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 vertically on its tip. It starts to falja/w1cy 1(ntft t00ptl and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groun0 tw pjf0n/y(1at1tctd? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the zrplsb)y265 o p)mvq--fj q1oj7 ghz ,end of a thin string in a circle of r bfq7)y-z rz mj26os,gpq5hvp)l-jo1adius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angula 9 u,gsyj9)omrr momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whe ,)ju9rmygs 9on 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 at a ri+2kp1i09elp i tm8 swate of 1.3rev/s If he raises his arms to awi2 me +s0ip t1ikl89p horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one swj4 twt(/2ovh ymm )j6hown 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 tuck position. If she makes 2.0 rotations in 1.5 s when in the tucyw(6hvmw / t4m)2j jotk position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initixzvx p3v fo+c+s,z:nu0 .s4rf al rate of 1.0 +u cv xfo.zp4s vfr +3,xsz0n:rev 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 rotating around xlv.v3gws ,w- u3s6 swa 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 diu3lv x sv3.6sww,sg-w sk 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 3.563gb++toaev fk w -5fi $rev/s$ 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 thpco ae:ojelj+(x13;,w. 0o vz3 srkrc e 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 diski 1( 6(q/twgsjbm fuyfs7k/j+ wxjm;3 of moment of inertia I is dropped onto an identical disk rotating at anf1+ /gq3yxfjwk;mi b/ s(smw76 (jujtgular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atc3:o;; f ksaago7da h0 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-gopyh;v ky/w/ -t2ps/eo-round platform of radius 3.0 m and momento y e/-kpp/w;h v2st/y 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 angularo3 aqhf/p(rqnd ) )n(a velocity of 0no3 )r)afdp/n (hq(aq.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into yntc;n7vp5l 0a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0%7v0nycnp t 5l; 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 exkxkikb ym(9 fj3qqd*0km2 y; 1cess 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 lf tq 2az/gbr gr+07f9$ 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 freel kvd0*.yq1ttr y without friction. The moment of inertia of the person plu*y0.dtr 1ktqvs 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 ajure: ux4 pc5)s-n-kst the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700s5- u nr)upcsjxk-4e : $kg \cdot m^2$ 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 gro. w:td i. :hr.hdwbu:aund with the end of the rope lying on the w :h..rwdd. uha: tbi: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 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 si7 kbkttjarmw9gc+ 2z0 * .pu3pkr nf*9de 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 latter case, treat the Moon as a particle orbi 3 rnpk *.mbta0fk*cug+tr29zkw jp9 7ting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 7*u t4yzpynqnlx8 8g183 mt yi1 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 t fx.e, wv)ezr/he 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. Calculate the torque deli).zev fe /,rwxvered by the motor.    $m \cdot N$

  (a) A yo-yo is made ofbru/ f4k (w(ae two 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 energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long (wre(b uf/4 akstring, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the r:igs7z2vq.k d ear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were5r2 7elm p8c.maho lq- rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentlqa e l.o85mc7 hr2p-mum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use en2meoa7 89+ l9fvika jr+fyqo ebizn:dyc-;04 ergy stored in a heavy rotating flywheel. Suppose such a carroke4m2z9i- faca09+eniol; y dfv y+q8b7j: 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 “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 illustratppfb7 x6re0 5ses 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 horizu7.-6bdzz; lovg l7t lhzk/ l)ontal 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 masst p 8 thh*fc(u)t7 wx/wz3hd htu-5h3y M and length L can pivot freely (i.e., we ignore 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) (htd8whtwpt3 h/-h u uh)7y*fc5tz3xthe 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 vertically on the f*sa5+qbl9 s(e prn vvy)x(wv+loor, and we want to exert a horiz( 9+v *eywn)slapvs +(bq5rvxontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with sh5je i( imjn-*peed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal forcimnhi* (5jej -e $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 ow8 k +d+a4ump,b( cs9cbub e/af length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating itebwb(amks,ua948 +/ d p bucc+ 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 bodybfd 19nbf4, iy ba1j7a as a solid cylinder and her arms as thin rods, making reasonable estimates for the dime1a9a, jfibby147 nfdbnsions. 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 b epdz/z5-s;gwr90u- x+w eyoof two cylindrical plates, of mass+; ewxpbs0w95-erz u/yz -o dg $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 along the looped rough track of Fig. 8–58.rw-ro 0nk:4 1z/)hpwg2 xu0wr6 jund o What is the minimum value of the vertical height h o:h0 xnwujwk) rpdwgz60 urr- o1/n42that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do noe:nkw / ll0gd.t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 renh4dyo *. b)rvvolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleranbohy .4r)*d vtion 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