A bicycle odometer (which measures distance travelede)y fp5i,hl,h i, bi,c-;hmy ftf+ 5xo) is attached near the wheel hub and is des-,+xlyhi b f,,f5htc,i m ie5of)py;h igned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant 7cz51 0afn7* m ;ba6s *7npvew woyxlyangular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s ango n7w6a*b*7mzyfv1 w;el pys5xn0ac 7ular 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 bhz+n5. nkefkvj3 z-9j*fc5d ye described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exuygu-/znw:4 kn.4 bt a- sg,zob*v 71efpz wy)ert 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 clnm13(q5bvo.f m*cfnp9j fqt6,5 n usit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thim.95joqc 6nnf,ptnuclv f *m3 1(q5 fbs.

A 21-speed bicycle has seven sprockets at the rear w.)5bt tcjifp*/0vmgudm 9; yx heel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedxvgct.m0d u j bp9/im) yt5;*fal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have sle0x/q-w bofq 8xnder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis ofxboq0xf/-q w8 rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (64: v 6utd hjv-)0x p f6 ttzlagvyja+8udr16jFig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? mqv2(y9nhak0l)awc(pa 2v3g:w5b r pIf the net torque on a system is zero, k95ap (v cmrwhal :gbaq p2w)0v n3(y2is the net force zero?

Two inclines have the same height but make different angles with the oo wq4gwo u;ip2 4v;h0horizontal. The sam 44hiw 0;;w pouvgoq2oe 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 rolling (from rest) down an incliduh-f1 i 9rvp( d c1vpsym:af-;j36sw3opa 1 bne. One sphere has twice the radius and twice the mass of the other. Which reaches bd -mupfoa1phvcs ;r(ad s-f3 3jp 1w1vy9:i 6the 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 mass. The;d0vnpz d+ 0juy 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? 0du0 j+zdpnv ;Which has the greater rotational KE?

We claim that momentum and angular momentum are conseryd,ibh49dg e .ved. Yet most moving or rota iyd.4b d9eh,gting objects eventually slow down and stop. Explain.

If there were a great migration of people jqdgac)p . o6(u(jcm+toward the Earth’s equator, how would this affect the lengthj(u.6a)c cjqpg(m +o d of the day?

Can the diver of Fig. 8 hdmnxba d6 7aqyqti1s .94/n.–29 do a somersault without having any initial rotation when she leaves the bstd bin/yxq ma.14 6a97qdh.noard?

The moment of inertia of a rotating solid disk about an axis through its+t gs56 okdvt+q /g/xr center of m+/g+ v6srtd/ oxkgtq5 ass 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 holdz*;w p2 5ro nrbc;po7wing a 2-kg mass in each outstretched hand. If you suddenly drop the masses, ww*7;;ob r nrozp5 cpw2ill your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicalfmwk2 p5s g2v2-g7g pl and have the same mass. However, one is hollow and the other is solid. Des-2pgvlm 22fwgk 7sp5g cribe an experiment to determine which is which.

The angular velocitygx1o p0*bgc,f, fd1t d of a 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 tangenticg,fg*o dtfx11 p0,bd al linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotat:t :)gujgzdr45ui1 ta l6 lwj8q+i m3wing turntable. What hlitug5 36uz:aq ):dwt8gj 4miw+1 jlrappens if you walk toward the center?

A shortstop may leap into the air to t yh+,h 0iga;dcatch 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 roghhiy0 ,dta+;tate in the opposite direction (Fig. 8–36). Explain.

On the basis of the gaom9j-0tpdj8l4k s.law of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propks 8gl. dp t-j0moja49eller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30y luvmdzb930 8k,.dyz $^{\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 becvkl574dpt0 b fxhj ;a5ause of an amazing coincidence. Calculate, using the information inside the Fkvtpbda l ;5x0 754fjhront 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 divergfoj) -8igy4z t (5lnsmciis04es atc 4n o85lmti y4is0-ijz( )fsg 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 ro-;0x: jfruvgsap25p ztate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades 5:2-s0ugj ;var pfzpxslow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chil y(m7 yniijz2m38lgy3d. If the ball makes 15.0 revolutions, what is its diametm3yzymi7ni( gj 32 yl8er?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many :.cza p lrc+ nf3. o2d3is/vma8x xznof6v;*g revolutions do tovznxcsc ;l6.3 n 2xa8z praff gm3+dv. i:/o*he wheels make?    $rev$

  (a) A grinding wheel 0.35 m idji6pr d 5fsv( *p8j3zn diameter rotates at 2500 rpm. Calculate its angular veloc *z(5s6pjvd8f pjd3irity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–3;bdq2 cf+hus*b (pzg4c m(9up fjm-t,8). (a) What is the linear speed of a child s*( cm ; c buhzp(tmpuq-fsf4 +d9,bj2geated 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 vel5a+ *oeay2g taocity 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 sp,5/u(q0y3wc e iwmr zeeed 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 centrifuge rotate if a partigf7(qz h*x)rjcle 7.0 cm from the axis of rotation is to experience an acceleration*(fx7rj hgq )z of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to ) zf;t,h.dk x i +0f0lto.ezwe280 rpm in 4.0 s. Determin; elwt+i)to0. ff0 ,xhkzez.de
(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 radiusi9-9 :zxps: v6yuit ix $R_1$ 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 A5 9sbu y2x-8zkyzue 0wpollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter o-59xb2 w0k8yzeyuusz f 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 acceleraq-(xwzxkf4 l 5 yte)8ltes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in f-k yl)w84 xzqxtle5(this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 124)of mwblla 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 rfy p4f bnhzfoz1,0y1 ye b1n2mf+:;6hm dmr* the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.rf mn4 ;m +*bh2b nyo:fefpmz0f161r,hydz1y
(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 b9ntz2u 6r//jkd,qq68 djn zb(xrvk-360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in6nrqnkzdx q/j r8u/bk ,2jbdz v 6t(9- this time?    m

  A cooling fan is turned off when it is running at 850relt x8s*dn); dlv/min It turns 1500 revolutions before it come8sdd;*tl x)l ns 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 revolut4ix mwp)5wj9h ions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have p9mh54 wjwix) 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 revol,* mlp2uf dodix+(t9a utions as the car reduces its speed uniformly fru,mf alopid+2( td*9x om 95km/h 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 weight f iljs:wefqt*e :k34 5on each pedal when climbing a hill. The pedi5fst:4:j qw3 fe elk*als 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 onks.vn(3 c 4u)g7kx lhd the end of a door 74 cm wide. What is the magnitude of the torque if 74(sck3dlxv)h kg.un 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 shown in Figc)d s+ m9,/6rq nozedb aixxb7 +03nib. 8–39. Assume that 3 xnmbn9 6z,sxb d0/ie)c+o+adrq7b ia friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to pty;9k.h f df815 zxggmie;6ethe ends of a massless rod which pivots as shown in Fig. 8–40. Initially the roe5f1kf xz 6g .89d;ithpm gey;d is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine r r3wpess kl1x-q)a d)4mao/p4equire tightening to a torque of 38x m3ap-w/kalq d )44 sposre)1 $m \cdot N$ 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 sphed;pjux b0f. dh i82 wanmz03c3re of radius 0.648 m when the axis zddjxnw. u hca03m3bi0p8f2;of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter gw+t yz4fb.3c. The rim and tire havy+zb3.ftw cg4e a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball0 pl o c;(etqtp-b jha,rya5lg*e *y/- on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Cayp *t*a-tpaec0olby-,/ 5( ehj;lrg qlculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant anguen p2-ue5vk 1g+; cvcvlar speed (Fig. 8–42). The friction force b5; -pve+uve 1k 2ccnvgetween 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 Fig. 8r 0wk 7c,v3dig–437 gci3,wvr0d k about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whosehf08jh d+ a5k4(avr ne 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 9pf: : fd8vfohthe correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg a f98d:fvph:fo nd 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 cylip0u/v e9/kz3 zinzo3 hnder with a radius of 8.50 cm and a mass of 0.580 kg. Calculk hz3no0u ezz /ivp93/ate
(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, wx1 odwo,m0swf +xb 2xp760q e9ajk)h accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven mez(vsv)p8 8ouhq,epkh .5osc) rry-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 andhpz8., 5qhv ()vepscks ou)o8 has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rp36hlv,a3xn h nm is shut off and is eventually brought uniformly to rest lx3ahv6hn,n 3by 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. 8–45lx0pe7f eu .*f accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whk2vqlhrm4(vsfgb3-x )s q .*zich rotates about the elbow joinh*vqk3m-4) qvlbx r(zsgs .f2t under the action of the triceps muscle, Fig. 8–45. The ball is accelerated 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 b qn)wv:2k i(zh2j9vk hlade can be considered a long thin rod, as shown in Fig. 8–46. 29zh2 q hvnvw(j):kik
(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 con7*)agfh l 69yy vkg8m54lwvr qe tgd/(sists 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 th -6fxuzrlp,wd49sks-e hammer from rest within four full turns (revolutions) and r,-p4x z sd9r-6 kwlsufeleases 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 inertia oabb7jx3 h7fbdye2w,hsb,lj ibx )b 9 x7j 6+9zf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqudnh7l*y p((-d- b kf4tnhg:ghoqh 6. se 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 ujg3)u jh5:(u7dl1cq b 4foftcm rolls without slipping down a lanehb ufq 5:7uc 4jlu3fjod g(1)t at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun eck s8f5xda6,6e;mjr.a2g xb as the sum of twoaxg.6 r ,fa xe5;6kjd8 mbsec2 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 7.5byt (xcx-vuceb( 5*eo 17 acw00 m. How much net work i(ct 5vx0ebua-71wy*o xc(ce bs required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wio.pb y9g5kuh/thout slipping down a 30.0 huky b /5op.g9$^{\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 verticallyg(j.q 8bwho:.xf kgqq-x g+s5 on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation ogkbq hgj5+8 : fw-xq(sgo q.x.f energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a t76s1 vfz/k icyhin string in a circle of radius 1.10 m vy7fck6s/ iz1 at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindymi)q8i(2+j4,oxfb g0 qn wnurical grinding wheel of rau4(g)8 y2q mninoqbi+x, jw0fdius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platfoz)pt3 /y-bcjqv yz o18;xaut8,xuj 9s w/j/ nnrm that is rotating at a rate of 1.3rev/s If tv;/3 xo n y 1yaznq/jj/8up8 u9)j-x ,szwctbhe raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–/zi+fzk 2 6-tlvsvch.29) can reduce her moment of inertia by a factor of abou hlv v6zz i.fsckt2/-+t 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotatq9je iouox a 1i*.x,dq p)8bm7ion rate from an initial rate of 1.0 rev every 2.0 po b9*x oje)iuqaqxm 18d.7,is 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 a vertical axipxy : t3sy;05x ww,kcts 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, approximyt,x 0s3twp5k;ywx :cately 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 obr lj1b-*n1fvt:w 6s26 lbkzjf a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earthldmmip:,r t1sf3k9p ug,;6 vw
(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 I is d s qylvwk58//igw 0d4lropped onto an identical disk row/84dw/q0illy 5g k svtating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4:x v q42abfrxw, u6x.u $rev/s$ 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 k .((ixg5vqgoblnw 6:merry-go-round platform of radius 3.0 m aqng:lx5g(biv (o6wk.nd moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angulx k;v.q:b-jm(2z . l7dqqktgqar velocity of 0.8.v7g:2x .j (z qqdtqq bl-kmk; $rad/s$ 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 coll vkkd2;yi.gj5as j4l2apses into a white dwarf, losing about half its mass in the process, and windi j2j k v.4sg2a5dilyk;ng 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 e1d0(xmb w6v0 kdrpmr 0xcess 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 9 g1ndiqko9po,sjk*8r- u0 5 y6bbx yr$ 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 freem4l e, 16)du2wvbzusekvw07 gly without friction. The moment of inertia of the person plus the platforb we6,wkdg47m2)vul0z seu 1vm is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-goe 699f nemhgpmk7.0 h,xzs1 nj3 wei9z-round turntable that is mounted on f0hwek 9h3nz9gex,pzm1 i.me 79jns 6frictionless 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 ropkhujdtio6 ; 4:t5b)z r6+razte rolls on the ground with the end of the rope lying on 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 spool rolls behind the person without slipping. What length of rope unwind ;r:zi u a6z+ho5t6rt4j kd)bts from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the E k3 hl+dms/co:m5w0yj arth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, tream 30ow5shlm +j:dc/k yt the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest g9 zj5vukpcmtd v dj(79r/*;xat 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 w5 byjkvn x17rra,d)7 a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at crvw5y1nx7ak, r7 )bdjonstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disk +5ggd4+che7ew -wswxs, each of mass 0.050 kg and diameter 0.075g4w7+5cedexwhg+ s -w 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 string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whp lrf dx:l .n(8y4f i2fxk57uieel ($\omega_R$) 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 ou-34: zm-)jwxrpgrux fgk8c: sr 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 w:x-r8 cr4jum )px-wkf:3 zgsgould its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storc wlu;da(r4k6ed in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diama ;rc(ud4wlk6eter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a3 fa6d zd0zr 3uv (77rt7rjirxn $H_2O$ 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 horizonj 6 bkjr.s91s.efjs9 c4u+m aytal 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., wedc.7-p9sy vk q 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) the angular acceleration of the rod, and (b) the linear asc7.p9 q-y vkdcceleration 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 vertical lo+t ,45hbg v2x+hnxbly on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step +vx2o+h4g,t lbh bx n5against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road;aj36,bayjd c,la8 f suv3v/ / hyho5b is making a turn with a radius The forces acting on the cyclisyc8d,sah3v3 fau/ 5/jjl ,6;ohb byvat and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins vx;7l0vqwv- y9k)e fv whirling the rock in a nearly horizontal circle above his head, accelerating it from resy; q f vvkewv)9vl70x-t 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 /pj,ahi z48pct5,amp,bw- z m arms as thin rods, making reasonable estimates for the dimensions. Then calcu ap j/cp8 ,m,-,4p5mbhizwzatlate 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 co.fvkf) s wztz6+71j djnsists of two cylindrical plates, of mass)v7j 6z 1wzd+ft.kfs j $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alon/j w5 ri 8(j,lioxb ast/j7pd-g the looped rough track of Fig. 8–58. What is the minimum value of th 7bo r(,jx ajw8-lpdtjs i/5/ie vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ass iv y,d2v olbf19ds3:+g+aaoyume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as+, -s8oxw g yulakq*scspq tog-*5(* r 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 pg*gx(**-5lwcutqq so+sroka,s y8- 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