A bicycle odometer (which measu6u8n -o bvcpz4ry ctq3./ mm.bres distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels./ .qtyzn-mru o6cpm 4vbb38c?

Suppose a disk rotates at constad6i.s-q zq /mt5p3wz qnt angular 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 magnitude of either component/5qmqz sz -qdp.t6i3w of linear acceleration change?

Could a nonrigid body be described by a single value of the angular vel3:dva +o 0eyhhocity $\omega$ Explain.

Can a small force ever exert a greater tor 18p5y4rdob1pvhof 2e v/.nviz qb q6)que 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/ /5s2g 5 q5fyfqk+kcjr.wpw n with your hands behind your head than when +jk5wqw2/.pk5yc5g nqfr/fs your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprocksce0c)ga* 6le.jm8g7 t /qps7tyg y8 uets at the rear wheel and three at the pedal cranks. In which gear is it harder cejy ysu80c7 e.tpa gsm/gl8 g7tq6*)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 jm6hnb3 +l8hs sbmh r(7mb ts:8z*ut*fast have slender lower legs with flesh and muscle concentrated hit+ mmhmsh n6 :(zlbh r jsub8t**8s3b7gh, close 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. 8–35) carry a sr awp l9+z/uo2:nnp+long, narrow beam?

If the net force on a system is zb, hg2)hy3qrn ero, is the net torque also zero? If the net torque on a system is zero, is the net forh hy3g,qb2n )rce zero?

Two inclines have the same height but make dis0mb , *gv;yr+8nfp)za o*aw gfferent angles with the horizontal. The same steel ball is rolled dow0 v apgfw)y*z,;b8o+*m gnsarn 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 anp+5j7dgf g ii m(cz0v8 incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom gfjd +g0iiv( p78c5 mzof 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 axdyy a30mr. ddv,vw9nd ;-hn8 nd 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 greater rot ; dn-3xvy.ar9v8dy h,nm0w ddational KE?

We claim that momentum and angularq1- nsz e d.x:j gr)da)9qt(g .w xf.5ok1avfp momentum are conserved. Yet most moving or rotating objects eventualdv.1(d-)9 gwt.zeag q.)xa5fk sqjo :fnx1 rply slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, howt-8 xydfipj9 1(ihd q.72p(6mhzpafg would this affect thmhi ((atp2d9 8fpz 1hj7dix-f.q y 6gpe length of the day?

Can the diver of Fig. 8–29 do a somersayz4uik i* +q2wult without having any initial rotation when she leaves the+i42wzuk q* yi board?

The moment of inertia of a rotating solid disk about an axis throhgofg60m2t5f j t f2j6ugh its center of 6fj m g5o2j0ttg6f2fhmass 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 s-g5- l aww +(dxcg:abltool holding a 2-kg mass in each outstretched hand. If you suddenly drab (-w-g: wc+ xdagll5op the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicalzqeihy1 xo/ck7 (et;9 and have the same mass. However, one is hollow and the other is solid. Deiye (/k 7xc;he9qzot1scribe an experiment to determine which is which.

The angular velocity of a wheel x2 e+tskho*x (t2/drbt.e t9brotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the /r b*.2kx etsbte9dt2 o(hx t+angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turn*6 ufad y87bmttable. What happens if you wal fuba d76*8ytmk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As nxeep-acv0xbj + 9e*ufnj84 8 ow0qg,he throws the ball, the upper part of his body rotates. If you look80fe g p8v4uj0 e*e9+na cqnxx,w -jbo 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 modmxe . g+s.)w u -d5kx1a3vdqbmentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the se )uxd3 5dvqa.wx1s gbem+-. dkcond propeller can operate to keep the helicopter stable.

  Express the following azjb q c d6:tw4z4y0p1mngles in radians: (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 coincidq7g 8bf lh5m/cad4g g+ence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon mflh7cg5gd8q/4+g b a, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dive8 (xukuq e/it r+r.q.brges auq/ik+e.q ru tbr.(x8t 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 rotaa3sv ru+/8xdbi:7v y wte 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 bi8uyx av:sd3 bv7+/rw lades slow down?    $rad/s^2$

  A child rolls a ball o )nchzb/:f 5adn a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its nz/b5d a):hcfdiameter?    m

  A bicycle with tires 68 cm in dia 43guy- s )aio3xoozeb43pz9y;1 xinjmeter travels 8.0 km. How many revolutions do the wp 3a;s zu9ojx3144bigooiy)z yn3x - eheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its a sb)( lx2,.gekx;cqr ungular vs)x k,c(g.breu xq;2lelocity 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 4.9d tvkfxasz95 (v83aq 0 s (Fig. 8–38). (a) What i 8qa3kxfd9 t5z vs(a9vs the linear speed 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 - +2bnzpyqw +-ygcl je*.67s0jlbk lrm 9ekk2(a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin8m/z (:fdcvuj+8mil i t
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from thev85 r -n 2srfya8mpaobi:*eo3c/h mx8 axis of rotation is to experi 2mni oecb v8raf8so/xyh mr38 :ap-*5ence an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniform .h)tph30uy0mrny 69 ,vwif krly about its center from 130 rpm to 280 rpm in 4.0 s. Detvkn3f6yp0 uri tw)m, 9h .r0hyermine
(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 radiusdtg(e m5 qa t0fv3*dn4 r wpbo-t:cj-, $R_1$ 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/prss yi b vf7tb44l+, aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from n + rtlsibyp/f v47b4,so 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 15,000 rpm in 220 s. Through d(e t,v o:(wile1c.18* mskhbzd.o jz how many revoluti1l 1zs( i,.bjwze:tohd8 m*(d.ve cokons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.ut6mlfoi(rec d7j9 sq3x *c-; 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 flyina09tz:jgq 50b2 /fmwh/tobpn g highspeed jets in a whirling “huma 2hg:qfo9/mab0b tzn5w/ tp j0n centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly 0+o7mb4x q 4pe)1r:vymzcvun from 240 rpm to 360 rpm in 6.5 s. How 04r: 7 pcy meb4v1ovm )quxn+zfar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when i+ cnyurjn),hwvhlsa8 ;/ j2hzo:j ,x8x1e:xft is running at 850rev/min It turns 1500 revolutions before it comes to a r/jfa)s8 8 uczl, hwjx,1:;hv2e+nh n ojy:xxstop.
(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:4e.b m) 1-khau rnihx reduces its speed uniformly from 95km/h to 45km/h The tires have a d4:ihe.a1ru-) mkx n bhiameter 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 revolutih(xn y4pxt- )9uz -7 )iif+oo(sdpjynons as the car reduces its speed uniformly from 95km/(xo-f+ d i 47z ( )ts9yy)nxo-hjuppinh 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 iffcaa;t u :cj1v2 lsn.*i8t2bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a ciru28v tt.iff:scj;i a n*ac l21cle 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 door 74 cm w omepwi1m+4rpy2 +8roide. What is the magnitude of wroe4+2+mp8p1 yri om 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 shown in Fig. 86e/(ekbbz 7sv–39. Assume that a friction/6e7 bszkbv(e 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 th vfkg i-z(f:+ke 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. Czf: -k fv+(kgialculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder 13dkmmxhy hy,w 4.6r6ww m1pi head of an engine require tightening to a torque of 38 4xhw3 hk1mmdim w ryw6y1p.6,$m \cdot N$ 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 sphernbppf-:q v.*he of radius 0.648 m when the axis of rotation is througv p*p-f:qnh .bh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameypl0t x n( tk/.juzevo,hr+j( 9e apt2rk/ 6y;ter. The rim and tire have a combined mass of 1.25jrejpotn9u( ly/ h +p t;t/e.6azvkk xy0(2,r kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a zve7mmxk ng.(d7e( jsx/u6i* thin, light rod is rotated in a horizontal circle of radius 1.2 m. Cal6vmu7ni7s * exex(z/ mdk(g .jculate
(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 angular sq-qw qtnd eyag6(/y6 la6;j/qpeed (Fig. 8–42). Th-a66e6dwa(yy n qj l;g//qqqt e 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 of point objects s lm8 -on37v.zu;cttwixvnvw83wk;m +hown in Fig. 8–43 atxn+nw;ic3w3-8ovvw ; z8tm u .lk mv7bout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose totac:m5,( ,e kus)bw+b.ntw sviyl 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 sc5h3r0i z,v cspn* *fnpinning 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 rhcni30n p*fz ,rv*5csadius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mascchg;f av ;tl42 ajr66s of 0.580 kg. Calculaalrj gvh c;2f;64c6 tate
(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 aq3 1 d1sr:2d kfrikwo3 bat, 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 tangep vzb+22y9d0o vstc4x ntially 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 mep4dvovybsxc 90t+z 22rry-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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatkn /)mi+b u4.r pq31v7kagneo ing at 10,300 rpm is shut off and is eventually brought uniformly to/e)3orb1 7kanq+4u gi.v kp nm rest 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. p3 h.dh4i 9 7(bmfxd mxpsa-r88–45 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 a(i6)h *fg le,cep(be the action of the forearm, which rotates about the elbow joint una,g i6b(hfp(* eel )ceder 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 blade can be consim9aon -9wxg.oum1 j fu.up+8bdered a long thin rod, as shown in Fig. 8–4n bmj.fuogw8 u1 pu99o+x .m-a6.
(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 consi:1i*6 sivz.h lcxs h;eb29eq0yxwib 9sts 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 full turns (revo)1 xi f-yst6fvlutions1fxv)t-sfiy 6 ) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of iner m:/es82sacua tia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 +dkkjv1-db c m ed3v0/nm7z e7+3+ ko:haahkq$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radi e.xnuq isk)c4hu/ 6lk * ;dxn(,ml )fssl)h/xus 9.0 cm rolls without slipping down a lane.fei ))ll/uxkks(hdqms)6u,/lhn*x ;sxc 4n at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eneyx vd 6-mngng5 ym/y1+rqtfj9)rvd+5rgy of the Earth with respect to the Sun as the sum of two terms dgtj/qdxmr g9)+6r+nmv51ynyy 5f v-,
(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 oar j2ouo, ox3(6s5ro ff 7.50 m. How much net work is required to accele3o f,rro 6a(5o 2ujosxrate 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 fromupijas,2zb1( rest and rolls without slipping down jzaibu 2s(p1 ,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 t:o trnhe3gq 7,o 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 conservationhnor q te,g37: of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin st* a+xh-1u,6dkxn-rrqoo w z 5dring in a circle of r-5r,do-ua6oxr+dh n 1* qxzk wadius 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 uniform cylindrical grinding whee7nf0v: qd/t,cs7wdd2 jdr 2tll of radius 18 cm when rotating d, dj t/lr2c:nt0vq s7dd72fw 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 d yxt0 )bq9p,a7iu.ry rate of 1.3rev/s If he raises his arms to a horizontal posxt)7rq0ba,up 9i.y dyition, 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 thex/ sb,t *z6oxn one 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 tuck position. If she makes 2.0 rotations in 1.5 st x,ns/o*x6zb 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 spigw4/ b5tzy1/lugfk 8i;st2lop8 y.e f n rotation rate from an initial rate of 1.0 rev every 2.0 s to a finak8we8ygp2igsb o5t4uf y / lt;/l1.zfl 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 axis+(qetd 1 hq5ujpum .dre;(l4rqz )y. d through its center at a frequency of 1.5rev/s The wheel can bq p.r4 e; 5(le )q1jy(.uudqrhmzddt+e 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 after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 .o 71ypkw2gcr) mhl*n $rev/s$ 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 Ear6hkk:can o4)d* q)*4ng4k-myqkolz wth
(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 dropped onto an lw7q:.64 wkw1dpfb mpidentic q wmkl d.4pf7pb1w:w6al disk rotating 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.t76il,b hhrvmp4) ip m4 le84m4 $rev/s$ 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 centbr;i 7zwi4o kt*mn4-n er of a rotating merry-go-round platformormw4z i;b7int-* nk4 of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotatqc ,)l 2mc3woring freely with an angular velocity of 0.8 2m3, lc)owqcr $rad/s$ 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 eventua:s*-li c4+e 5hygb+ levmmm5 qlly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existm45 +i mgs:l*evl hm+y-b5q ceing 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 in1prligjao( ur10 .f7 i excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 6y33z4ej;x r-eb(7n cdnaer d $ 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 rotat1b:zg akm kg1.e freely without friction. The mk 1z ggkm.ba:1oment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diametmr*.vx i2 t jq(8j bvlhg bgk*t-o1)7ber merry-go-round turntable o r vg)mt( h*lqg-*i.bv tjj12bx78k bthat is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls yti *+a2d4lmcon 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, Fii* 4c2madylt+ g. 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 side always faces the Eartx5ff16 n,n (vln)nuvq h. 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 orbiting the,vn nxnu)f( 6vl1 5nqf Earth.)    $\times10^{ -6}$

  A cyclist accelerates frh7hmdt1l*, qc om rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape o hp2rzccmq-63cu, fcdph)i)cy: 6-myf a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleratiocqy3-mzcf,hmc2)r6pic u- yp:)d 6hcn. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kp;6v p-jy8pjzg 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 tp8pyvzpj6; -jhe 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/u , yc;ak7 d f6hunhkq9u7*ikl5phg0 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 mt43n 4q0vajk5sf)fqu .o8qy3xm xw dl: 6mf,of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-qf3 x4.d0vqmmw 4ffa kyo)su:x,3jqtm6 l8qn5uarters 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 automobile is for it3m6-7gv6 ;an jmd irrk to use energy stored in a hi n3; amdg6vkmrr6j-7eavy 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 “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 illustratlf/wj.ak/ o8o es 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 on1 cri*fqel0 e8 a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we igno) 9uq5 a cpq2t5piw/itre 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 acceleration of the tip of the rod. Assume that the force iq9c pt /2p5a5utqwi)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 verticaly 7kmxih5f64 hjnz e3.ly on the floor, and we want to exert a horizontal force F at its axl3.zin4 x67 5 eykmhfjhe 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 s:yc: 8 o,4p/ ckdbsdzh0f1l mipeed 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 forcel4ic8 p, cz/0d fsb :1dkmho:y $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 ro fb j2c dv9zo)w-k.wel-l0p6 qck into a sling of length 1.5 m and begins whirling the rock in a nearly .peqoljc0 9 6 wlv-wz2d-kf)bhorizontal 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 bod7 n0e uzsiv.+x bo l8ma4vi 74lr*,pney as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular spea0limue+4p vile,vos 8rbx *7n.n4z7eds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consisaqttg vj (8j7;ts of two cylindrical plates, of j g7av;q(ttj8 mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 thc0;tgp 579 koxhy1v6np /utyje 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 highenuk/ v7pp6 ht tyx0g;5cj19oy st point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do j17npk;gku /unot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its + ,jz/bpnu p f oidoi.q4:;4jhspeed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each oj;di+u4 j nbp,f4h.z: q/poi 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