A bicycle odometer (which measures distance traveled) is attax93.gkciu w 7k24pth9kbfp i7 ched near the wheel hub and is designed for 27-inf2h7wk bki pi c9x49tpgk73u .ch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Do yqox3x)hko a:au 7wjx/a q;- w8/yq;bes 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 compone3x ; kbo/u-oxxhaa qw/a8)q;:7yw yjqnt of linear acceleration change?

Could a nonrigid body be described by a single iq//4 7 yezgsoqqh0f(value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thaj .h 2emo6ht2u-j+)gc bjr lr+n 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 yo6d9) bu-i(khlz 8xa 2 vmu7gjvur head than when your arkm7hb 62jd9z- xu 8) v(ilgavums are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has 1gy8lxp29 f7jkuya v;yqby86 seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a smb8 klvy19 6qypyjfu2gy8; x7aall 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 se 6 5)ya.orxmwe1xl0bbc.z/a lender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain o6/x.e5r.emzawb cby )l0a1 x why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35)t3jg5v2tlmq x-p )) ud carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? Ia .eag1.5 akenf the net toa..egkea5a1 nrque on a system is zero, is the net force zero?

Two inclines have the -uh5h o1la-twsame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the booa- 5-lhtw hu1ttom be greater? Explain.

Two solid spheres simultaneously start rolling (8 rfeq 7wn co/d,dj*fo-r/e 8jfrom rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Whifce/r, do- 8n *7woj d8qf/rjech has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same rad e-/gs*(cwxb0q he91 3yg trynius 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* -x tygh9cb sneregq/3(0yw1 bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are cons gh;x 3td(e/qcerved. Yet most moving or rotating objects eventually slogd;xq ( c3et/hw down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouldc7zbrk ii m.3: this affect thzr 7im i:.kbc3e length of the day?

Can the diver of Fig. 8–29 do a sommxf,c x)n*f0s5 /p2ztfb dbx4ersault without having any initial rotation when sf)x 2 5/pb4, ffnmsbztx*c dx0he leaves the board?

The moment of inertia of a rotating solid disk about an axis through its cx6 ri xwy1)n;lenter of mass;nl )1w6ri xxy is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-ks9exc)t3x u5 as- /uybg mass in each outstretched hand. If you suddenly drop the masses, will your angular vel 9ec5yxxss/)3uba-utocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one i);op ej,h (nabcef8d; s hollow and the other is solid. Describe an experimeeb; n;hfoedjc,)p 8a(nt to determine which is which.

The angular velocity of a wheel rotating on a horizontal axl;bhzgv5 z7 -gte points west. In what direction is the linear velocity o;z hg7tgv5zb- f a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large mfi7 8m3n(3vb,qvku t freely rotating turntable. What hanvibt33q mk(v u8m7f,ppens if you walk toward the center?

A shortstop may leap into the air tuj65k5k kl,o y /2yhaio catch 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 legsyhu6j2k5ila /yo, kk5 rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of ar h:de;e h- oul7oj ;i6rp-r1 ,z/iyxongular momentum, discuss why a helicopter must have more than one rotor (or pr/roro7p ;z i--ud,eh1;xyj el:h6o r iopeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angled8 ;ra vouqkqi .+b3g/0ybj9ws 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 coincidencewmjj ;w. t wums-osn;f+ :yj5:. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and jn;-m 5+uf. owj :tw;:wsy msjthe Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Th,3f8/ )o pm idoqqm:1qehk812hrlk doe beam diverges at an angleeqmdom11hq 2 88k,ohofk d:q)p /lir3 $\theta$ (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.coh74ilgzg. ei; 2x2ym 6nif+ When the motor is turned off during operation, the bladez2i;heg n4g.iofymc +76 xil2s slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to atp*mq,hbgn8( lrech138yj+ inother child. If the ball makes 15.0 revolutions, what is its diamegbrhtjqe 38n*m1 (hp8ciy+ ,l ter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hrm2lgj6/a* )fi7 l.z)e jv;hpq xe )myow many revolutions do thelerjx e q)v plh.g)6m7; 2*/yz aimjf) wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at vy b 6()jvzkwf)n8.tv2500 rpm. Calculate its angular veloc v6vt).b )kvyn wjzf(8ity 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 o36yf td7,zi3icg/agf;kysu d6 -7c g4.0 s (Fig. 8–38). (a) What is the linear speed of a child s/go a6- dccdfg7 3f guy zy;ki6it3s7,eated 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 t;o u 5sr(ays/hhe 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 of a p6p*e o lqrq6o u,ag*c)oint
(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 r/i 0f jkwg:*y; f8yr.idey +yhotate if a particle 7.0 cm from the axis of rotation is to expfy8/k:g*.hi +0i rjw yf y;deyerience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about -gsyw4 tfupv/)bo7z e 74qtc0its center from 130 rpm to 280 rpm in 4.0 ft0bzsc-7yo/ve7w)tu 4p4 gqs. 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 radiukjwlgsw h+-+3 s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacenco(mk /*l 8 fwpl2b.jcraft 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. k(/8co *2f. bpmwnl ljThe 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 -d 2z.eantpim*9:y i56xu3w7jg )lfd 4hudx nfrom rest to 15,000 rpm in 220 s. Through how many tg -nya4).5 *hfmlndji6 xwddpi :2uz 7xe39urevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm i txsd+t (j*y+un 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flyio(: ,nb(afvfp8 xku/ ung highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching itbu,fnpk( vu:(xf /o8as 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 3uywv*ae9w 6ndz,l3 /n60 rpm in 6.5 s. How far will a point on twl3nz9 v wu,dn*e a/6yhe edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running v*4urv 78b7ulr :qer qat 850rev/min It turns 1500 revolutions before it comes to a 4q8buvu* l:erv r7q7 rstop.
(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 its speed unifor+a, zx4j (rx.kyfs28a y(x-xl hqj2ds mly from 95km/h to 45km/h The tires havs a (4.2(arjzy,xs-xxyf2+kxqjh8d l e 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 f-q4xs w :y,6/ckpve 0e upewv,.5 lt)svi1 terevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hav vq0kwfevs:eye w416u lcp,p5s-, ).evt /xite a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal whet9zgkljl zwd13-a3 gy s4i 0n8n climbing a hill. The pedals rotate in a circle of z3-l49y3az0wjtk sdl18gni g 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 lp8pwnu98p9;lsge00fhu x z z/c.b+s end of a door 74 cm wide. What is the magnitude of the spn bc9eu 8psw/ u90;g8lfphzl xz.+0torque 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. 8–39. Assum+ak9) c.r,xhmisgc dcf* 71l qe that a friction torque of 0.4c)dhxf7a *c9qk,clrm i +1g.s $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends .vp 80ev(lkno iei,qvi9 /1hnof a massless rod which pivots as shown in Fig. 8–40. Initia9i o0k1/iv(e.lve hipv8qn,n lly the 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 of an engine require tightening to a-to0vyqpgy.(,3 b rfn torque of 38pqg,vr.o(f3 by - 0nyt $m \cdot N$ 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)cmzhfnbdf96z57y9il 4gt fm(9i(sp.8-kg sphere of radius 0.648 m when the axis of rotation is through its cens h7(py9cf9m 9 m4t gil65znfzi()dbfter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diametey t3v1l08ha iu s *xzth3byv0,r. The rim and tire have a combined mass oft1lh0z , vaxvy8hb t0*3s3u yi 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 thz nnl /r947nqbin, light rod is rotated in a horizontal circle of nln q9r/ 7znb4radius 1.2 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 potter’s wheel ,yevx wi7 j4cgt.k;4urotating at constant angular speed (Fig.uk c 4;.v4xg wj,eiyt7 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of tha cei8wcikrqm+ 3-( z:2ugzn4 e array of point objects shown in Fig. 8–43 aboqkiz4m:nc ra+2-u cwgz(38 ieut
(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 total mas ouv8o5 vc4jg e:oq.)zbue5:ls 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 spinn)yew-pxkb 2: r0-f-9b ala nyming at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–4-yp)a 2feb rynka 0x--wl:9bm4. 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 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 massd/m0y2fs d,lc /+h,1meqjwuh of 0.580 kg. Calculace hd+f,qum/hl2sy0 /1, dw mjte
(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 batpqf- 5hqmx/ i20n7j+mi7lmi e, 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 merry-go-round and isu 1(tbc)efnd 5 able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the cf(u5 )1dbtnemerry-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 rotating at 10,300 rpm is shut off and is eventually brought lhc/;m w jee-li +*/ 0iyshde5uniformly to rest by a frictional torque ofmi;hi el/+ */j-w 5cl hs0eedy 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–f *k,p;qbkxzi*s;;ia45 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, whichfklvo:m.3t-g9-v ys )*vw mds rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is mvwtyo 9vk)s-gl:v3.*f sd m- 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 considered a long thin rod, as shownqb ))f m-5zc,gsvc6-aq ra* v0havjb1 in Fig. 8–4vc-0ma)cbb 5 *qrfav,qv-gz 6h)sja 16.
(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 consizdvx.2/r9j0q/,6 io bfjng w5-vehu h sts 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 (rev-zg :bgq0y) .r.dg:p(scfdf qjtej:0 olutions) and releases it at a speed g::-dyc0:rp jb.j0sz e (gdt) fqfqg.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 inert909 ukuivv 5gwia 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 torquev+g lg skss cct kpy1*s8-x699 of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down as ph-/;ly ;3etpbfybkh2m, a2q-uc :w lane am2b pfp;a2h- uys c-,bl/t3hwq ke;:yt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of theqw16mhb ez k)5h*ykm 6 Earth with respect to the Sun as the sum of two termsmbke 6)zh1hy qw*k 5m6,
(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 fr2yu d2k1 hr;kg and a radius of 7.50 m. How much net work is required to accelerate it ; 2dryuk2rf1h 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 fr/p (q gmb6d7bph 6ym: ;ezce cqb:dm27om rest and rolls without slippie (2mzdqc7dmbg h:ycp p:6b;7em/b6qng 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 fae wjf sg6n)/ :s6uryp(ll and its lower end does not slip. What will be the speed of the uppywr fu/:g(jp6s 6n )eser end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the-lm up6b )nftea)sfn; -k lc+4 end of a thin string in a circle of radiusfp+utac6kf));- -be l l4smnn 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2g,rvrloi 9(.sgd(s-ny s2 m n(.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating a2inrv(-grs(.dml(ys9ongs , t 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at u.nib88wi o1x* 6gvbm his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his armn 8 b1mvi. o*68iuxwgbs 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. 8–29) can reduce her wtnfepeh. j2 9r.yfrz0hn6d 70k7k y-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 wh2 h n 6.t7kyry7nh wkj09.p-efd erfz0en 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 rotation rate from an initial 5j7i ms+7r4o0h g g jw2zr7gxjrate of 1.0 rev every 2.0 s to a final ratozj7gx7 m jhrr5+iw 47gg2 j0se 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 vert ou .ks*qg)-3p7hlvxa ical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wv)pqu.7*gsox3- hl k aheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skaz 1:);c 0tnmaw r4wp.zm(s niyter 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 angula-t) (wet8fxpohao 75uqn 1g djfm67n7r momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is pyxnoa;j 2ke)5)2mph dropped onto an identical disk rotating at angular h);)mn22p ypoja 5exkspeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 0*crx n x40aad3lh+9 95sw* y)yqn fedpiayy)at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg - 4tdengn- zl0stands at the center of a rotating merry-go-round platform of radius 3.0 m andg4n de0n--tz l 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 angular velocity of fxm qwc2:4hm *02:4*wh cfxmmq.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 a w)tpba4x:0yicoz-3w/tr3 i 0henfpg ) hite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the xca tg- )pwb n40iif 0t3:ezyphr/o3) 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 exha4sn:yam s0r6vwnaqlqj v . (t7c1+ 5cess 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:sz xtiu6ql$ 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 kt 6/d36bj3ehbm it8h o /min(rest, that can rotate freely without fricdj/n6t8m/6 (hobeitbim hk33tion. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diamete6im z0 aq -hmf9hymtxdj3 -8wc57p,ahr merry-go-round turntable that is mounted on frictionless bearings and has a moment of inh m7-pi0m q 9-azx,cadj 86wht35yhmf ertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the d 0 oisq6b yx+jqt325+glxhv,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 per+2xstj5oviyd,b q +x gq36lh0son 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 favlkc f-x9rom1kt;8d, xqym(m *t;ny9ces the Earth. Determine the ratio of thoft*;1m8y (-xvxmk;k9dlyrt qmc ,n 9e Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest /37g7 bt84 0 tec+ jncis/xlygx)fibu at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquwztq).n 1*spo fimp34 ires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delwzpp4o.is t) 1*qnm 3fivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindr/zwpi6h )db q*7u5d/sepj 2 bwical 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 db5 uw/qh isb7dj)z*6ppw /2e 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, honwg (l kq-v3 a*5ed3yb c)+yqlw is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were r,udepzw8plop+k ;r 4/otating 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, whpo8 p;l ku4zepd,w /r+at 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 4j.9xud d w01ac9m4tyucf)w jit to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 t 4y w)u0fdwd j9cj9.1xc m4aum 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+wz kwy f t9dwy68kd;: an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed 3mlbw ;g,g62tx:i 6 wtvvabm4v=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 M1 hgc5ndpudevl,84fo, 6+erv1) t qm f and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–5485 1 udpdvqth ,1,fcnvm+4elf6gre )o . 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 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 xpwvqxcx1 09d i.nj,.floor, and we want to exert a horizontal force F a,. dviq9xwjnx1 pc0x.t 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 speed v=4.2m/s on a flat roa a2pv)c6go*thfkhl rfzl. :8- h.ab2 ud is making a turn with a radius The forces act6cv)azl *h2h2pfu-.b rofathlk :.8 g ing on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 c ,y7bv4v ) 2jyy3xfyb4lmst;m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest tvb t4 yyjy,7 2) b3cvmxf;ly4so 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’is6q:6 x4oiok 79:* w rfper ln.yff-qs body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly af.l fi wrqeoi94:y6*oksr -pxf: q 76ngainst her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofa:sd6 l avw(br9z7(zh mz(aa d9v:7wzh r( 6bslass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 trzdrzlg(b 83,f nz96 nback of Fig. 8–58. What is the minimum value of the vertical height h that the marbllr3(8ng6z zbb 9, znfde 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 ftne5* r llt*,i8c q/wassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions asjot2wyon03z 0 sx0h/h the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wh3/0nw2tzoo 0h0 xy jsas the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s