A bicycle odometer (which measures dist.id3w:;q,umaxa 4h utance traveled) is attached near the wheel hub and is designed for 2ud t : xma,i4aq3.w;hu7-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rtft)o-4g4pc2 yciwll( xx a*1 im have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, wla g2x ctl-f* p)4x(coi41tydoes the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be descr tvkvhnm/qd i0pz1xg7)d9nl)*jx 0s4ibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a gfbrht,-m)w /xreater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind 5b(klc: *n*8 q d 4xjc)ijzwknyour head than when your arms are stretc( *j iql)n *ckdkx4bj :8wcz5nhed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tb.i1p d.twd 3ehe pedal cranks. In which gear is it harder to pedal, a small rear sprocket or aetw di.p .1b3d 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 0i;og fbhm76; dzyp5hable to run fast have slender lower legs with flesh and muscle concentrated high, close d;oy5 6hhgmp zfb;7i0to 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) 3v:j4xj+g ndu oboh 3f9w7dm-carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If025s tx (ews(zay abh( the net torque on a system is zerw5 (szebh(a0sa x 2t(yo, is the net force zero?

Two inclines have th s9zo:*pe8l16gx.grac jl f o;qry2 c-e same 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 bottom be greater? 8:1rp9cegrol;6f j-z.g*sc a yoxlq 2Explain.

Two solid spheres simultaneouspz ,r0t9 ffdt1ly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which0t9,zt df1prf has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same rqz 3ergil tza;+5g +n:9w0lpdadius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotatg q3lw05p 9zg+:ne+ldzia; rt ional KE?

We claim that momentum and angular momentum are conserved. Yet mos ki *gm:;lewk f1ua/jq(tj g17t moving or rotating objects eventually slow down and stjmkgjl/t;:gwa 1f 7q( kei1u *op. Explain.

If there were a great migration+)jeilw //lnj3 l 3htr 4wffd4 of people toward the Earth’s equator, how would this affect the length of tiwr3w4jl /nft/) +lj l f4e3hdhe day?

Can the diver of Figfyr4n1;-rp9 7yw ww iwe1 (tid. 8–29 do a somersault without having any initial rotation when sh4f7pw1y -1ry;nwe id9 wrti( we leaves the board?

The moment of inertia of a rotating solid disk about an axis qm 7e8o.+(ow pivxmg:through its center of mass is7.qoeow gx8 +m v(im:p $\frac{1}{2}WR^2$ (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-y g -* wp:hr 6xlji8av+uh(;ar- xc9alkg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity inaxc:lw*6pjlrrg u(ia-8; -x ya+ 9vhhcrease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow anpc 4ii8p*v sa(c d pm8.lq2-)meqxo,qd the other is solid. Describe a m, op*pi dvxc2mi 8l4-ea)qp(qq8s.c n experiment to determine which is which.

The angular velocity oq vlvxki/tvf)y y* .6 t9kdj+d+tq;qm /t18hpf 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 tangential linear acceleration of this point at the top of the wheel. Is the angular spe t k8i69d/1.l q;t tv++yyvkq vxq*)/dft phjmed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turn4diiw * -qs+oketi g4(table. What happens if you walk toward the centi-ioig(q4kew4*t +s d er?

A shortstop may leap into the air to catch a ball and throw itmh n.gm:5pm 2e6e l4aa 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 rotate in the opposite megh m2a.l: n4me6p5a direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angula:4b) qrzawcd nre28q 7r momentum, discuss why a helicopter musq azw q:c28 errb)4d7nt have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglesm*6obh 2 vh 5tu.lcp3k 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 coincidence. Calcubqkdxgz a0zk+;4tf 8 7182ghlqha .up late, using the information inside the Front Cover, the angf dpaz71qzb2x8tgakhq4 .h8l0;+ gk uular 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 Earfuo/ qmqq7mq/( h8;zjth. The beam diverges at an q/ /mhjq z7; m8fquo(qangle $\theta$ (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. When the motor is turne :odn.1g2 uqz7d(kit4y zr -jdd off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? g4 tz.(27 :ud zk-qrdjiynod1    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the babia0fo6 )ejv 7- zh:clll makes 15.0 revolutions, what is its diilez7-vc a6ohf)0: jbameter?    m

  A bicycle with tires 68 cm in diameter travels +(+xi :yqzyeo r 8(wdi8.0 km. How many revolutions do th+yx:io qw((ry8 dize+e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diame3osol) q* 0.2ucq bkcigjs3-k ter rotates at 2500 rpm. Calculate its angular k)bs-.0* q3klc3 qsijgoo 2 ucvelocity 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 complets /fzdw0)vs 3z 3ls3yte revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centes3dszfslwz0 / v y)t33r?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Eartgp*jz)2/ sklpu hrzz : ,i34ldh (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofrxu 1f;dqxuo/ o1r1*( 2ju j rmszx9j6 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 particle 7.0 cm from the axis ,zuwr gf -mpw7.ls8 5hof rotation is to experience an ac8slz wm, wg5pru7f .-hceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c*v(magevc8at 5(d *bk enter from 130 rpm to 280 rpm in 4.0 sk58v(**teb(gadcv ma. 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 radiumy gi 2t8d6:sms $R_1$ 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 Apolf; )k3e r4;u:fbdxm pglo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, tkg u;fe3:)4m rfx db;phey accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rp5/o5hynjsly nf g.y)okxm*+hn ;39tl m in 220 s. Through how many revolutions did it turn in this tnln)nto*l fk +jh; /y5sg x om9.y3yh5ime?    $rev$

  An automobile engine slows down from 4500wvgxzt24 f,+ hfg v+.t rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying e6n7yll0 1n;w ad*rl*bou p2ghighspeed jets in a whirling “human centrifuge,” which takes 1.0u0;le* 6gyn* pd oa71wnrb2ll 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 ut wi-x d17;cerniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge 71rex ;twic-d of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 150oi7 evvx,. 1zn0 revolutions bv.i,e7xzo1n v efore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fmn;q3meel 0te9+;bx i rom 99qe;l;mb mneie 0+ tx35km/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

  The tires of a car make 65 revolutions as thej /q ngmtv g+a3i(4lw9 car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter l+ g/v 43(j9tgmwa qinof 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 (p07vmsez w311 o x/eez8qsxfon each pedal when climbing a hill. The pedals rotate in a cir/e qz7m(8 0 s31zfxx1esewvopcle 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 ofio,;6n(+ljx1. wms*mdg bgh v a door 74 cm wide. What is the magnitude of the torque if the force is exerted gs+ .g,m(jl1w vibmo6n*; h xd
(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 t 7b5.+ z3sy0+swj 5i uogvvyethe wheel shown in Fig. 8–39. Assume that a friction torque of +g3o+tes i5y. wvv57z0syub j0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends oc0ogutcda. s0g--2nvf a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate th0s.ac ovg2ndtc- g0u -e magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requir3qme4,n4, ldumcrz /l e tightening to a torque of 38 ,umc,erld4l n4m /qz3$m \cdot N$ 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 inertgz yhl x4((*mcia of a 10.8-kg sphere of radius 0.648 m when the axis of rmxhzl *4(y g(cotation is through its center.    $kg \cdot m^2$

  Calculate the moment of ineek il0g2 ;l+xgrtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combg;i2klle+0xg ined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end g(,v+ 6j* x3n;u fl1bryed hgm5ol8ia of a thin, light rod is rotated in a horizontal circle of radius 1.2 mi ar d5+gunfy*em8 6h( lv3ob1j,;xgl. 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 rotaio,l5pf f8f+nting at constant angular speed (Fig. 8–42). Thi lnfp+f, o8f5e 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 showni .3 xemr:)npn in Fig. 8–43 abmn p:3eir )xn.out
(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 ato(0ion .nsilc4 ms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spy tx(m bsvq:4u:q fgi-q3im 9+inning at the correct rate, engineers fire four tangential rockets as shown in Fi(vq+y tq:xfi miqg43bs m- u:9g. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifor4y gpfnm;gn )1fx+7z)s0wv a qm cylinder with a radius of 8.50 cm and a mass of 0.580py)xgaf;f7nm)4ns 01+q zg vw kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating i:s aa h;ur;e2)bi* hslt 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 anv2zk(j mz8q(c d 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 dis(qm(c 8 vkzz2jk 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 it5-w* id b5/pe *ehypds eventually brought uniformly to rest by a frictiy**ebd p5 d5ite -/pwhonal torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ballpy d c2r ahs.)-4y4vm.+-5tipvvmtr z 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 f,: qed/krrys;*-w 6y-nvvkf (pe)st thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fro :syy dt-6vpker;)v(k ,-/wr sfe* nqfm 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 nustqlf g, ,e/o65y7l3 qs0icconsidered a long thin rod, as shown in Fig. 8–46. y7 6nt/i5le3u,0ss,qgcq fl o
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mass pvo fvm;j, ,pfy: g 2k438n3byxnb.wles, $m_1$ 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 accel;kvh1/ lakme +erates the hammer from rest within four full turns (revolutions) and releases it at a speed of+ emk1ka;v/h l 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 momeny)cttd 7u(xqkueh k* bp6+a)3t of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tc.*n0tg e-ctp c6 4qn68m4pkz0aztd aorque 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 kgj 5 5athpm4q)e and radius 9.0 cm rolls without slipping down a lan5q ht)jae5mp4 e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofj*)j t4njjsa . two terms,)nj*t j js.aj4
(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 7.50 m. Hy(, b pucf.e.rv xdr0po,h2h 0ow much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutiocu,y 00f2 r,xvh.er .b h(podpn 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 h6w* yibu0qz * le2xt9rest and rolls without slipping down i2*b*hx q6w tyleu90 za 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 verticanggu xs+g-ytk j,1x4 2lly on its tip. It starts to fall and its lower end does not slip. What will be the speed of the uppesj2,gy1 +4u-g tkxgxnr end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum. xsy0jn xz/b8.kvb e, of a 0.210-kg ball rotating on the end of a thin string in a circyj b,kx b0evxz.sn8 /.le of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular msjx8w ib.s8 55u)si 9dept zu1omentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whedxi8)sss etuz1u5 wi8 9pjb.5 n 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 platfca.o:pylq87x d1m,r1km,o v x orm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizo1p o qx ly,,.cv1mordkm:87axntal 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 Ft9nap22 aibat*zt5(h 5 zqik;/f 8vr wig. 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 2w 5/2z;ht*a kqa8ivabtnti95 p z( frmakes 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 rotation rate from an initi3vm rj7)m0lrya43br oal rate of 1.0 rev every 2.0 s to a final3mj0yrm4l r3b 7o) rva 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 through its center at a freqz)jshb 4/r uwl xs0vnw892;rfuency 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 c h9/2 v4j)w8lr usf0n;rzwb sxhunk 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 mome;u tnqr0lkjpbvvotz/( 44 e3-m3l5 pzntum of 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:y xf fc6tx6p+xra:( *rw8u z-rp5iiv 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 dropped onto an id8/l si. qce)xjentical disk rotating at angular speed8x/jql ei .)cs $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 9wt6hd (ucb/p$rev/s$ 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 rotatin4whdu/gyq 23 cg merry-go-round platform of radius 3.0 m and moment of inertia 920 h c /3ygwd24qu$kg \cdot m^2$ 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 angul a2drbeqb wg0v29 pk3o+ fkz24ar velocity of 0.8 +f229ka or0 gqpzvkdbwb 2e43$rad/s$ 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 collay jc)c7/ce4 gopses into a white 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 nearesty 4c/o j)e7gcc 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 involv8x v)c. vaa,w z-mwlf)y)n m3ne winds in 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 -o e.l 1j,yrsf$ 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 u u /b.;9dmvga*43cp1tqoasi, initially at rest, that can rotate freely without *p t1/ 3m9ud4. qscaubgioa ;vfriction. 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 diameter merry-go-ryg(o 8pnd5x6 sound turntable that is mounted ono(pgs8 dxn65y 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 on the ground withitma ,*g pmuuyec)ih1*2man; f+ ur +b)-zv2z 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, a z;uar+- m)v pu1y *mi+en)g c*2iu2fzbt hm,holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side anjc.vvda, g;1k8w o1ulways faces the Earth. Determine the ratao;v,uwk .g d18jn 1cvio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 x e1tb9o c *+olhx2*num/$s^2$ 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 obab .wlc*(wx 9f radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the l* (. bwwba9cxmotor.    $m \cdot N$

  (a) A yo-yo is made of twc 7b8a4jxu.gn o solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin sx4cajg .bu7n8 olid 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 ot0z-z.ecfjw * f 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 massjd10eh-j vie ).f5xzi 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 would its rotation speed be? Assume that the star is a uniform sphere at all t-5jf .e1)0 ezxdvhi ijimes, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-z k*t-glr a,qu76z 8eppollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical fteu6 *q -7,gklzpzar8 lywheel 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 illustrates a* zlc/81cowc mn $H_2O$ 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)vkmb4/ f m36j (cx+fkh is rolling on 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 f.zk 2bt7rmm7fl f/f1jreely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume thaf klr t 1f2z/jmm7.f7bt 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 floor, anbe.mgl y40;8dce c,gl-wkxn 1d we want to exert a horizontal force F at its axle so te 8 g.g1-,4mc clnby0wxdlke; hat 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 road is making a turfjsxd 6y28 69ub ss1min with a radius y9bjuxm62 1 s8si f6ds The forces acting 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 6*uw6ba uv)wl 0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle aboveu6awb *)6uvl w his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods,2 jbur98gkm0 a 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 againj 82k 9bgmrau0st her body.   

  You are designing a cl*-jhc/fou(h( i1 o3ilx)8 cmvbo jts(utch assembly which consists of two cylindrical plates, of mio3oc(b)1 lj foxm hct v/uij8((s*h -ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig.izmbb-u *m0yl c2yji6l0 w );x 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the lbjy;0ii6ly 2*wu0 bzm l)-mxc oop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not o+jil ufjj00oin(ni-p j+da 9 /p4*qsassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions bf6omoe 0x3xh,08 m 8)r,d+ iadyyuzxas the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was tmxid30xm u a, 0of,o+)yedb 8x8hr y6zhe 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