A bicycle odometer (which measures distance traverr (x wyyt)9poyxux+k2x8 dtn k 3n*)3led) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bi x* tutnk3xo( rk+py)x9 )8wy dnx2yr3cycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poum7f 2. bpr3sfint on the rim have radial and/or tangential acceleration? If the disk’ss7bfup23 .fr m angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a singl( l (yf*wh 7+7yil2aryibxugfvf/x30e value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expkuf /z j4 ncftku7s /63qnz..dlain.

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 your head than l2xy; hk dynrc +;5r,twhen your arms are stretched out in front of you? A diagram may help you to answer t yr,c+d 5l;hk;ynrx2this.

A 21-speed bicycle has seven sprockets at the rear wheel and three a z vvduwxn73k6l. ;4hmil+q; mt the pedal cranks. In which gear is it harder to pedakvw. m; 7;ul v3il 4xz+6qhdnml, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs w(fce rh+gq-bezz 6d9n7/0lud ,yp z.aith flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of 6+d0 zzcr. hpguqaez(fybl9 n- ,d7 /erotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lyi- 9he:cxj w)-usc/long, narrow beam?

If the net force on a system is zero, is t 4p8cj ,dcu1xuhe net torque also zero? If the net torque on a system is zero, is the net forceudp ucx,18 4cj zero?

Two inclines have the same height but make different angles with the bwck lt6v/g6u,6riysdmc6 4 2horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the b trwk4,62/svm 6c6cl i6dguyball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from re*yz b npa,gn06llr(bt 5gee7 4st) down an incline. One sphere has twice the radius and twice the mass obgynb,peeg(6n5 * 0a rt z7l4lf the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same msy+mfcnl qot hs,gu92nz;a2y3: , -mradius 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 energymn qfgc+s-o:,muha;s9t,yzm2yn 2 3 l at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momv f c8;zyv gl;7j b*d fufeq/f/v9)*rsentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain;jzl /*f)f f/*;yf q eu8rvd bcgv9sv7.

If there were a great migration of peot ly-(7boouppn wzbxy z* 7ht+-0)hv+ple toward the Earth’s equator, how would this affect the length of the d +xu77nott bp pz-b(wzh)-vy*o+h 0lyay?

Can the diver of Fig. 8–2of2ego*3zram rvr)k7fj-uqy)t -l /:9 do a somersault without having any initial rotation when she leavesk/3qozjotl *-2y 7vrur f er):afmg)- the board?

The moment of inertia of a rotating solid disk about an 9ctjfbd jx(2,pz.fx .axis through its center of massj ctz,xbx. .2(f 9jdfp 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 k;tawn, 5jeg)rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly j;enag, t)5k wdrop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is 7: (to72 cvxucg s0dzphollow and the othe7v c ut o(gp0xzc7d:2sr is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotlez4 pb--*ysu ating on a horizontal axle points west. In what direction is the linear velocity of a point on the topl*bz-ye -4usp 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 freely rotating turntable.m v)uwt36x1tzq-czjq +s 8g e/ What happens if you w31+6-q)q wutjcvzt szeg8x /malk toward the center?

A shortstop may leap into the air to catch a ball and throw it quim;4-xzxqioe xzik *zj z1-ox:hc6 46hckly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips anozmh ;4qi:x zkc1-6zx *xi hozx4e6-jd legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conser1rjithf-d- 3n7iq ;wjvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.1 i-hn3fdj j t;r-wqi7

  Express the following ang.ww(y--kb-s ;z8me yvcw 2gedles 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 Earc i+ p8:qg(wbmth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earmw( 8 cgqbpi:+th.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 s *ko7t,w+ 7+xa rbqidkm from Earth. The beam diverges awqa+sx+ di,kt 7rb*7 ot an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a ra-hf /vn 7s/qipte 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-/q7ph s/f vin blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anohfy8-f 4exp047hxvsqther child. If the ball makes 15.0 re hs8xef0v -4xhf47pq yvolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revfw+(es bxv64x.xj 5 3fxls 2pvolutions do the +xf x 2vwpj5(4 v.6 3ebxxsflswheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatevk5fch7 k6 )lxs at 2500 rpm. Calculate its angular velocity in 76xvlckk)5f h $rad/s$ $\omega$ =    $rad/sec$
(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 c8.g d(n,y abd ewcd)p0omplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centen adwg8.c, yeb pdd()0r?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity oealuwymz1 ay1w.k 1,0f the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sped7b ti *t 8.hk ovl8)bv:wpm9oed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from *6ebhee,j q2gthe axis of rotation is toq,j 2eb* hege6 experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unh8l*t lflx)q w6+w u(yiformly about its center from 130 rpm to 280 rpm in 4.0 s. Deteyl hlf lxqu)*6t8w+(wrmine
(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 radiusclq ,acpj.95s $R_1$ 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, astr9mg; hjc,gxd5 onauts 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 no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thoughmj,gh;cx5d9 gt 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(0 +7xpi3s y 0g0mvgei+spv tx 15,000 rpm in 220 s. Through how ++v gv0xs sxpep7ym30i0i (gtmany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 120 y)ce3n55xbhq0 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 highspeed jecqvx9q6 nrl.c0j z72 4uic .cnts in a whirling “human centrifuge,” which takes 1.0 min to turz 79l4c cx u0cj r.vinnqq6.2cn 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 from 240 rpm to 360 rpm in 6.5urb9: 8c,hwpt x8q3yo s,cu8t 3:8o9 rxhpwb qy. How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It rwjm)+;+;* ahiumkemk - zm-xturns 1500 revolutions before it comes to a stopmm mxj-z; u+khi-ewk mr;+) a*.
(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 makeqcin iy,.ar 89 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0 iy,ac8qnr9.i.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 the car reduces its speed uniformly fifrbibp-ih ):; 6z9sv rom 95km/h to 45km/h The tires have a diamrp ;isi-h 9iz:6b)bf veter 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 weigh yja:ypi811 cat on each pedal when climbing a hill. The pedal pyjyc8i:1aa1s rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. Wh /zux n4flbmg /k*df ks/ gpg.)g)-i6vat is the magnituf6f *-/bl/dg)ugxn m.s/i z)p v gg4kkde of 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 53mu wgsu,gw 7Fig. 8–39. Assume that a fr,ws5wu g 37mguiction 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 the ends of a massless rq j enkcb1*8f dofcwh- o:i8*3od which pivots as shown in Fig. 8–40. Initially the rod is held in the horizofo 3i: 8be * nhwdcf-8k*jq1contal 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 cbs rb3//hwhs0*i 4obtorque of 38 0hrbwib34/h/ s*sc bo$m \cdot N$ 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 sphere of radius 0.648 muck p -d*l*6es when the axp*k*6euls -c dis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycz7*hi (hn3k yvle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (vn (ihky7 3*hzwhy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of u-2q1a4 a ks1* ljtbnda thin, light rod is rotated in a horizontal circle of radiud -4qa1bnjkst *l1a2 us 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 bow9 y3* o)sppkujl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between hey*3 ujs )p9kopr 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 objects9qw ol8c6x xez5;gis 4tyc7k( shown in Fig. 8–43 abozsg q9 yc8l7ew5t64cok; x(ix ut
(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 tkwi m6nev);i4 wo oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the corr8 vztatxh:,ey x8:a8kect rate, engineers fire four tangential rockets as shown in Fig. 8–44.a8 h:8z8x k xytavt,:e 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 wit vaoqp4:ltrvqt: h54;za t3w,h a radius of 8.50 cm and a mass of 0.580 oq w5:la;tv:vrqt4 at,pz4h3kg. 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, acceler*bp d 2 )beyqlc98ll,lating 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 ce *)ddw35 s zq tgzcvy5),ukk(u1f8l hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume3zd *5g)(s k zduke1l,t8yqcuvw)f c5 the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 1k sf. 8zgd:w7pwc27p i0,300 rpm is shut off and is eventually brought uniformly to rest by a frii7: c 8ppfgk7zdwsw2.ctional 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 accscgd; +h + j2d)gj5fyzelerates 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 actioni h5-e t yx,b8ujhu4*/aaa-e(dwr*wp .6qen x of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. jra 5*u 86edxxnb-u-ypahw.q(/e *ithaw4,eThe 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 considered a long thi0 d8zfi0nb( hnn rod, as shown in Fig. 8–46fdb(0 z0n 8hni.
(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 consn93 z;mg3lrb e9;l;tx 9ohytaists 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 hamme3tasnoq krbj17 yw 1t6 z2kta6ix(8 b.r from rest within four full turns (revolutions) and rely. n86k1kwtt a6 7 o1b( tijsbra32xzqeases 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 hj7l(k4 ecqz1a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqueh .1w(g7j2za,vd vpe up gi0(m of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass /)u8;w rdzmo38 ml ovu7.3 kg and radius 9.0 cm rolls without slipping down a lane at 38mwo;3dv)lrm8 / uouz .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of thpst wjhxzw55k/je: 7du7idjft+ ;c*20f o9ese Earth with respect to the Sun as the sum of twjew0i/w7f2 5e o k9d *+ fstdxzjt psj5uc7h;:o terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius 6qd/:szebfdfc p+, o cas99fp-8s3kxof 7.50 m. How much net work is required to accelerefcp6dkbo +af3 -p9 s sf8z,:/9c dqsxate 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 andjf,9i0znk *wzy+ovdtk-j 2 1l mass 1.80 kg starts from rest and rolls without slipping down a 30.0 19ktovj y+fkd ji,0 -*l2zwzn$^{\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 fall and rls*bgj .f3yhvtl rj(u0;m2* its lower end does not slip. What will be the speed of th.0 * *ltfvrml3;jg(uyh rjb 2se upper 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 end of a a1/qj* lptsx+ssn ho*3vf-j2thin string in a circle of radius 1.10 m at an angular speed of 10.4jsh3t no v x*+jsslap/-fq*21 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg ma3v7k qoby7; fo 1wk7(hqwc;m00opauniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 7f 3; 7vh1;bwq 7ac0wo(m0oykaomkqp 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 rotateq7/ f.hr8 ,dkr 4 *pj.izjn55ousepd ing at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speep4 8s 5znjhp.dq r5juf ede,i/o* 7kr.d 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 w.y9at+cazye(d z;2 hmoment of inertia by a factor of about 3.5 when changing from the straight position .dy h9cyw +;a2a (etzzto the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her s 0:i6b57uvi8fy2i)xqvo hbuspin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of y)s02bx5hi:u qv o6vi ufib78 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 freq qg4aeup;fzocw v/w556e (.mv uency m5;upa/(fqg . w5cowvev46ezof 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 wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentu*dsi()t -1t kzx f/ qm +lksu/)mebkc6m 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 angulary )/msfga+ iqm+vkub: b j+7/w 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 tdskrhb*bdw 7 a0+k:vkj *b.;va;sy ,moment of inertia I is dropped onto an identicalvy;: s07.aajtk* dw;s*k +hrbkb vb,d 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 atr:/.b(wnv1g 5p mc2;l v5txwkqh6czz qm0y7 n 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the caw a1k5ui svm3-j 6ba6enter of a rotating merry-go-round platform of radius 3.0 m and moment of inerwkia65a-bjv mau16 s3 tia 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 vtgz u9m2x72i/ vq x3dgelocity of 0tgx zdu2/ xm7q2ig9v 3.8 $rad/s$ 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 white dwarf, losing about half itvc 02rzi5u ,i clo8rl4s mass in the process,iclr,o82li0cv 5 u4rz 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 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 excess of 120*+fxs7* r gyuf)z62,cls -gd b(dcizj $km/h$ 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 x7ccjd bp:3br8o7 x,y$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely wit:+87 -i dzca xav6off .ka/atwhout friction. The moment of iner- d. caaw/+a 68ak7fzv: fxoittia 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 diamef*p 0gmg 8ibiv9),+w wdaa4svter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of d,)9v0gi4aiv+mpbwawsf *8 g 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 end of the ro a1 pipxi+p6.upe lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of m. ia+i16u pppxass move?

  The Moon orbits the Earth such that the same side -,:lyv ds ga6lalways faces the Earth. Determine the ratio of the Moon’s spin angular mome6l-lsdva : g,yntum (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 resa+5f f; vtclg1 6yb8)fmw,1wx r(sv ect 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 rltbd-j0 (6sbof radius 0.20 m acquires a rotational rate of from rest over a -l( 0rs6j bbtd6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricg ;bf+ c 8wk,fw-wjoe2al 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. of+ e; 2wbcgk ww8fj,-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 ang+yoc 8uv00idzg m )jz7ular 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, buiquri0)8* hgm t with mass 8.0 times as great, were rotating at a speed of 1.0 revol0u) imgr8h*qiution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy st0v wf.tr (fo2sored 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 m and mass 240 kg, and should befv.2r s(0wotf 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 illustratedbc u1*: 4nvvms 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 horizgd/y sxtc08t+ y3e*ky ontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M qn2o *v.4)k1e;-bg5ttmw kypdc cre.and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (bemtywre.-5)c.2 k p4 qd k 1cv;gn*ota) 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 3 g *dx83uwcsxh +tv:oon the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests vxt g o8hu3swc*x3 :d+(Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is o-oojio+i)2g4 un4p4ek7-pt4sbta ukg q :t(making a turn with a radius The forces acting on the cyclist and cycle are the normal +p o4g-42i q(sitkpg otu4 ua:4ot )kn7b-eo jforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and)dy2wj6 vd f-g;kn+zn begins whirling the rock in a nearly horizontal 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 fe-yvz2dn;dg 6k jfw+ n)at, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder s xc9*gu.oamwvlr cby-7.c4(5 x7gw s and her arms as thin rods, making reasonable estimates for the dimension57aubcl4wyrc9 xvo*m g.w-sx( 7c.sgs. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pey6;orv+c mvjr9q. v)lates, of mass rm .v v)ovrceyj+69q;$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rougoc( 5co t(npj0 feu91nh track of Fig. 8–58. What is the minimum value of the vertical heigo 9(tf50(opeccun jn 1ht h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assuotzs h k95 h;q+wi6 (8th.jtfume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as theq(-jcr grc) c3 car reduces its speed uniformly from )qcc-jc(rg r3 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was 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