A bicycle odometer (which measures distance traveled) is attached near the /* y)uywdlen. 0o j4dswheel hub and is designed for 27-i*dj)dys4 n0/e. wu oylnch 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 o)n/ + strb+ccqn the rim have radial and/or tangential acceleraqtrs+b /c+)cntion? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single va.6r i i-srws5nlue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thiog cp6wuf-7;*eyk p6an 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 hand3qr3d)vgc5vve id6 e jv8x7q3 l-vw1 ls behind your head than when your arms are stretched out in front of you? A diagram 8cv33 l7qrq 5ed- jv6)dv3wvx igl e1vmay help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at(v57 gvox1v huz/ 3bmiquk+a; the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket origv(a v7z1oxqumk ub3;v5 +/h a large front sprocket? Why?

Mammals that depend on being able to k .2 v ic+q80u..kox tsnnkg2jrun fast have slender lower legs with flesh and muscle concentrated highx0q+ntsk 22ciu vn kk.jg.o.8, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (l42:taep9r6 iga8 i heFig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? p8y ld- aa*r:tIf the net torque on a system is zero, is the net fo *la -t:rda8yprce zero?

Two inclines have the same height but make different angles with the horeegp rs*6. h.os 6 0+bzng5xnaizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greatern0 x*+gphesa.en5bo6 g z6.sr? Explain.

Two solid spheres simultaneously startkv1 5jhe0 fkz nn)h(d+ 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? Which has the g1k5nv(+ z edj nfhh0)kreater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder40eno-k gs(kwlzx:j1kw/v0 h have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which w1k (sekkzg 4xhw: j-lo0n/0v has the greater speed at the 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 conserved. 9exq7 p,ts9ut7 ik7yqYet most moving or rotating objects eventually s7t 7 799uxeqikypqs, tlow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wo i rt)nczzg: xz;ze /k9ox95g f:r39niuld thgz9r9::/xkzo9g x c ifet;3) rznzni5 is affect the length of the day?

Can the diver of Fig. 8–29 do a soyo((-6efp) ehgb 9v/b2ss ny xmersault without having any initial rotation when she lebs/y(y bveo2 6 9-fgnp)(shxeaves the board?

The moment of inertia of a r0, o,x 9qucxhw uzr10rotating solid disk about an axis through its center 1c oxrq9huwu, r0,0x zof mass 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 hc56 -5 wmwtmxstool holding a 2-kg mass in each outstretched hand. If you suddenly drop5m xh6w-5tmwc 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 hollouu* x:ab)ptpj rf,e34 w and the other is solid. Describe an experiment to determine wh*u 3t ,u4frep:axb) jpich is which.

The angular velocity of a wheel rotating on a horizontal axb .va nzs5hz3/,hd x, sp7qqj-le points west. In what direction is the liz nsvj,hdq-3 .,zxqabhs7 p/5near 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 speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntablkmks-r:o j d;4e. What happens if you walk towj-; mok4:dsr kard the center?

A shortstop may leap into the air to catch a ball and teq/,ph; y0crj6x o*dg hrow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will noyh;xco,/0rq j6ged * ptice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why6 ys5qxru s+cx*uhel/hb36l 5 a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the hel*3sq65c6lu use+x5lx bh yhr/icopter stable.

  Express the following angles inz3tz,u8 nyp+ s 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 becak3 hg6(w49osq(i bi,cc2c- 1 asxixuzuse of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) ofow h,6qbagcc1(ckiiz (4ussxix 392- the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mooecna13fwtxc97 m bpz; w)fc72n, 380,000 km from Earth. The beam diverges at 7 tc)fncc93wb12; 7axfzmpwean 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 blenderp-rp6b4wu n 6/6hw0t8qbh oumwws) -e rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bladetm6h)-pws04wb 6b u ewwhp/ 6rn-o q8us slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anotherpt+ny7 nb e3m7 child. If the ball makes 15.0 rme7+3 tny b7npevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kmjbticp8l5322 ray r m(. How many revolutions do the wheelsr3 at(mj2 5lb2icp8yr make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates atm ()durr q1gj,-l- fzd 2500 rpm. Calculate its angular velocity in r lj)z f( ,-gdumrd1-q$rad/s$ $\omega$ =    $rad/sec$
(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-hal 1 )3i (kb8hhhzqf8round makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seak q(hb81 hzahlfi3) h8ted 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 os534ux+hwfy 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 speed 0javp lqtp(70 2x; gsaof 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 7c6 kfy ob4r- ( 3,t,k,.lvazgio :ciht.0 cm from the axis of rotationr,.iolgzc3 ,i4a by vt :f(k,kot-c6h is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whee+hz2,b;h j)q cxy sxd uuh;x/1l accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determinxhx suxh2 cbj1h,qdu;zy ;/)+ e
(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 radiu yr3i -r1yv)v2 uksb7 o)wea6s9 q:iurs $R_1$ 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, astronaut5d raz(m;th:zk46 oly s 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 thought ayk;d 5r6m4 :tz(oh lzof 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 1 1bw:1a4tlw ss5,000 rpm in 220 s. Through how many rwas1t:wb ls41evolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in qkrz6) ox b-yy06qy8t2.5 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 highfo/ry m9z: wt;yxe;i0 speed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions bef:eimw t y o/;0r9xz;yfore 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 rl4hhosj,a-b: e*j px:pm to 360 rpm in 6.5 s. How far will a point on the ed:sxj oe 4a:,hplbh*j-ge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15i0rzfy 4 10(zy d rwu+qwe*pklp6 -ow bu;w9s*00 revoluti fpero kip*1+zwr0ys wq4wbwuy6-0d lu;(*9zons before 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 revolutirmuz 6wq523sd ons as the car reduces its speed uniformly from 95km/h to 45km/huz5rwm 2d3q s6 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 the carfaiycoi ett0tnb .mi8w0(g 0 2xr2,.(k4 zhx r reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of.ax8iz( g n,wytrb h2mcto0(k0ifrtx24.0e i 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 tbby cs 6.c)hmak/a w57 )df(jweight on each pedal when climbing a hill. Theska f b ccbyt6jwahmd75/) (). pedals 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 by kpy27w id 1;d;n6cnof 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if1k; y6;ddp2wc i7nnb y 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. Aswfljy sf 2.h.w tp 9),j )pfsxl0u/v*lsume that a frlwj9 y sv)*f2jpsfthf 0ul)p .l/w,.x iction 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 masnr-xj;+ha/ 0ols p -gmsless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and dirmrn-las+0gp j-h/xo ; ection of the net torque on this system.

  The bolts on the cylinder head of an engine require tigh sv+c5w ) bp*mdfxv91htening to a torque of 38fp v * +bsc)1wd5h9mxv $m \cdot N$ 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 m when the gs(d( 98bqjqmn ,fq+saxis of rotation m sbdg9jfn,q+q(8s(q is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whel.irs xk)y nhsj ,59.sel 66.7 cm in diameter. The rim and tire have a combined,5x.) sihl. nsyjrs9k 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 endmzmar32-y6/sd xw: m k of a thin, light rod is rotated in a horizontal circle of ra3y dxzw :kmr -m62ams/dius 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 rotating at co ) wd c3o:qmc.:cukdh.eq uz8(nstant angular speed (Fig. 8–42). The friction force between her handsdh .zm3 .kc :qwoq8ccude)u :( 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 objecb+b5zxg+ez,f2 / oxjrts shown in Fig. 8–43 abou++5oz 2b,e bz/xjxrfg t
(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 atomcf-r hc,yu*djr.nh 4 psw8 .k1s 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 correct e9lzj612kl1s di 2 iqwrate, engineers fire four tangential rockets as shown in Fig. 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 reil92 1 lzd e6jq1ws2kiach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a o8 c:..nn,;2-b evopgxqb+pqgoe1 ooradius of 8.50 cm and a mass of 0.580 kg. Cg.vqqb:8-opoennc;o,.be oo g1x 2p+alculate
(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 it from rest to 3 mt(y, tqqt7,z, f2wu r2(aw oe$rev/s$ 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 is qf5/euko) 9woable to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m 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 acce ok 9wfeo5)u/qleration, 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 eventualleq6 rf )loxg 1cunl88)de 0rv,y brought uniformly to rest by a frictional tod)rrq8x80u) eg6 c1fv ln,olerque 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 u7c++ ib0 i: mtng.zli3.6-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 for27 9kxlz /7)ykq fkwv ov,+prbearm, which rotates about the elbow joint undero/9 bvlfrx ky) ,w2qp+k7z7vk the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be consi 3n6 w; lvst bc9p,*9 + x2ptonmuagi2qy71atfdered a long thin rod, as shown in Fig. 8–46w t,tx n+obql1m9y2snf7;a v6ai9 3*p g2cput.
(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 massesv*asgib/qc )cdn41 0 s, $m_1$ 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 fouransqke4/ g,nnev873n) d a2 hf full turns (revolutions) and releases it at a speed of a38ed4nh kns 2vannfe )g,q 7/28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia j sbspoe 4g.p:;4tkcjs4i5/w 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 to(cg,4d1(pz*w/ x) r fvxh utnerque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7h+n;.-fpx90vop p aos .3 kg and radius 9.0 cm rolls without slipping down a lane -vp.of0o ;axpp+nh9 sat 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 o 565ait/tm u8 7+i o5cwqrrdbef twbre7c5rdtiaq t8+mw 655o u /io terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much yp4+ bffx8y6pnet work is rp y8f bf4yp6x+equired to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wi -pcrrh;nvyb w4 pf7(0thout slipping dowrnr b7(v;-wc4hpyp 0fn 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 itx2bm lz57 k7ni)d8 uybao4 mnyvzw-87s tip. It starts to fall and its lower end xkm a-un7o8nl25m 7ywy4d87zbzi)bv does not slip. What will be the speed of the 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- yvp14u3e)qa 06uwfpgkg ball rotating on the end of a thin string in w) u6pupg1y4va03qef a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg un15v8d(y 9n vz.l clneky;m ilk ):u z,zdv*kn,iform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? dnzn:lykn, ykuv * mlz1v).;lv z d5c8k9,i(e    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hanl- -i 8,d7ob 9d)qa+mjdiscnl ds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, coq -ban7dl )l d8+,jmdi9-si 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 flm4mupa rz;5kx 1/w( in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the str;4pmw1 k5 zr/ufml ax(aight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase hejkk j4m v;b9,kr spin rotation rate from an initial rate of 1.0 rev every 2.0 m,kkk; j4jb9v s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its ce wwvf8z+0z4 efnter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 fz0w 48e+f zvwkg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnij ymn4iw1w 1fne(o,u6wzcmz :m12ku *ng 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 Ear8c*uk3zedz v2eb p )d.(2 lixhth
(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 ek/acv a v*g.sn nl4pky/-e(4inertia I is dropped onto an identical disk rotating v.4lask/4(ck/va- ynne*pg e at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns srqt :p: tbcb4( e4ki;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 stands at th +r7oq7jm exi*ap0/zp e center of a rotating merry-go-round platform of radius 3.0 m and moment of inepie o* m7zjq0ap7x+/rrtia 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 ; (74iiwjeb2 *rw1lm+wjbrba *o5gqzis rotating freely with an angular velocity of 0.mqrli rwe; ijw+gz**5j(17 bo4bb2wa8 $rad/s$ 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 c we ya1vy9ra-,8 yz;dr/ 3xwroollapses 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 nearest integer)wyx/- ;9eyy v awo3r8r1d,zra$\approx$    $rad/s$ (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 *hnsirb8je ;+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 0 7 5y e(mwsjqkzrv0fp)7a3wn$ 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 platfor c7ec l q7dj7w)fwj. loq9dy) gy/dvin*)/y t,m, initially at rest, that can rotate freely without friction. Thtyvygll 9d)qj f, /*qj c./7)7)owd ednyw ci7e 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 edgyx dn:5ax*0pk e of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearingsx0da:nyk 5*x p 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 g qswlmu)g8+6ns.- /d5t aqzew, * hlffround with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool+uq8 )sw5 hel g/* dl -naswtfz.m6f,q’s center of mass move?

  The Moon orbits the Earth such that the same side;h nq/5zn4;r0ruogn7 o mu*bh always faces the Earth. Determine the ratio of the Moon’s spin angular momentu;zou nrnmhro5b;/0* nhq4 u7gm (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 r t jfl5,np 8sh.4eza1rate 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 c 2jtrjd00i4rk ylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval 4 0krj2ird0tjat constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and di2os urp6 sa59samets62 pso5 r9asuer 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the reafrso9,aj.v9 zlug1 h dv)6g( ar 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 siz ,/2kj.a ,are a,pkyxve of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-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 r,pe ,j2kka, y.ava/x angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutrnk-x j0,ipl )*jtsf02 ihx8uq m.y :xion 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 flywheel of diameter 1.50 m and mass 240 kg,r.myu pj8*ti0 )q: kflxxi02hn jx- s, 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 an 3-2ln6.agjqltx ps3u$H_2O$ 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 ro,tnpw0p2e ;k zlling 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 freely (i.e., we igno h6c(y p9ifcz1re friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as showni9c h6( p1fczy. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and l*1f :obk :aq;h rkfu-a2k o)ca/o3inwe want to exert a horizontal force-foi1r;kl uh*kof na/3k2)caqo: ba: F at 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 road is making a turnth3p9si 03i ur with a radius The up9s r i330ithforces 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 0.50-kg rock into a sling of length 1.5 m and be uj10(t2dlfh hgins 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 feat, and where d0jt1 huf(2d hloes the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her ttg;je a(6q( karms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outst6jt( qakeg ;(tretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consnwrtqrl m3q i mz-, a(;,jc)(7 z,wmihists of two cylindrical plates, of -w riw3jr()hlmzqmi n,z 7a ,t mcq;(,mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looe xf yod:d5cs3s6 i;3eped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop withoute5d is;o336yfdsce :x leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do noq37dlxxfat r9x 5co3 sbz:2e:t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolzc v*8fv6 ;3wthnnjz)g: 2wflutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wavzfw2 8 vg:h;6czfn lw3*tn)j s 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