A bicycle odometer (which measures distance traveled) is attached w x/sv0 khw9wbcnli s:1.(/ qjnear the wheel hub and is designed for 27-inch wheels. What happens if y/j09 lv: kb (cnxwh.i s1ws/qwou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poi9 3r3c7lpf jf(oq rhw6nt on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change3c9q6 lp o3r(frw 7hfj?

Could a nonrigid body be describa,trt ga,gl ik+dru)n :q6t27ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a large1r ufueh.,(p ir 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 your head than3z1izqi 0xq/k when ykix3z 01iqz/qour arms are stretched 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 the alt5czs:bi 0-f)(/gvf1fa. e0t rvccpedal 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 a5lf)i a :bc0rg/01ectf z v-f c(.svtor a large front sprocket? Why?

Mammals that depend on being able to run fast hb wd f3pmlcq-fi0 )lzb:1i0m2ave slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous:1 dp )mi 0mzw3bb2flfi0q cl-.

Why do tightrope walkerskzf bers4 tht//159z kzkpn 2, (Fig. 8–35) carry a long, narrow beam?

If the net force on 0kxyg)m 6oso .a system is zero, is the net torque also zero? If the net torque on a syste.xg o6y0m)o ksm is zero, is the net force zero?

Two inclines have the same heightg8z;e uxd p-c99n1 ceygp:by; but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ba; pn1zg uc99bxe:e pgy-c8;y dll at the bottom be greater? Explain.

Two solid spheres simultaneously0uldjvwr+0xf,2 9h r u/c1qtj 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 th0ufr qc u/+02vjl1, hdtwrx j9e incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the21;lo gvd u 94.c9mo sov0dqeq same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the;vo.v g9 q2oeo d49m1lsqd0 cu 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. Ye606y rx3hfkm xt most moving or rotating objects eventually slow down and stop. Exxmf36ky 0x6rhplain.

If there were a greaa:efrl( gq2m6 t migration of people toward the Earth’s equator, how would thf2 (q rlg6me:ais affect the length of the day?

Can the diver of Fig. 8–29 do ca; 6a w5ef+6v:visn ka somersault without having any initial rotation when n+cviafe6 a 56w sv;k:she leaves the board?

The moment of inertia of a rotating solid disk about n oip, 0j(10icsixqo8an axis through its center of maso0q1 0nxj os iip(i8,cs 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 u 61b knd, qq7zr*x2dp: cc4jprotating stool holding a 2-kg mass in each outstretche,dpcdq qr u1p2:6bc* znxjk74d hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical an wnj b fwdxdfzz23p0.q;nk/t 8:so 21kd have the same mass. However, one is hollow and the other is solid. Describe an experiment ts0b1;kfw3dw 8/fpo2j q:2d .tznxknzo determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points w0wy q 20 p9dw2lpeka8fest. In what diwpe yp0 f 9d2wl82ka0qrection 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 speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotati)qbz0 j/ eln8wg0my7m ng turntable. What happens if you walk toyzge)80/lq7bw mn mj 0ward the center?

A shortstop may leap into the air to catch a ball and throw it quickly .ogrhrc+n 3vy -1n*fi. 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 thecg*or-n vhirfny +.1 3 opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss whixq7e09c9mi65p9tv/g fg u zwy a helicopter must have more than one rotor (or propeller). Discuss one or mo69mtzveu w5ipqi/fc9gxg097re ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 gc a6;((-il njql(icu $^{\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 Ear). dab0jconeat8r x .5th because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radianso0. rbeax tn. cjd5)8a) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 kmhjm2tmwp7qwtz,bki2.9 : tv , from Earth. The beam diverges at an t7 2 tmb,tv, 2qw:.hjm9kiwpz 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 rate of 650 v/r*u1 7wssdw0 rpm. When the motor is turned off dds /7s wruv1w*uring operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball g2hp z 2ec(ywx7q18xlon a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diamete(wxep lx8 h7yc2zg 1q2r?    m

  A bicycle with tires 68 cm in diameter travels 8.*20s6fa58ejuuomzum ( twu 2h0 km. How many revolutions do the wheels ma2w0e*2tumau 5jsfzh8 u 6oum(ke?    $rev$

  (a) A grinding wheel 0.35 m7f35475immvba .f pu16,k kte u scrzj in diameter rotates at 2500 rpm. Calculate its angular vel56f7bkmi jmfsce4,k 5zutu. 7prv a13ocity 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 compwrzl n:(cj,imuf 2g3:lete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the center? (zj r:gmui:c3, 2 lwnf   $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around sn4i ) p /r.vs4q w1vji9ks.bjulq1w7the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of 0dm4a xs9t/iwa 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 pa2t +brd)ms4zsia ) jk9rticle 7.0 cm from the axis of rotation is to experience an acceleration oft i+j) s )m4k29zradbs 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelob ii z *3.y;16bxcxrserates uniformly about its center from 130 rpm to 280 r so cx.3*i b6xz;1byirpm in 4.0 s. 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 radius 6ylh9 .bkcld/atd .s( $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard u 9.iwggai2. mthe Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evm g9w.u g.i2aienly. 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 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 15,002 vq,nhbm9 zf00 rpm in 220 s. Through how many revolutions did it turn hz,02qm f nv9bin this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.ovhc0+( /px. l fh 6h4uqzp(sryp5*k r 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 fgy. 5e9ax2 s0n ux:k cea:hdd4or the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before ryu54a 0hgn2c: eds:xkd9ex .a eaching 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 ih2ozxjt7*ua 69rlb 4from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? 9ao64i2l7b xthr juz*   m

  A cooling fan is turned off when it is running at 850revknxg+ k+6qli 8skfj16)j*kpp u n-t6i/min It turns 1500 revolui6nj-qgi)+1 p6k*nt+fjp6 8uxsl kk ktions 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 65p99znm8e9db +t sfepm )k4p9b revolutions as the car reduces its speed uniformly from 95kmmm)9p9tne4p+d eb8z sf p9kb 9/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 revolution vm /1w;g8irvios/ (gns as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a di1swvr/ion m8g;g (/ ivameter 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 putsv6ab0if .( yp(-hqoe r all her weight on each pedal when climbing a hill. Tha.0i f(-pe yrq(vho6 be 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 forc5(gciq wv2 pjx+dd,7 ce of 55 N on the end of a door 74 cm wide. What is the magnitd xp 7gwd v5q+2cj(c,iude 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 Fig. 8jb4;m9r9m -qv a,h7w6-scysjh30p )ko gkzuv –39. Assume that a - b ;9wak3chmojk,9jzhs 7rg-4upv q v0)sym6friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attvzt s)( hml7j h cd(x4befsv;25u0x5em;g y*gached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal poxe)5 mg ;vhxz2s0d(uyclvts gf(j* b75; e4mhsition 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 (os03;z ex zg5uz8 e hdpfvx(3torque of 38z 5vxxg;p3d(8e zo3(e0 hsu fz $m \cdot N$ 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+ 3ey 0g+d5psbd)opyp of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation 5p)e+ s +gpd3odpy0 ybis through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of av8.j amh35wpm bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of tam .3wvp 5jhm8he hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horx7 ;:ctgbtzyz/71ik*gmhoz ( izontal circ*gz izg7 bzo/ (t;1hkx:cmt7y le of radius 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 5 wwmnbw9 u;f3wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay f wm5;9nw3uwb 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 shown in Fig.f+ow c hya.q;s17nx-n 8–43 abow-f. +aqnoyh1nx ;cs7ut
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total massn7vsg )g5tlz3 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 spinnii r1.(,dgon nn*dr;zqng at the correct rate, engineers fire four tangendni ;n *gn(r 1qr,d.zotial 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 reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cy6le9 j*yasf abz9m,okgo s(, )linder with a radius of 8.50 cm and a mass of 0.580 kgsga,k ms,9(6)zey o*fob a9l j. 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, acceleratingah*yc0- m-rytv 9lu1 4snv.r71 ncnar it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is 27u5.hcct tk;tyk2 7kkgnqo; able 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 etkccnot2 q;725.uk;ht 7kgk y dge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventualll9lghmuh )g q10k6/bjy brought uniformly to rest by a frict6bll km/0 1uqj)h9h ggional 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-w xnbt3,2q3mm 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 bdl;r.4glyae- i *(mxx y the action of the forearm, which rotates abou 4e*y ;gaxil -dl.x(mrt the elbow joint under 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 conet m k4fv616ppkk)3p-ns8 fwu sidered a long thin rod, as shown in Fig. 8–46.1t38f4ukpkm 66 v) -wfseppk n
(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 massesoeo-) yqd y1qxk6t,o+, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (h*wx s;bihq5vr-d 3 p7revolutions) and releases it at a speed of 28 p;7hx b*-r3 vdi5shqw$m/s$ 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 momentu*jfj+ 3h*uylou kj 1z8r6d8b 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 torque l( v)i*b(nb1 n2 ulbebof 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls withou xs s+8.ijrdr69el kt7t slipping down a lane at it9de +6j7 8 rsrsxkl.3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of thecm*xx(oa3e 1es)yygxd2cn4n)p 5 s7q Earth with respect to the Sun as the sum of twgxnnx a)3 d o7)2514yspqye me(sxc*c 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 of s. -z1drd4 yzx7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per x-.zz4sd rdy18.00 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 witu :h+w/a0wp7d 8 qfnuvhout sld/0w wun+7hp:a ufv8q ipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fallt wtqv,4 g0km, and its lower end does not slip. What will be the speed of the upper end of the pole just beforeqv,m k gw0t,4t it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of x/r ; 5,dyh:zuj .uohha 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angularh/; jyuhuozx 5,. d:hr speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical 4cicebo bt o5pvp9-0d, s)0 zlgrinding wheel of radius 18 cm when )-, c0bvp zb4i t5dpol9ec s0orotating 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 hi vi/xqc0no z3.57 pkt3anw71ve6eecfs 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, the speed of e5nfk vwqt/3cei1o 7v3.7 0zpa ncx e6rotation 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 moment of inertia6glv:m3;m i :8mzsjp n by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the t:mv3:68z gmnm pil;sj uck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotattz uj.l:gfw+t:.gmc 3ww 2g,a ion rate from an initial rate of 1.0 rev every 2.0 s to a final rate owwat,.u+.:23twfg : jzm gglc f 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 rotatingf jpp)9p0 t6j9k me8sd around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency ofe8t9 sjfm d69pkjp)p0 the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentumtdk3u7b4h8sw /mz;-0 rbb0uam7 juqs 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 momju(e ( vhn7x*xentum 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 mome9l90cuxyx3kpiimq 9 mz1)-rsnt of inertia I is dropped onto an identical3m)mlusk 19qxc9yz- pir09 ix disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsh csq7 1(vsw vw/yw()x64y swm 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 the center of a rotating merry-4*kadt w /h, hmh9 rvyd4ac1b)go-round platform of radius 3a 4/9d vbh1rycd4)*m,t hkhwa.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular3g *uf/ys7-cloh u4ks velocity of 0.8k -g3 sflyu7*co h4u/s $rad/s$ 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 evenrf *mdpjtbu6f/gzemp. +8b9.tually collapses into a white dwarf, losing about half its mass in the process, and winding t 9p/.rfg*+6edfb.zpmm8b ju 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 involvv r rgb0+vl:t6e 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 :how4zjpaw+::*no xw$ 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 withoksa xo( )5d4xh mvcb,,i-+;)jvoepx out friction. The moment of inertia of the personx-4 ovop5d,(v e+bs; c,xaj)kioh)mx 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-roundpm4f(f+ arys r yxo)jm0b18q5 turntable that is mounted on frictionless bearings and has a moment of inertr 41q(fs r0mxyfb jo5m)8 y+apia 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 withm6gqs4a/ l--jmgaps 7 bh l5c+ 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, h/lpgq-ljm6 b+scama5s7 4- hgolding 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 Earthpul1z 4(0htlruyy -8u such that the same side always faces the Earth. Determine zu48 1u-yl(0trpulyh the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fcfyrq 5*e 5)76aeylbc q1:qk bjoq-a-rom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0a gvi 3e-.qsb20z: hrpvh(+h8q +qluf.20 m acquires a rotational rate of from rest over a+s v:f3bhhpz i2e(+a h-ru8gl.qq0qv 6.0-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 cylindrical disks f;jqphyt /e78, 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 diamete; j7/hyetfp8qr 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 thn-,pz*( dk;v(tknd up e angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, butoi gw: j/xh ug7580ks;yc0s xoupvi*1 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 angularw o vy/ix70c0uuoh*gp5gj:;1ksx s 8 i momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pols*rscti2 )p jxsme:kl:ruy83rob a5j1 50n p6lution 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 cylindrix3) l p nroa1jkpess:yu*68 j20icrb:rs5 tm5 cal flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratv3m2 os4rz2y6nyxs dl ;y5w-yes 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) iy d, lnv9ifml24h d+97 stykb1s 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 an ceoi2d7e9g /gd 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, determc9od/ 7ig2g eeine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing v1f 8*; d ,futyi+yesdfq3jn 0hertically on the floor, and we want to exert a +83hys* f;et, f 10jund yqidfhorizontal force 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 -qq, cko8mf2or14h-hm/zlg 3/p h v:s en,gaproad is making a turn with a radius The force gpohvk /me-4cgnhr,:lp3-2aqsq 8f h ,omz1/s 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 qemd/5 *xrg: fak*b0g 0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accele xbgfkm0eqdg */ :5*rarating 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 so pw7-1i vkbf+ lheio(5x,c1rllid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Thec+1 rf lx1o(l7-ep vi kw,hi5bn 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 p*(t ril7 (thi:qwh*zn lates, of mi (hr7* zh*ltqi:tw( nass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 l kx5 ly4x 7tcdi0qzw2/lxr4 ,track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must 4x4i2,x0/t k7l5 lrwld qc yxzdrop 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 gyhzssv 2y;/(do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 4kto pn g0h2)94riptdi i7 l.n/ szo,b85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What.2rdp4t7i ooin bnkzsgi )p 9lth /0,4 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