A bicycle odometer (which measures distance traveled) is 5k gp7; +zarwjattached near the wheel hub and is designed for 27-inch whek rp57g z;+wjaels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constanbbdba rjp e/4/4* jb1yt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential accele1jd/ ear*4b/b j4bybpration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describn k+fcdq jms(*f5f4*u ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thanbqo(w)gq mhq89uqj ;, 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 withbx:q2efim28olqkm8 ) your hands behind your head than when your arms are stretched out in front of you? A8iq:mq bo 2fe28 xlk)m diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at th0yw m+wpm 9y2ee rear wheel and three at 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 sprocketw+yey9w m2 mp0 or a large front sprocket? Why?

Mammals that depend on being able to run .5g7 1bu6bm1dr(qzdk ,7m2hqzlk a hefast have slender lower legs with flesh and muscle concentrated high, close to tl u 25,me b(dh1b71zhk k7z.ar6gqmqdhe body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walker (86ldzp z5c9zdpo+tr s (Fig. 8–35) carry a long, narrow beam?

If the net force on a system ispfs -rq : 8ctq)-5/udw*rg ner zero, is the net torque also zero? If the net torque on a s5r--ufscrepw: * tqqgd n8)r/ystem is zero, is the net force zero?

Two inclines have the same height but make disyhrs * oj e+)ixni+)1fferent angles with the horizontal. The same steel ball is rolled down each inclix1io)h *irjse +yn+s )ne. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from restfx9mecfty6vi0 8o92 w ) 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 greater speed th09f6 omit fw8y9cexv2ere? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and thnt2)m- :,bwpuw 3 zwzy8ro n0ve 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? W)u8wvyn0z2brtwopmz3 , n -w :hich has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum ajtpw: -*ub/dgp1 b)ojre conserved. Yet most moving or rotating objecp )obwj-t :*uj/g1pdb ts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woudzcf*gt:p5dl* 8jr +7nc(x2gsdc 4sgld this affect the length of the dag*dc5jp7*2dd 4sng xc8scf+ g:z lt (ry?

Can the diver of Fig. 8–29 do h.fxv4/:z mvxq 5t7egd ot4*w. e;yqqa somersault without having any initial rotation when she leaves the board?hv v g5eqz4. qtof7:tedmq;*xwx4.y/

The moment of inertia of a rotating solid disk about an a2owyn;xf7h8 eg(a zb k/ev(i(xis through its center ofnez(8w gi ;h(bvxaoe7ky(2/ f 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 lc0 a283bwvy cdr0 ;pson a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or std;0 y3cpb svlc w280raay the same? Explain.

Two spheres look identical and have the same mass. H ub*uqnmc,;rogis537 d 5sfn; owever, one is hollow and the other is solid. Describe an;m75f;o5gsnnuu r ,3i*dsq bc experiment to determine which is which.

The angular velocity nbhzhi a5-63nu kfw77 of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of theu fab nni7-h63w7khz 5 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 standi-4og djwl 2g1:(il nsmng on the edge of a large freely rotating turntable. What hap-wm:sl4ijod(l 2gg n1 pens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As/ f 0z2l (b6cqi+u- gscred-ej he throws the ball, the upper part of his body rotates. If you /(c0 q+ij--dcbzr6ul2e gfs e look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of coifswa+u ;(n8j*mbf8fy4hl : nnservation of angular momentum, discuss why a helicopter mus:ywufb4 nnhi88m ( *jfl+;fast have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) hqv4rw)izq* l0nz .s7 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an t3x8 jc+s pjj,amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Eartcjj83j,sp+x t h.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km f94+a( e-scde+d+5xfjc hlm m srom Earth. The beam diverges atledde m +9- sc4mx af5hjc(+s+ 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 rate of 6500 rpmbu-tsr-vc sua x7 n9,0. When the motor is turned off during operation, the blades slow to rcv t0ux, 7s-nsabr-9u est in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ba s4er.,sqn+un hqg(g. ll makes 15.0 revolutisnu .+.rgsn4,qh( eqgons, what is its diameter?    m

  A bicycle with tires 68 cm in diamete,v5ts8t kbvt27id7xq/ca g c; ,u+cyzr travels 8.0 km. How many revolutions do the wheels make? +/2vy7cbvtxgc8;a,dcq,z5ik7t tu s    $rev$

  (a) A grinding wheel 0vy ho5fmia-zs/5 bd1*o3s5hd.35 m in diameter rotates at 2500 rpm. Calculate its angular ve3oazhf hd55 ds/5svm -*ioyb1 locity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38).jb/hfzauu5 au; /d2 .n (a) What is the linear speed of a chi;uaudz/ b5u ./ja2hf nld seated 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 /;/e*qf7*d b lmxakxhd4 ld2 ivelocity of 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 o0x p71vu ns -ydrgw1x4f 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 partil5/6 4x4thv;jp7qe u 8tfe zzocle 7.0 cm from the axis of rotation is to ex4;h6ef t8 oz tl4/e5xzuqjp 7vperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itsml 7zp4bbgv59 center from 130 rpm to 280 rpm in 4.0 s. Db9 bpg5l vz74metermine
(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 7crjk.lksi4 2ik(ey/ 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 Mmxka2 rbvxp,w5h32n ct-fs-tf49x y. oon, astronauts 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 of as a cylinder with a diam.2r35-h cs axtp 9 4xn2vb-ytf kx,wfmeter 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 re0bc7g f p;a9fbst to 15,000 rpm in 220 s. Through how many revoluf; 07bbfg a9cptions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcult9 ohhcua o :.br;q3vr( l*by:p0zml8b+xq)v ate
(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 jets in a whirow: e +q6,7bomwyp i1rling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final spo ,+ rwbqep6 yi71:wmoeed.
(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 qprpn.)yla .qgc:ng/jd5e03 .5 s. How far will a point on the edge of the wheel have traveled in this ti:c.p5ndrq0apg y3 n l .e/jqg)me?    m

  A cooling fan is turbf868x e) 9c,td cn ir*bmn;ytned off when it is running at 850rev/min It turns 1500 revolutions before it comes to a8ryni*)b tt;ec69nmfb , 8dx c stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car redut0ldls6(x-xc wx +h1 mnm k:m(ces its speed uniformly from 95km/h to 45km/h The tires hm6hdn(m 0 -s t(k: xlxx+l1cwmave 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 thf:q m()hcg sk-e car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8qhf c)g ks:-(m0 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 id4,p7nxgauk7 97s lzbike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 zdk7x9 uln7s7 ai g,p4cm.
(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 creb.a+)c cpok: 7gt ai *d/wh3m wide. What is the magnitude of thpk)b *t7+wc rda3:e .g/ icahoe 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.m1m b:ve ndotp-v)-t8bof3x 7 8–39. Assume that a friction t o8f7 xbep v:1dbn-o m-vm)3ttorque 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 r0ih; wkneeo0 3od which pivots as shown in Fig. 8–40. Initially the00ie ;e3honwk rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of anqqnjs:g /5aw 78gco( y engine require tightening to a torque of 38 8 q5an :q7scogjw(yg /$m \cdot N$ 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 0.6w tlezz6nj :te 4;1 ra+p1wt.c48 m when the axis of rotationn4e.r:p6w+elj;z wctttz 1 a1 is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 f- 5f:huhny+v to5pk: cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub uff:-tp5k5n: h+ovyh can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin,jmr2 u2gji90*lu.cezrw;fu9 light rod is rotated in a horizontal circleljj u90 ugmr w2u.zfei*9r2c; 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 wheel rotating at constant albsy8g z n.hr5pw*r6p/ycn65ims 4 w/ngular speed (Fig. 8–42). The friction fg/y /mic 5*n6hyb5wp nssr pz.4w8rl 6orce between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of ine9k kotbp:ioba)2p6iat h-c: (rtia of the array of point objects shown in Fig. 8–43 abhpkpt :kco:b)a2(bi 69-iaot out
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total di z0h/52 rcfwmass 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 corqv.mz0qln 211non .5bq 1zj4 sdh yj,vrect rate, engineers fire four tangential rockets as shown inzm 4 q.bdn5y2qjh 1,.0zs1ovn1 lnjqv 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 k+*/sh ;z0b 3zgth0bbv 6hmawlq e8m9a uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcu h9;qsbz/0+ lhmwmz*t3bv kbe 0 g68ahlate
(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 swig1r;zgxqev99 bw z7i5 ngs a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on p/ nrf sw6;z8ss.c g3wa small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform 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 producf;g6wspz3n ws8rs/c .e 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 andi83gao 0*oiv o37qnu39 ps tqq is eventually brought uniformly to rest by a friv uiasgi9n 33o qo0*p783tqoqctional 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 3.6uqm xah 9h84o:/e ;bxv-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 foretfs9zn ) b;zr sfl-3c4arm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated un r4ff-z)n ls;t93b zcsiformly 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 yv( :cfhf.82 *ezqgovc j32c oconsidered a long thin rod, as shown in Fig. 8–463 *2cqfhz(8 jegy cfvc.o:vo2.
(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 masse1jib-rvuo638y ut+n is, $m_1$ 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 accelenn.8 hyxz4 (gkrates the hammer from rest within four full turns (revolutions)y (8knh g.4nzx and releases 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 hasl,odwv2a2 ,jt)tu4j v a 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 r8 3 8eumm(otji5 f3rwdevelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipmuq gr(,5idk -v/e +wnping down a lane at 3v (5ng /ed-qu+irm k,w.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of j5 czo- 3m)kum6 ow;:nb-5k o4z yafvgthe Earth with respect to the Sun as the sum of tzk3 6u5bomg:zo4)wmj5 -caynof- k;vwo 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 o- e/1awpj4bj2b t. pmdf 7.50 m. How much net work is required to accelerate it fromwm- pejj24db .b /p1at 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 sh1g xo 1)oh1(omph+w rolls without slipping dosxh+moph1 w(1 o1h)o gwn 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. Itcw.iweib/:c4;kk,+fe/u i t p starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole ci, wt;wikicp4 /. :/efb+eukjust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotacmm5 f(s 2fl;qxe32lbting on the end of a thin string in a cirx ffl( slc53 emmqb2;2cle 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 :j8eqev nd6jphoa ,pqbzbe 406(4u:a2.8-kg uniform cylindrical grinding wheel of radius 18 cm w4jq ave p:60(de h,nqbou4e:6z 8p abjhen rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands xts(n+2)t d wgyg32(recb pq* 04dguwat his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position,2xr y0 w cbeq g2gw3st gd(ndu+p(*t)4 Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her movzr 6k+;k5 xqoment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rota5r kqo;x vkz6+tions in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1. 4 g6d-oeegzv);5 ekb)*q/smg+wywhe0 rev ehbzg)e sd5gw4qo );-/*k6+ew y v megevery 2.0 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 roxiwtq40 u:*snh 2 hjj 4cpkp::tating 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 thepjtx0 uh:kj*cn isw 4p 42h::q frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular mom s.vw;rtv c:)rentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum oa.cp(q v :2txqf 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 cylindrica cn ,9ishu96wzl disk of moment of inertia I is dropped onto an identical disk rotating at angnwih99c ,zsu6ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at c*vjc jryk .jiht.phl*:0 j)-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.km; 9mphqa p37u 2fui-go-round platform of radius 3.im3hm. u2u7p9a qp f;k0 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 rotatinjp nx u54+.ycqg freely with an angular velocity of 0.8 puq +c5jyn x.4$rad/s$ 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 eventuoh p8j 8mc hawo:h/32qyun45i ally collapses 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?h 8382w/ ap m5 ucoo4j:hiqhyn(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 windyoc)o8c(cw pazl c b6/m )k)k5s 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 3/qfsnr 77h2ess ts:s$ 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, initw y:ja e/9 nd2*ygmyl,ially at rest, that can rotate freely without friction. The moment of inertia of the person plue2jd*a/ly,nmwy gy 9:s 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 w va3r4;:i0fd,npu 3 xo.wdz ldiameter merry-go-round turntable 43d,wdzipx r.a;3 u0 nw:fvlo that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope ro9ux 62mfyss- mlls on the ground with the end of the rope lying on the top edge of the spool. A xfsy ms269 -muperson 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 mass move?

  The Moon orbits the Earth such that tht se0dy+nw m/59fsgnm()-hsx e same side always faces the Earth. Determine the rf mw +nsh9etg0)m5sx-y/sn (d atio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r rovzt0aisrkp,t drt6cxdmb8;687s+o; s(-aest 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 ofo8onm /rg i+5/5 )xzgi twi;ms radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant ;)r/ngiwiimo/ s x+558z mgotangular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricalu 88w;jvrw;qiacw- :t disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concent-8w:quj8vc wta;w ; riric) 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 them 52r,lbc +imm angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass gf7.twi+ t/ 9ko t05hypvii f)8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gra 7+) giiytptt/h kwfvfo 95i0.vitational 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-po0tjq,g:qkgb2m:1 x r 2kwgd*allution 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 flyd0jg 21g ,k*mk wbgq:x ra:2tqwheel 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 illustratek5* j )fm95 :oavqonb7u y.loms an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface att; 9hl u2ix/dd 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 anjq; b3n 1vvdbk 1d5y0gd 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 (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 cen 301;5nvdbd jvbq1g kyter of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing verticp7;cv )js +wwsf/gwp1ally on 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 (Fig. 8–55). The step has height h, whepsw)gsv w; f7wcp+j1/ re h

  A bicyclist traveling wpn1l f52gwv;hlx: ek,ith speed v=4.2m/s on a flat road is making a turn with a radiusev 12 n;xwl5 pgl:,kfh The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock in1 riy8yn-bwlucd3 q:-to a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest ton:du-bycy8 lw ri3q1- a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and 1..9djeoh *treh dneyd-hw3bnju9;4x tv6; b her arms as thin rods, making reasonable estimates for the dimensions. Then cauh je6b.*e r9v 49;;n njo hy tdd1.3tebw-hxdlculate 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 oy-93kig ap aze5oe 9f100isk if two cylindrical plates, of massk 0a5yp90i-1ie ig zksafe9o3 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rougzp lfx h05e)*w7ec6xjh track of Fig. 8–58. What is the minimum value of the vertc57je*p zf6 lx e)hw0xical height 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 h,o p*1z1wnss assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rev7p:w o0*f1q ,q s95agaylh xdpolutions as the car reduces its speed uniformly from 90km/h to ogpxfw5qh 7 :0*p ,1s ylaqad960km/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