A bicycle odometer (which measures distancej 5meive7 p;wdj kr4s i--7ep2 traveled) is attached near the wheel hub ejej-k7 7 sr5dv4; pmewpi2- iand is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poixh mkgf6c00g* ir8g oo0n y4ip*)ouw ,nt 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 acceleratiofm*rxypo0w)i0o,ihcn80* ok g6g 4 ugn? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the anguj- 7ezunp 2(lkmu c+w3ndi6 8flar velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.8t sveqi93/xqf:k vhz1 g2h 2c 8p:huizxj-/t

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 difficl0glpfqt -66dh:zfpo. -bh 2g ult to do a sit-up with your hands behind your head than when your arms are stretcheq h bdf:h2.lz lfgg60-otp-p6d out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear whi6w9sc9jxsh:pu5z. k eel 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 sprocket or a large front shsk:jw5 x.p6 csi99uzprocket? Why?

Mammals that depend on being able to run fast ha)ird 8)uk9v0ax xr:ij s 3dt.gve slender lower legs with flesh and musclx.i38)) vrjxrutkdad:ig9 s0 e concentrated high, 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 (Fig. 8–35) carry a long, narrow bl * ekl7 208ysmoipq:keam?

If the net force on a system m8 ac8o z(9lynb/v ,zqis zero, is the net torque also zero? If the net torque on a sy8q l anc vozm(/byz,89stem is zero, is the net force zero?

Two inclines have the same height but make different angle(t rf,mb5esl)s with the horizontal. The same steel ball is rolled down each incline. On which t 5 ,sembfl(r)incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollb2x qt nj9.71hdmn.yh ing (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of thnjbh 1t. 9md.n x2q7yhe 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 the same m jtppb gu5b jm;)t-vrc6/2 71rr mth7kass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the gp-tbm 76gmhb;75jcvru rt) k/jr1tp 2reater 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. Yet most moving+c-3oc0gxj c -ihl+je or rotating objects eventually slow down and s +cc-xoi+g0e l-cjh3 jtop. Explain.

If there were a great migration of people toward the Earth’s equatorymcz a 65tm(i4, how would this affect the length of thecimt(4a 56zym day?

Can the diver of Fig. 8–)5zph11fgxa v sw,mxyf77 xi229 do a somersault without having any initial rotation when she leavp)f5f21zwhxi7v 7 gsm, yxx1aes the board?

The moment of inertia of a rotating solid disk about an axis througlz 1cbr0y00h.c4y )pil ji zc3c1ip0wh its center of mass 1ccpc04irp cy0)3zii0ly01 zlhj. bw 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 sittivv36t ovp cwun( +1.heng on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity. hp+6v3(t ev1onuvcw increase, decrease, or stay the same? Explain.

Two spheres look identical and have t+bubal *ryb+.he same mass. However, one is hollow and the other is solid. Descru*brb+l+b .y aibe an experiment to determine which is which.

The angular velocity of a wheel rotating o.ufdvx glp6 o bxqb3wcp-,5 ;5n a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point a bb, 6 ;dugl5wo-vxf5 xpc3q.pt the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a largd h nu*) 1fwak/jm/3ooe freely rotating turntable. What happens if you walk toward thmf ko/ h* /n1daj)uo3we center?

A shortstop may leap into the air to catch a ball and throw it quickly. As h atm5y/4m1uf ze throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (F1taf z/m u4y5mig. 8–36). Explain.

On the basis of the law/ nh/sbqp.8 kd of conservation of angular momentum, discuss why a helicopter must k .q d8nhsbp//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 raem hg;-xc6)u.jd hmg6 79bosmdians: (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 Eart:g 83zmqup4ls h because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen os 43um:8lgq pzn Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at. u 6i9xludnqcx.w i21.ss,xn the Moon, 380,000 km from Earth. The beam diverges at an anu2i,dq 169xw .x.n s cilnsx.ugle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor ve mfv)sc(1y z-x64jf is turned off during operation, the blades slow to rest in 3.0 s. What is the angular ay)fj 6v -cxm 14zvefs(cceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on0ufk : zz;.ieo p8ru5g a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diamet5ugzz ;f0pu8.kre o i:er?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How(5;j obbya3)of .fwn s many revolutions do t 5jfson)(wb aofyb;.3he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its a -*4k(ixc)mxzj dh-f gngular 4g cki-j*d)hx-zx fm( velocity 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 m)s wuz:azg5r1 akes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated :uwgs rza)15 z1.2 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 the Earth (a) in it,d ++i/iy3vx mjl-5udhedx v, ptdr)9s orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe-8yf wc jget2 mh 5ws) i6p+dz80xb:jwed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrif oi;s*ta b s.*i:h4fxiuge rotate if a particle 7.0 cm from the axis of rotation is to exih :.*ii4s*;x aob tfsperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniforml zn(sr.4d, ihly about its center from 130 rpm to 28 .d(l r,hsz4in0 rpm 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 radiu)5caprha * m,ds $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the A e7nj;rexeo nvk7 q;wtj()t;1pollo 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 tho 7vjn q(7k x;ew1jeontrt );e;ught 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 uniform2yo0pu gdnua8n*4/ 4mw9nke bly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turne /nuw09nabd2kom48nyug*p 4 in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcula3224 /kgo yfgc.xonhm te
(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 high nsn/y98a9l,5uivqk e ,e2qnlspeed jets in a whirling “human centrifuge,” which takes 1.0 min tlkeves 5nu 9y,nq/qn a, l9i28o turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates udk ol ;8n ey.y bhzj5.i2 ryx)oq2d*o+niformly from 240 rpm to 360 rpm in 6.5 s. How far will a poe i8.)+orx2 yz2 n; dylqkj.od5 yo*bhint on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off wpulx -4c79ush1h i)rbhen it is running at 850rev/min It turns 1500 revolutions bp-ui9b71rc)l h 4uxsh efore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its spe;7sjefm b)gb,5 z -2nvbc-ley 5e( rfded uniformly from 95km/h to 45km/h The tires have a diameter of 0 -7nef)v g (j;zbf-dbes5 rem5lc, b2y.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces it 7d-3rgcdu nnt(r* pk2e6ylw-s speed uniformly from 95 3(nnp6dc7ygrl2ew *r k-- udtkm/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

  A 55-kg person riding a bifx(6doalx1k 8 7dh-hrfvh4r,i t 1+k hke puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. h- (rk1xhoflit4 d 7+hhf81 kvra,x6d
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm widw npjzb9dd8ae/;: czjc. cv*o0fq 41de. What is the magnitu/ zdqd4 p jo e.c8zf*10nwv dc9ac;:bjde 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 hw/53m4itne2tt mvx *shown in Fig. 8–39. Assume that a friction torque x4 t* wvnie m/t35mht2of 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 - id .ydank0gqte4cb76 q; jx9rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and theyak tj.q bi ;x94geq6dc-0d 7nn released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require; l6wyd d k56 8fbmwfera2+ch9 tightening to a torque of 38 w9b d56fa;68+e lcyw fr2hdkm $m \cdot N$ 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.ut 8lhd-cef ge/5tq,hly 8 4:y8-kg sphere of radius 0.648 m when the axis of rotation is througldt ft5e8 y g/cuqhh-84ley,:h its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The 6 zkw)2w+,s2kz+s qo2 t6rzwp+: ypu tic(qly rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignorec 2q2+26 siq,k pow:zuzy+lt6w+pk)ts zwyr(d (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin,0mo c 2x9kq (ahi ag7 )+mxxwwsym06v( light rod is rotated in a horizontal ciayw9o0agx q6 v0(7c xi)mk (2xsmwhm+rcle 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 wh/l;gnk; ofe 5p-m:5jdec onk,eel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay ieg;n:-p ; m5 jf,ekl5n oko/cds 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 twho.1 4du.m hxhe array of point objects shown in Fig. 8–43 .u4o.dmwx 1h habout
(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 w8.i3+zujnut 7sfc,phb n c+.vhose 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 cylind7eoc, f9z hms0rical satellite spinning at the correct rate, engineers fire four tangential rohc,9 7 o0sezfmckets 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 cylinder with a radius of 8.50 cm r: s snc4kw21wand a mass of 0.580 kgrw:1cks 24sn w. 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, acceleraz/x9 knuo p8n)ting 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 g6:nw) mmzalrf/ 4* nv2utt6jis 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 k unzlm2r)4tm:awj6 v n *6tfg/g) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut hf br q7./s*mi2p(z bc 5r;fxroff and is eventually brought uniformly to rest by a frictio*b mxf5rqr7hsc rp.(2 zb/if;nal 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 a63:2bz:ggf n n otk,x;xime8 zccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is throw:dnm- 7swdkc-.:b t yzn solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The balz 7::s.nmdc -dtb-kwyl 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 bx -q: kgnkaub91ug +c3lade can be considered a long thin rod, as shown in Fig. 8–4 cg+n1ubux3q :ka9kg- 6.
(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 consiswx j+ 3kk15(alg nm)htts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fqz6r3yz 4:xb gour full turns (revolutions) and relea:gr 3 y4zx6bqzses it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of iner6l )w;uoj qfx1pnrl. 7tia 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 deve90-szqrr kdof 8/4sc ivt9y/dlops 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 withy*zjj6n20j9ydkbhc,c )( ;zm: ldddeout slipping down a la k 2l6ddh0ycn)y 9;*,meb:jzdcj (jzdne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as ;wb)ssz*uqb 5the sum of two qs;wz)s5u* bb 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 msq mf4ehu)zd/( +q5q kuch net work is required to accelerate it from rest to a rotation rate of 1.00 revolutiomk+ 5q)fq/4q h( sduezn 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 res6a t84 tesj:wvt and rolls without slipping eav :jt 864wstdown 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 fall 7* tc;7ato kywm5pu;eand its lower end does not slip. What will be the speed of the upper end of the pole just boc* pawkm5euy7t ;;t7efore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of9.v z1tsh, ;9kh kfb:nm3yf ff a thin string in a circle of radius 1.10 m at an angular.fhfkktyf9,: nh9;b1s3 zv f m speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momenty9n-o-gwkze:uy :5k0vac k6bum of a 2.8-kg uniform cylindrical grinding wheel of radiuauyny:kg9 e5w:cz0kvkb--o 6s 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a pmn+e kbnt rf yu,p),t+9 qk+z:latform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizoput,+ertn)nbkk f q:+y,+m 9zntal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her momen-9a+qsh/ p o8pm75 qk ka5(fieovl*bst of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If svao*(q-fb hi5s+qpas/9 57p8 kmk loehe makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an init aa 90-(rlt,2ake;z eb9ebzv xial rate of 1.0 rev everzexav992 t- ze ,rbla( ;k0baey 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 rotating around a vertical axis th d)es5 4 dofjwru)3g1trough 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, onto5 e ds)wdu3frotg41 j) 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 momee,dd*s ggfw/dp9+ q6:6oup+ d t3 det6sk 6yecntum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Egh2p *j9z36 znwfml p3arth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto anfn npp *5b)9nq identical disk rotating at an bp9*n n)qp5fngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 .;yoas m q8icjnl-/9u$rev/s$ 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 kgjrthycu2y jh1;.8qx jr0xv ag:/;y d 3 stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment a0u;:yhrdg./cxrqyyvj3j tj; hx28 1of 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 angular velocity o2y c.n6p das4mq8vg6b f 0.6s.vb dpc284gy qmna68 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses itepi 7d jp c;s/2es1vnf 552dknto 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 ca5epssd/ f kjvt2cn; 7 i21epd5rries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess(9kt9c;+vmay( e syse 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 x zr3bs(1(p4mj+ o lyh$ 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 rotagm-l7;m2xhw9+ c c :adsp(grmte freely without friction. The moment of inertia of the person -:2p;l9mr + c7d(m ghsacm gwxplus 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 merw b;dpoe7czwu28 zes3ta*9g.ry-go-round turntable that is mounted on frictionless bearings and .b z*coa te;w829zsepu7d3w ghas 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 grouny;*jn+ m5gtdxd 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 pejxngmd +5 t*;yrson 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 thvo3 vw:o,q3 eca+(mrgf t+5uuat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its oa (cueoto,3fq:+ugm 5r 3wvv+wn axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 9.p gqjf5 tvj(yq73lu1 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 o / kmskv+g7-vjf radius 0.20 m acquires a rotational rate of from rem+gk skv-jv7/ st over a 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 cylindricalnzm4/lo/rofpe*h :s - disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculath/m* 4 fslon-or /:ezpe 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 o .. tmiynxe6f2f 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 Suoc gdueub0-8q7c)b9 qn, 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?8qc oe0dqubb)9 -7 ugc Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automob1oo /;pd6ohqolq6t r 5ile 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, 6/qt6 o5o oh1 lr;pdqoand 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 anj.x gvo/8s*p b $H_2O$ 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 at speem- +xsp1uow z7d 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 lengt3zgy)a pt xu 6x+nv,(ph 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 center of mass of the rodp(t3guy zv)6,xap +nx , as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. I b78pe6pvr og*t is standing vertically on the floor, and we want to exert a h6b*r go7epv8 porizontal 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 oncyg/q;/ gfd3f: wd/f f a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal fory/;fg/d df:c3 f g/wfqce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 ro/kuhj0l0 1refck into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achile 1jf 0u0r/hkeve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solidiov0(hi2cv3eor(pp8l tl o 5) cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate8pvcl3ih2ietv (o0r5lo o)(p 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 c:jpss yu09x- slutch assembly which consists of two cylindrical plates, of m 9yx:0ju-ssspass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rg oannd1bnj *;v-ys7 ;olls along the looped rough track of Fig. 8–58. What is the minimum v s-b; ;j*gnyvo nn1da7alue of the vertical 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 efmj8 xo sw 5y*/zhwy82q 6+frassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniforml*7,ioikecmh ff1 l4i: y from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelerationfeioklm ,: 14i*7cihf 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