A bicycle odometer (whilp- o, szcbkdtl;m4/3x (s ks3g7fjl9ch measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bcg z- bl p97(o 4xskkd ltf3,;3/sjmlsicycle with 24-inch wheels?

Suppose a disk rotates at constant angulawxj9 g +p0q4jo;xpv l)r 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 acceleration? For which cases would the magnitude of eitherjgl;x 9qp+v)0 4wj pxo component of linear acceleration change?

Could a nonrigid body be descr*vw7njs k 25pvccjmz4:g 7ep+ibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? E k 4dvsa47rce xj5xn8,xplain.

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 yo6 5w vqi:-ziqtur hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer q5q6 wti:v -zithis.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tp jshf40 ux+d-li(u.khe 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 orxp lf0ud h-ik +uj.4s( a large front sprocket? Why?

Mammals that depend on being able to run fast 2 .i;1v,inc1akjd swz have slender lower legs with flesh and muscle concentrated high, cloz1i 2,i.skv ;wn ajdc1se 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 op7jag*u r4cqt-/g1u d) fnf*cf )h-ylong, narrow beam?

If the net force on a systemkk ;b1/r b0b7 dlg7pdv is zero, is the net torque also zero? If the net torque on a system is zero, ibkv dg;77lp / rbk0bd1s the net force zero?

Two inclines have the same h( g9uj5vfo l9 .jrp+hueight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline .f o 99lhvjjr+upg(5u will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rzbwbe0y el .-x5bqh.;lq.zp1olling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which zew.l h5.bxz-q.b pl;ybq0 1ehas the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radiue:b+z4 bxhn7kstni ;pu(suz jc7+58us and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotationalps+ku( n :bei n7+zzhb u4us;c58tj7x KE?

We claim that momentum and angular momentum are consez 5jqf8ctc5f5i -ub*arved. Yet most moving or rotating o tq5ac 8i ufbc-55jz*fbjects eventually slow down and stop. Explain.

If there were a great migration of people toward dp28m-jvyux 3 p q)(hgthe Earth’s equator, how would th)ympuvd 8p g2 -hj3x(qis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having a6q w hzv,enyn8(i. 1tany initial rotation when s1 i teny.v ,hqnw6(z8ahe leaves the board?

The moment of inertia of a rotating solid disk about an axis throug7ipy (osszmmx .m54j: h its center oymx :(m4sp5.jmzs7o if mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on anmg3i95bk 8s q*ybih/ a1u4e3wtr7gb rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explaibqt*5e93yu3 ihg 7rg4mw b i1nbk/a8 sn.

Two spheres look identical and have the same mass. Howevera5ml 7ji j52fv, one is hollow and the other is solid. Describe an expia2j 75l mvfj5eriment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In wyx 7fnu4)j/uzhat direction is the linear velocity of a point on the top of the wheel? If the angular acceleration j)fux 4z /yu7npoints east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntab jz 9: u4leuou2kw+(ocle. What keuo 29 ( lcuzo+:w4juhappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. Al8kthy3cfi ol5pqau )//1, ovs he throws the ball, the upper part of his body rotates. If you loo8lo5 1aiotp)c/,/ q3hfkvyluk 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 conservation of angul,6y6, i8uxkb:hy xqcmb fo 09kar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or k kmqu,h6y6x fbci09xbo y8: ,more ways the second propeller can operate to keep the helicopter stable.

  Express the following aq/lzaoxczc; w*(g/t 9 dvmo/9 *b3bgingles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculat7mz*q.ebbbtl8qz/s b- d r*x3 e, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon,*sz8 *3q dx.t- b7zlbrm/qb eb as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam d -j)g aiiai*j6iverges at a6 a j*iij-)igan 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 rpm. When the motor ftt:y ruq 9t/1is turned off during operation, the blade9f1tqt:/ru tys 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 on a level floor 3.5 m to another child. If the ball make,6otq9hx (/ fh 7nap ia2fd0xys 15.0 revolutions, what is its diameter?6a,ax nxo0ipf/2( fyhd q7th9    m

  A bicycle with tires 68 cm in diame2+nfz ;iu pjieg *g7rn9ruxzu38+m c3ter travels 8.0 km. How many revolutions do the wheels ma+m2 3r ri93 nz8j*ecng; ifzguuu7p +xke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 25:h0k / uck0tydc1-pxeh1w 5cs 00 rpm. Calculate its angular velociteysc1- h : 5ukxkpd0h/ ctc01wy 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 aimln2be 2 .g5*dm4ih4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cen. iml*m5 d aenib42h2gter?    $m/s$
(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 or003vn if y k(,shheri;qqt3, cbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pou pg-59(9arjeait 8r epo9l.lm7 po-tint
(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 particl .:ltk- fxxz69n/ 0h. kpm.tgkrt 6towe 7.0 cm from the axis of rotation is to expeh. g6tm.z x/n.lkt0-tf o9xkkrtp6:w rience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to4h15bu ied7w -kcavthant /2u4; m0ph 280 rpm in 4.0 s. Detuipa;hn4 w2v1 4 btk d07hh-t aecu5/mermine
(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 x qo5 2mcma.h;xigxe :1f*l-p$R_1$ 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, astroo -m;j -zrd9.3ggaa qenauts 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. r od. jag-9egma;zq3-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 15,000 rpm in),n xgz6ajf7mlaiz5 :oj 1,yn 220 s. Through how many revolutions did it turn :x,gan,1)mly5 6a jzz j7nifoin this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5qa*2quooi64uw x sh ubux, it9:7 cg tuh2:6-z s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying hig+a ,ctecd((mn w f:su9/r/ad9r5y pgyhspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revom5uc w,/ a9:gtrd+drf( ce/9nasyy( plutions 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 acc;phiqg r jah8r((* 6yoelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this ti(6rhi;jh8 r oy *qgap(me?    m

  A cooling fan is turned off when it is runninguh.te( g8+oe7jnfy; b at 850rev/min It turns 1500 revolutions before it cb8g;+j7( unefeoyt. homes 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 revolut w efzw4q+1q8w9e*r jiz1u3tuwg.i/ gions as the car reduces its speed uniformly fr9jz. ii 4f g31tqw/1ug+r8u*weqwezwom 95km/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 revolutions as the car reduces itsw 4.bpk fqi.q x8mye: o )c)w)kxy/ij ++vk+hs speed uniformly from 95km/h to 45km/h The tires have a dim4yok xf)ex)8/ ik .. pwivbc+sqq:+kyj)h w +ameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts ali*r*w6r5 ro1k(ivutqz 0v 0lt l her weight on each pedal when climbing a hill. The pedalsr*1virqvi rt k0tzl 065w*uo( rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on th9 ,t kx.bfs/dse end of a door 74 cm wide. What is the magnitude of the torque if thes.k ,/ b9dtxsf force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–f0 m;fxgax /46gzzgl*39. Assume that a fricti*zma0x 4/ f fzxl;g6ggon torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod w+osuxhzz sp.,k z;h( )hich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and .(z+szzo; hu)xps, hkthen released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head uvpr*+y u b+y/u0 ni+lof an engine require tightening to a torque of 38yvp0+nyb+lu u /riu+ * $m \cdot N$ 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 momentv-xi*lw xe*4yg72 h sw of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is th*hi slegw7xw2y-4x* vrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.s,rkbl.bbb.)sv k1 ,d 7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The k dv rbs1bls.). bk,b,mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated iynx/:4hk ri8no: hh1 un a horizontal circle of radius 1.2 m. Calco:irn hh4yhnk: /u8x1ulate
(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 rovjqq(p .cz0l am- 3z i59z n34n1odm8x+pyxdotating at constant angular speed (Fig. 8–42). The friction force between her hands and m zx3 vqypa. n- (zmo4dx0q13+jznp 95codl8ithe clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of tv j)d7gyei qg;ot763the array of point objects shown in Fig. 8–43 aboutog ;vgj7qd y3ei )67tt
(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 wlw f1 jkvwq2vyzg ywg7.a-:*8hose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical s,gf2kbdongu8 hw 7 s;f***r gnatellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 36*w*n;g ,827dhr f* gunbfkosg00 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 lb/z ey2ti )hsq:z 1)jwith a radius of 8.50 cm and a mass of 0.580 kg. Calculazyil:tbeh j))12 zqs/te
(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, accvm7bvl3zt51ah 8rv +of i(ix3elerating 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 ablvl1rg)a4: c2x. yci o q t-9dkrl5no8te 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 (eachca xt8gi9d5r qr.4c ylo nklv12o)t-: with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut 5vxj iv8ulyir4oh6 :)off and is eventually brought uniformly to rest by a frictionalvj4lhxu: 6 or58v)i iy 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 acceleratx-b,4qbi*/0 oxnn xix es a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown c59ukbr4mzzr6 b( gh*solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniforml *ch5u64 9rbbmrz zg(ky 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 conkg (8o ydl3tjh2i2-a fsidered a long thin rod, as shown in Fig. 8–46.dkyit(g2oh2falj 38 -
(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 twosn+p8a. du)bs 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 four full turns (rea l 2yzzy 9rzs(a6y0a.volutions) and releases it at a spee.(z9zs62y az y0ylr aad 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 moments *1f8d-rz46p rmcanl 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 of 2ymc -7gch0e3b 80 $m \cdot N$ 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 slipping dowitsc*ny: 7.z lszg9j2n a lane at 3css7g i:9lny.zz* jt2.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with res6v1q* mffo yf+pect to the Sun as the sum of two tey1*+6 fmofqvfrms,
(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 16404g:ujek(bs6 jxmkb( 1 kg and a radius of 7.50 m. How much net work is required to accbxk1sj(( kje4mbu : 6gelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and masiny+,ffbwfe4j h 9/ +;bo4 tpvs 1.80 kg starts from rest and rolls without slippin9f;o/hbptj+ 44+ f e, nivfbywg 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 fall and its2merk( lrj 7n+ lower end does not slip. What will be the speed of the upper end of the pole just before2(mj7enrl r+k it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rota-r2 uogmn gkikn6n-- 6ting on the end of a thin string in a circle of radius 1.10 m at gu nnk- gi-ron-62m6kan angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniforfi0 efagl.g n7-w++ qpm cylindrical grinding wheel of radius 18 cm0f. wipqe-n7+gfagl + 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 s rw4ts(:x/+6g d8y/ rh jpjpneide, 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 rotation dec s t4dx(rp+p6jwe /ryhn/ :8gjreases 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.u9lxy6- 3hho.g x8-ouqw -whdu/ a )ov 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotal-hdo -- 8o.v w6/)uoq3x uwhu9 xyghations 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 o i4aq0d(wug u7f 1.0 rev every 2.0 s to w u04dqagu 7i(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 ry4 *ul3(kcfvrotating 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 of the wheel after the clay l* vy3(rcuk4f sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnx cp-u4 pa)sgk2i gza68u,y 9zing 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 Eapa7,5ca szs 0d(0qd yuz4n a)crth
(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 dropp) liymt,c, ,vpp:r*xled onto an identical disk rotap:vipml,*l , xyrt ),cting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsnx j*4vb:cz3 hi91(z .sc z7 *lnqtmin 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 thy noa5d)1mhw f18i55ck0yle ve center of a rotating merry-go-round platform of radius 3) ka851vlhycodynew 5 f5i1m0.0 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 rotnu- t2jr qrrep) c 8o95g18ly(gs05z *exqgq pating freely with an angular velocity of 0.8p2ren50eo()-jqsrg xz t9lr1*q yc8g5upqg 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing aboazx ,jy- 7o3neut half its mass a7exjyn z ,o-3in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (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 involt mxc2 1etxb/qo6a.t:ve 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 pbr1j d:o iz 5,ou m+ri/:/yi+eb4q lf$ 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 pl wt uqg90b6r/v jchqpd0-2 .kvatform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus theh-9 u wbgvq6rdjv k2tq/c00 p. 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 mers g)2+1b9hmk wnr9y.w 5gnrrw ry-go-round turntable that is mounted on frictionless bearings and hkrggw299n r yh5m1.)w bws rn+as 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 ground with the end oe/ tungb+a2,3u rim/ff the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the sp ibtu,ea3/ rg m/fn2+uool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Decs 8oht r.xu :/kko8u:termine 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.) o ktxu:.s:uo8h8k c/r    $\times10^{ -6}$

  A cyclist accelerates from rest at a r aj0sg.2 ;ormdate 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 0.20 m acquiresn bbwcomk1c/g-)*yy ( a rotational rate of from rest over a 6.0-s interval at constant angular acceleration.c y)m(gw*oy/b nb1- kc Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050sg,ud oc s91 hl18hq+acb3k, t 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 calculate the linear speed of the yo-yo when it reaches the end of 9 18 o+cukhb ,1ld3 hsc,sgqatits 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whe) 3um(9fdsxre el ($\omega_R$) 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 8.0 times as great, wkh,9ep0 2xjo g , uejo s7ssz)k(l(j*rere 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 oj g,er2 7k*(,0)skelx9ujh(ozjpss its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for n cdd*a8mp3n.e lpn)(it to use energy stored in a heavy ro.dp p(8 3)c *neadmnnltating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should 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 as+stmxlcm; vf3m at()49 kx, mn $H_2O$ 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 g5g :j ruebvcecndag,:,,84c a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore frz todq6 5+.xwhiction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the m o5.x6d hztqw+oment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius hzmzlp-lv,8 rmvs m(:u(jf 28 R. It is standing vertically 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, wh (s8,zmlfm hvp(jl-r8m2 zu:vere h

  A bicyclist traveling with speed v=4.2m/s on a .w8m;ubi rf7mo62u4 ;k. alw mmx5nuaflat road is making a turn with a radius The forces acting i8uxmm2b; .n4mrau5;uok6aw. flwm7 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+lusv- n;kzx 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 to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this fesnl ;v -xu+kz1at, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rkxocxl( *40,xx jyn:gods, making reasonable estimatescxy 4j:nox, * g(k0lxx for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylh2ncgq(i -+ymr-g ,j,drc2y9fg u d5sindrical plates, of ydjr,nrgi + s5m uc( gdyh-,c92gf2-qmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ainp 9e--;cmu0-z6y 3xwemg twr 5:n pwlong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assumpxmw5n0-t-wrp; uc :yw i6zee g-39mne $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but :nsbs:wy+r(f do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revol9qysb.0 m0zts utions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 mms0t0y9zq bs.. (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