A bicycle odometer (which measures distance traveled) is ruh5 xztarfk8806 v y-.knd9rattached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch r9f5.xtv8hk 0znduk yr6 ar-8wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim h i/urwtzg;xh 5vz18g9 ave radial and/or tangential acceleration? If the disk’s anguwx1ig;/tvu zg8hz95r lar velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body bf)6e5*(at efulz o6 yse described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torlw-v di:*)+3:bfliy)eqkyb x que than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with you a.gc+tykdye2( 1rd*tjfq / y:r hands behind your head than when your ardrkty y.yf:q+ (1e /j2ag ctd*ms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle ha6oaej , ) yzxlsww) g7181+*yz zv+v- diuqqxhs seven sprockets at the 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 sprocket or a large v1d + xsqv+jz)yu7zzgl*yq-1h6 w ea), 8ixwofront sprocket? Why?

Mammals that depend on being able to run fast have slender q107c438 zs.z4paucel mkzy q;gvhb) lower legs with flesh and muscle concentrated high, close to the body ( ch;zpul b0z7ay g3mcs.k zq) q44ve81Fig. 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,nd1xi 6w6:bf q ;9kghr narrow beam?

If the net force on a system c(zqxm+x:a) ab .odhr t2 f,a5is zero, is the net torque also zero? If the net torque on a syst)dz:(a o rx2+f,b ht5qamcx.aem is zero, is the net force zero?

Two inclines have the same height but make different angles with thex i- ;vs-q,y utgphe** horizontal. The same sesgy*iuq;h *t--xp, vteel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dog ggs wpt1gn*x5vs:mg 4um;+ 2wn an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom ofgwgp+v n1 5mgsmx*g 4:sgut2 ; the 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 k7 x* cbt;dat;radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater spee b xatc*dkt;7;d 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-+ybnd-oxntzup3; n,o 11 t nt. Yet most moving or rotating objects eventually slow down and stop. 1yndt- ttpoo,ub+3nznn x - ;1Explain.

If there were a great migration of9 z j-uyk9lhrf 3 (8u:u5r8/oqyedcfr people toward the Earth’s equator, how would this affect jcy9( :9ed3uk8uf5z/ yh8q o-rrrufl the length of the day?

Can the diver of Fig. 8–2k9 xk; yep0(bj9 do a somersault without having any initial rotation when she leaves the b b e9kj(;y0kxpoard?

The moment of inertia of a rotating solid disk about an axis through its cent aptykjh8z g4;m.ks7b1k;p4u er of mak.44a;t psbzk uyp8jkg;1hm 7ss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool hobu,77c.l)syz oni 0 holding a 2-kg mass in each outstretc7z0u7noli hy ,b sc)o.hed hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and lb m/(o/sk7afru ,h g gs360nj;g1 crythe other is sofc;lrsnm6h g/ag0jrb37o( s, kg y1u/lid. Describe an experiment to determine which is which.

The angular velocity o elb4 *4t:2nha oqyx8grxox--f a wheel rotating on a horizontal axle points west. In what directionyx-4eg t lxqbxo*-o:a2rh48n is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on thw whg:r3a4:ll9xhwr)gny, d 4e edge of a large freely rotating turntable. What happensar hxd:l3l 449y:w,ghwnw )r g if you walk toward the center?

A shortstop may leap into the air to catch a ball a6trn 8) yts8) qyy )mj d.x:qdx;egzj1nd throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate i 8 nst .1tyx;y)m)zgrjd6qyjq)xe8d :n the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of anmews l i9jrn9i3iw .;4v6wx4dgular momentum, discuss why a helicopter must have more thanwnxr4iw; 9i6lmdv3 eij9s.w 4 one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anguvgdajwyhg; 8 .58 6wxew.6n rles 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 coindkcchb i- 3*(z+uz+ qecidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earbz*qh(+-u c3z cedki+ th.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at u8jmor c8hja0w 3 (cesm.8s4f the Moon, 380,000 km from Earth. The beam diverges at an aer(c uhsc8 8mo8 j3af4s.m w0jngle $\theta$ (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 v(5r7t4 96gnew xmjyj 3bk9 ukthe motor is turned off during operation, the blades 97 kmtjv64j5brn3u gw(y9 kexslow 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 fl*zv54ni : gbtgoor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter?gn4gt :v* bzi5    m

  A bicycle with tires 68 cm in dgoos-p7kbln;4j- ojx 8,4h rciameter travels 8.0 km. How many revolutions do the wheels mak4sj7jo ; ,bongx -p-r4o lkhc8e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotazi4 4aw ;.l2g (muaromtes at 2500 rpm. Calculate its angula2lu zg.4im4w(;armaor 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 makes one complete revolution in 4.0 s (Figtqw1, cly.wxm7dpw;,. 8–38). (a) What is the linear speed of a child seated 1.2 m q w,plt1m dw,;7 .yxcwfrom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of24wbb95kybs(z abw6n t( (rs c 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 speenp okr4.z 7elke3o88z-u8hm ad 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 centrifuge rotate if a particle 7.0 cm / nky.wve54 edfrom the axis of rotation is to experience an acceleration of 100,5ndvekw/. e4y000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its l+aaydi3bw 5 -jkq unw8,/ws ;center from 130 rpm to 280 rpm in 4.0 s. Determns -iy8lbj adw3+ w;w,5kuq/a ine
(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* /c oyn0bi2tot,rn:k $R_1$ 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 thp.8y5 vyov9 p8tj /uine 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 8pt/ .nvo8ip5u9yjyva 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Tdzelwhgmh6x.ml +xfbe* , i z9; ;y/4through how many revolutions d9hm.+zel lyz*mdg b xx64w etf/,h i;;id it turn in this time?    $rev$

  An automobile engine slowsmf85 +e agh r+tyfcv,- down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the strk9 sxu8ozm.et5*g6 ngesses of flying highspeed jets in a whirling “human centrifuge,”59 k6 *.uzgnsm toxg8e which takes 1.0 min to 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 uniformly from i1a 2yceht/amj /w, he8;k;rm 240 rpm to 360 rpm in 6.5 s. How far will a pointwki em/m,h;ej2/t y a;cr1a8h on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rev/6x-f )gq bm c.ka.qdqolutions before it.k/qmfaqgx6)d -.b cq 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 speed unifor 6ot bvt)d r3smxf4:/wmly from 95km/h to 45km/h The tires have a diameter of 0.8 r6fv)ot 3mbd4x:/tsw0 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 revolut vo/ s. una76cu-yq8bpions as the car reduces its speed uniformly from 95km/h to 45km/spo/c yvnu-q8 b67.uah 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 ad3:o6oa8zf k i8,jy0rsw i+ le bike puts all her weight on each pedal when climbing a hill. The pedals rotate o+0ziad3seo r6 8i, 8jfl:wykin 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 the end of a door 74 cm u xu/o4t8/yeb gpx z5(wide. What is the magnitude of the torque if tho 5/t8e/ uu(x4 xzpbgye 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 ab8 r9e9bn/mgum out the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0b8m9ur 9g/n em.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to: mi(*- :k rbk:zvldfp the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is k: m- bk:l*d vfp:(irzheld 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 an engine req// yzb98 ieubxvlz7/s uire tightening to a torque of 38 zuevsby//x7ib9z/l8 $m \cdot N$ 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 o 9/xsca)0myeinertia of a 10.8-kg sphere of radius 0.648 m when the axis ya9e sc0oxm) /of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter-nn6y u,odz1p/e02zgv1tac p. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (tpoen-zy12, 60gazcdupv/n1 why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horik5;lqdmk *0w(uxod 9hzontal cih dl9kum k0qod*wx;( 5rcle 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 rotatin4.:n -owa nwssg at constant angular speed (Fig. 8–42). The friction force between her hands and the claysnowa.4wn-s: is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the 0ipl u50+ e-/* fuq2 xnnbpsblarray of point objects shown in Fig. 8–43 aboutu ilfpslbx*00b- u pe5n+2qn/
(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 izvwm3 at u fddljo3+7z:v.t1lh* m1/ whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the corrwjt5p-. lfh(0 jptg/pect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady j. t- j5p0gtwpfp(hl/ 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 and a mass of e q3g9iihvo)g lmd+j4w73u3 evpwh1 -0.580 kg. Calculatj+ 3u d wewpvhq-3igie ogl7)94h3m1ve
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it frk*3y: al sob:zwl.xs*om 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 meg7eoox3 n*qq. rry-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 produce the acceleration, neglecting fe7*ox 3g.n oqqrictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off 5u ezm6i(/0z aq -jk ln2h*,s)f ftlogand is eventually brought uniformly to rest by a frictional torque of 1.5ehmug o ns6 (k0t2)li/zf,z-f*jalq2 $m \cdot N$ 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.)/nj ekj g/4nf /c)gna6-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 sfz3iq2 1hw0j solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps musclzs ji2qf301hwe, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shownk bg3gq7p2 u4t in Fig. 8–46.3gpgqb 4 t7u2k
(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 fldh)f4np6 c8of 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 accell +d dv5k94gpaerates the hammer from rest within four full turns (revolutions) and releasesadgl5 kp4dv 9+ 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 inertiqb u49 a)ql7+mhbc /c: ogee+la 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 qr6mop+ v6.se/tbq*v 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 sl9;ffui 0pt/vh.mpv( z ,mxv2zif*0 eu ipping down a lamfi xh( 0z/v.um*p;fezvip 9 ,ft2v 0une at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as theghwk tgwsf h3 9sx0j hww0ov3 77*qc8; sum of two termg;wth9 0 g3h8 co*fws3kj77vxwws0q hs,
(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, vlm-hloyq07r3bnmw gt1) 4 l 7.50 m. How much net work is required to accelerabhlyq tn031vw 4 m- m,l)lr7gote it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1xxrziu1 r40mxj6v:7a gf 4 n0g35kwpo.80 kg starts from rest and rolls without slipping down gvf z x6x43a kguxjro0 r5w:14 p70imna 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 starb ; p 4g-- ssaoflq3zeg.hd3dmuc6f 67ts to fall and its lower end does not slip. What will be the speed of the u-a ; fog-scz6u g4spheqb.f d3m7l6d3pper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg b x8fn6rt 8s m6z),qbsu ulgxc5.y+sw4 all rotating on the end of a thin string in a circle of radius 1.1zc,u.bg 4fys 5xmq u8 +ts6rn6 8wlx)s0 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8- x8th:5 w z/efa-p/blgkg uniform cylindrical grinding wheel o /txef8zwg :/l5hbp-a f radius 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 platform that is ro q(enzx84oet0tating at a rate of 1.3rev/s If he raises hi0zn t4e(eqxo8s arms to a horizontal 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 mjfqa au o c4:6wba1s3:yzl3-voment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, w:143wqf- j6obys a3vacu lza:hat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate froypt u3wa)ja6 bq,h/y, m an initial rate of 1.0 revuay3t /,) ,bywh6 pjqa every 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 through its cente8kskf*-*v i 1 0saphcjr at a frequenc-s08a*vkps j* fc1kihy 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 sticks to it?    $rev/s$

  (a) What is the angular momentum of a fig szb5h,*ezvt+ure 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 momentao0b v::qd7zr yj 6qr2um of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment xih-*x6qmif5j6 v7fc zd2;or of inertia I is dropped onto an identical disk rotating at af*rx zi6-od ;5j27mx6cqf hvingular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4s l c-l+/e 3j9;qt tutv9.othr $rev/s$ 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 cntht*; )re:ku enter of a rotating merry-go-round platfor:ue n;)rtkt* hm of radius 3.0 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-rod hm lcu0);qn7)sia/ qund is rotating freely with an angular velocity of 0.)mu ;c7sh in/l0q d)qa8 $rad/s$ 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 cv .:q nv up.*ioeq(;mf+dq8 kuollapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radi:.d o+nv eiqp(*vqum fu ;k8.qus. 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 involve winds in excess of 120 29utigrggyo8 n h9 8lazx2*(t/ dwm+p$km/h$ 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 7bz8fj8b awpf;e)ivot 0j (/nk4 yq 1j$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate mz5sa nmlbl;) 4mv+.y freely without y ml +vma;5n).mb4 lszfriction. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diametd,zcac5/n7e0 qo9rk mer merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of zcrqk7, c5eo9dn0 a/m1700 $kg \cdot m^2$ 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 of the rope lying on the r,a msz.po9+w 5s)buowg0o5 atop edge of the spool. A a5 uopr.0o aw 9bs+sw5 )ogmz,person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sid v 94688mttftuvp.s/c*et efne always faces the Earth. Determine 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 pasc8te96/vptm vft8t*. e unf 4rticle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate oqau r2c -x6uylw(c 4/bf 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 sh rx4t73 62hnzmhstop7kk*3(ne(tn yjape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at conn(k3nkts p*nz h4yj6emtx( t7h732o rstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical di0xy ;0cv ftonvw n5*rqu.(h)msks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg an*ntoq0.uw cxm0vh)( ;yrvf 5 nd diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the ann9jq wydu w te.nnfk:q* -:t37gular 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 8.0 times as great, were ro9 h2w c4ftvo:n3 yw8jdtating at a speed of 1.0 revolution every 12 days. Ihd 3wft2jv4 n9ow8: ycf it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution auto*okz5p emua+9ch9p6mmobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 m5* + ouaepp6cmhkz99 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 an- tw;,d2jr+rgev zt)z.luxai y ;+v ikz5f9(r $H_2O$ 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 hob, lip4gghn(u+5jv3 t rizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M an pqao gphqpi3( dplh-**ou) 8*d 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 center of mass of the rod, as shown. [Hint: See Fqahp(pupg3qpl -o diho8* ** )ig. 8–21g.]

A wheel of mass M has radius R. It is standin,nfe5o0 vcg9 niwb3,5:tb pong 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 hi,3beoog n:0bnt, p5 n5c wv9feight h, where h

  A bicyclist traveling with spen ) wbg,bkb-1nm4h cc7ed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are bnnkw14)7b b mhcg-,cthe 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 rocrthj9o 2 )c;1vap1vck k 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 achieve this feat, an k;9haprtvc)jvc112od where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinderdxeq*/ :5 datzz)rur7 and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretcheu57edz :)/rt r*dxazqd arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindricam usavw**zhuu209l)qo1 ,yud l plates, of uh0*9zum2 )s, auo w1ulvyd*q mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radiu8f*y v( z7imc eti(: t*xzb)yms r rolls along 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 tx7e *mv(()cttz zb:f *yimyi8 he track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but t0 ircqg6c4b7 do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as thhx0hdetp6 ;/c e car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the atx h6/0e pc;dhngular 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