A bicycle odometer (which measures distqy e+;(pznka5 ance traveled) is attached near the wheel h5n+(ay kzq ep;ub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at cooo *8-fuyhw,p9btoj.nstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component j- *oh uby 8,potfwo9.of linear acceleration change?

Could a nonrigid body be described by a singlebyg 6b2 l2owo6 value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque t:+ ij,k9lybnb,m 8is dhan 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 g1s)tgcx;qzqh:-;a awith your hands behind your head than when your arms are stretched out in front of you? A diagram may help you: qgqzx-t;c) ;ga hs1a to answer this.

A 21-speed bicycle has seven sprockets at the rear wheetf tyv/ z,p5e. o 3xni,uqy(;nl 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 oiy;x,u, 5 .tfpoz(/eyvntnq3r a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower lego3 ghl2sa5*0bro m q4os with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explaingomb 5h4 *o0o2rs3 laq why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a loa5 )mv xo5f+wcng, narrow beam?

If the net force on a system is zero, is the net torque a6h*- f ypx0utwu2*ryx lso zero? If the net torque on a system is zero, istwx*p2yfu*r-x6hu y 0 the net force zero?

Two inclines have the same height but make different angles w dm8 mzb3pd1d7d rks(9ith the horizontal. The same steel ball is rolledmd zs(kdrb17p93dmd 8 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 r jld 11(4xmz0kqd wut,est) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first?dk zwuq ,jt1x0ld 4m(1 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 mass. They f+hmq/eyk4 imoj:80d 3 lqjnm2u.ymo o+m- /pstart from f/joklyjndiy.mmom0:eh+mu38- 2 p+qo4/m q 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 rotational KE?

We claim that momentum and angulart1e-,x,b.kd x dbc ow0;cg2nn momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. eb.-kc2x to ;xd1ng,nb0 cdw,Explain.

If there were a great migration of people tob; s50ucboo gw98he b0ward the Earth’s equator, how would this affect the e8;sbb0w5go 0c9oh ub length of the day?

Can the diver of Fig. 8–29 do a somersault without ha.lk pw:wqx)- gving any initial rotation when she leaves the boarkpxwwgq :). -ld?

The moment of inertia of a rotating soqw0 9e; myikgp,2;tvi lid disk about an axis through its center of massemit9;g,v2qkp w ;iy 0 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 holdini9;els ce asi.+,i os+g a 2-kg mass in each outstretched hand. If you su.c9s ;+ilie,ss+oei addenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, ;t+v,z j):jwi luy8coxpbo lbip)qpj* ,*,k 2 one is hollow and the other is solid. Describe an experiment to determine whijj +k c8wuv:l jzbi*t*),ox),p p;ypl ,o2qib ch is which.

The angular velocity of a wheel rotating on a horizon(a/:gphau . xn: jlhz6tal 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,pal:. 6 a uj/hhxn(zg: 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 rotatingoh e9tf1hs ;a4au1;se turntable. What h u;aefsh;t o1a1e94 shappens if you walk toward the center?

A shortstop may leap into the air to catch a ball at v1to6rxhx6r n )65vind 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 in the opposit otr5v 6nx6)t1ih vxr6e direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discusspb/m9mbd s32s,cd bz) why a helicopteb9/, bz) m3sd dbsc2mpr must 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 an q;huy:75pf(2t s umbzuy6 ,ijgles 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 angtr0j5 k),p 6y uig8d 6:njjup amazing coincidence. Calculate, using the information inside the Front Cover, thu5) y pupg,j6jngr 6itjk:08de angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dxrbv67i) / qums+q,9 g-nl.hrh cdw5diverges at an angleirsq+ch6h w xq9rn v5/d l-,m. 7gubd) $\theta$ (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 is turn l-rfqbdatgblm),5)n0.zt:ned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades sldgb)0,nz :.tf)m qtn5 arb l-low down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to a0.yskdmjop8;71f xu/ .bmttq nother child. If the ball makes 15.0 revolutions,0.. 8tbq/psx y k mmj17oftd;u what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revoluhqoh gg(m g-g2w0qbln e ws2l)4)v).l tions do the wheels mabmgwqloveh hw4lg)l) (.s- n22g0q)gke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250grp* i::n.ye os-bn/e5h)dyn0 rpm. Calculate its angular velocity i:.i)p:d -ne g n5ery s/oy*nhbn $rad/s$ $\omega$ =    $rad/sec$
(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 4.0mrth ;(u;ve d+dzv *6q s (Fig. 8–38). (a) What is the linear speed of a child seated 1.m(r; ;qd6teh*zuv+vd 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 its orbib rpqk csqtsmn+q* --1v82z ;xt around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 6p pw+mv)kjq )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 particb.vw26au h(il g*:s lfle 7.0 cm from the axis of rotation is to experience fshvgbiu 2:.6wll(*a an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130s; .cfpceuj:ka(-3nhf z7c h ( rpm to 280 p(fe3zj-s;f u7cnc.hk( ach: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 radiuwe9thz 5 s.0fc(+zbuis $R_1$ 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 Ad 91 j+ tbka1gk(tbxs w5stnzx0f7 07dpollo spacecraft put themselves into a slow rotation to distribute the Sustk50gn +7wj1( x1btfx7 kszbt0d9dan’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a 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 unifo gg;d ovs(7c-f5)siahrmly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time? hsafgv;cd 7 sgi-)(o5   $rev$

  An automobile engine slows down from 4500 rpm 3tw(bk* vokenn ,;t8jto 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 stresse rw6s5v d;7fqdty2,y ys of flying highspeed jets in a whirling “human centrifuge,” which y7tfy,6s y5 qvd 2d;wrtakes 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 240 rpa5q/ zrws(s7 em to 360 rpm in 6.5 s. How far will a point on the edge of the wheel h7z5(e rq saw/save traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/m2ibe+ wnb8+ aiin It turns 1500 revolutions eiwn2 b8++bai before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speez ;cafia5/oq/d uniformly from 95km/h to 45km/hzi/f;a /o5c aq 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 its speed uni5k5-+ja f)/wuvw m yepformly from 95km/h to 45km/h The tires hav+ je5 kpw )mvuw/afy-5e 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 bike puts all her weight on each p8exthr;/proq (0 n-aeedal when climbing a hin-rqx h er0oetp8 /a(;ll. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on th .qq)8vawn4y uj.:m fie end of a door 74 cm wide. What is the magnitude of the torque if the for: f4y m.wnaqi) q.u8jvce 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:.t3-5p 1x ljj t vooad)ee+oi shown in Fig. 8–39. Assume that a frictio od-ole eot3.ijx)+:j 15avtpn 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 wh9yc fra7hh /c4ich pivots as shown in Fh/cycfarh 479ig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to 7,v(b b;+ nqbyq3u3yjwfwmf+(r:c fx a torque of 38(7fn:+uy(+ yq x vqwcfb w;brm,3 j3bf $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0 t*deh rjhh3/b8hml29+ ;zjmy-/ubby .648 m when the axis o*zr/+m l9 h-b8h3dyby th ;j/jmh2 eubf rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.f+sk +rd(vpj+ The rim and tire have a combined mass of 1.25 kg. The mass of the hub can b+p kfs(drvj++ e ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end 8ttqizu. l,s 3of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. tu3.iz, ls q8tCalculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at consf*lsqbwd/ e6oc3 )qps.-xa4o tant angular speed (Fig.w4a.o-c/soq fbqls)6p dx*3e 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of pbv:d5o//mhx 77o v hvsoint objects shown in Fig. 8–43 abou5:h hv/od v/7obm7x svt
(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 8em)z*t+.tq fnp q*auof two oxygen atoms 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 correct rat npw 26qmo+jibcmiu6 *df)dr5wn./ h;e, 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 force of eacw6 *+b/rdji 5 ch6w q;nfum).i 2pmodnh 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 asu wol+q(sl/d4(xc 4j mass of 0.580 kg. Calculat 4csu(ls/lwoq j d+(4xe
(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-/cpxyc r8i0ly 2el2)ka9 jmj 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 onxed8r01sy:nqh.db 4o a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate s 0bh8 1q:ex.ordyn 4dthe torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventuaq j;q9b zg8 iq6zoky-*2p9ij1:dhyablly brought unifgo q9j8 :zaj -6*iqyq;zpydbk 29ih b1ormly to rest by a frictional 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. 8o-;: 7ox ljtoar: 5 wsydsl((hkc1+f r–45 accelerates 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 throwsy j;vtv4f5 /bznp 5v0n 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 accelevz /5s4tj5yb;v np0fv rated 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 sho4kqq m y )v3jqo0-3nfzwn in Fig. 8–46qv3m0 o)4fq n3 yqjkz-.
(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 consi6kfj o- 9.giyysts 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 accel48am9v9yplfqmeex0h39rxmof c -t .(erates the hammer from rest within four full turns (revolutions) and releases it at a spee48yc3emaltm ffe qm999.o xxr pv-( 0hd 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 inertia obp /ofco8bv4 bmk.k ttq5;i.9 f $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 dyfj gy9,3 k4 ifxf):h$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.u8/lk0buy +fr/b :afm 3 kg and radius 9.0 cm rolls without slipping down a lane at 3b8my/u+ r /u:afbfk0l .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to7qbw; j6/9,)lq mx7cpwxtsfn k :-siv the Sun as the sum of tx7-fn xkt/w isc9jm, ):qvs7pl;bw 6qwo 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 much ne0;ce y oewbrk ;w(pf.;0gq,vmd/um5x: o9bpg t work is required to accelerate it foq;:;egoybm0b eux .5rfc0wp (/;vmg9dp wk ,rom 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 aaun.2 gs) ..w1xe: sqgmel4rund mass 1.80 kg starts from rest and rolls without slippi:gqemu.1 .aseg2nx )lw usr4 .ng 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 ve/-cfxvajrdhp 7lj, ar8 3cn1: wcju8,rtically on its tip. It starts to fall and its lowe r8,ar3x lf/7ja ,cw1 uc8:cvnpjdjh-r end does not slip. What will be the speed of the upper 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 ball rota e t;5zc/8r+dub ex,ckting on the end of a thin string in a circle of radius 1. r ;t/ez5dk +c,c8exub10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of3-i5om ek 5bar a 2.8-kg uniform cylindrical grinding wheel of5bi5-orem a3 k 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, hand6;ub40uk/y( riavt d vs at his side, on a platform that is rotating at a rate of 1.3rev/s Id ikv ;(bu yvt6r4u0a/f he raises his 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 Fr4azf,4 yul7,uwgte 8ig. 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 rotations in ul8yt,wf,447geuzr a 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 f 9iwhk5)4f6dyv nmi+7tt ta4mrom an initial rate of 1.0 rev every 2.0 s to a final ratitytvdw7n4at4fmh9m) k i65 +e 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 rotaim- -b53 1a qznyapv:d9vc:dvting 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 o- dvv:y5mz-a:qcb 3ip 1an9vd f 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 figure skater spinningzcc aro,--e+; lug hb4 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 ofez9b g,s1fzhp- ;p *nd 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 d0 a ys)cg9mv0of inertia I is dropped onto an identical disk rotating at 9ya0 cvm)g0sd angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 +a4mpw,lb b;h3*1h- p9oqi pucpaq 9e$rev/s$ 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 cente0 qu0u m (+kovn;7 xt2nnw4ukfr of a rotating merry-go-round platform of radius 3.0 m and moment owx nku4v+nm27 (kufto;0nu0qf 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 nj,*3thf5 //. x4 wbc,wb fdoqdimv7jangular velocity of 0.8 /3q4d wdtbcxjfjbom/f, .n* h7viw ,5$rad/s$ 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 v6isg )eral 9e28vsdya0bt(( about half its mass in the process, and winding up wib ( 6l8r9ia2s(v t)ea0 eyvgdsth 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 involve winds in excess of 120 qndrku + .5f9-jkbks -$km/h$ 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 ;ff/7nw4 h naz$ 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 at9cs6zkponfka n 5iz +z q7b898 rest, that can rotate freely without friction. The moment of inertia of the person plus the platform co q59kbf7zzpzan8i6kn+s98 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 .w 41mcjh:xznof a 6.5-m diameter merry-go-round turntable that isn.jwh 1xz m4:c mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end 6 m2qh2dz1 p-oaqio9 yof 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 aqyoi19p 2zq2-6dho mthe spool’s center of mass move?

  The Moon orbits the Earth such that the sau9h d2ebyz nt 4ec: 9:detpd*7me side 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 parti:det9u e* dc9:4yhz 7e2btdpncle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at aov2ov8pc5d m2a)+bz m rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m a4uy vyl/u2)lokx*sw -fcx..icquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the tor.slxoc - uv2*lyku)i4xf./yw que delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.i1r-( kl usd *4+x3,vd okvxtm050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of dxv,uo+s di1v3 *-rtx4k(km l mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear w-llmi/kd*c 8p qbdr(8heel ($\omega_R$) 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 kt sed1m9k * f *i;bkwh15yog;rotatif5 itys g;w o1mk h;bk*e9d1*kng at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy jb f; s u7h,h2we-dqf1stored in a heavy rotating flywheel. Suppose such a car 7sfhefjwq2 -1 uhb;,dhas 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 afsy pv wy6yijpiew4 m;.7 - l8)erat72n $H_2O$ 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 (hoooo,nex 848xp zia8 ;ijp) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (o6(q0qx v2izr i.e., we ignore friction)0ioz 2 qv6x(qr 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 Fig. 8–21g.]

A wheel of mass M has radius R. It is sg l7u1k kxpnqyss50. ,tanding vertically on the floor, and we want to exert a horizontal force F at its axle so ts un0p ys 7,kqgx.k5l1hat it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling witefo ll8/ 6e0ieh speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are th6 oie/8felle0e 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 into a sling of lengd*t 3m 9ahit.mth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head,ta*mt3hm .9 id accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinde5+a6fi(x +zu1gbjsqb ) l ea*fr and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater wibbz( )aj5f1 isxfeul q*g++6ath outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pla-5cbi2 wm(u /v+ wyanstes, of maaw-n ycb2/ wisv 5um+(ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rfie 1sx3:utz5 ough track of Fig. 8–58. What is the minimum value of the vertica5 31iszxfuet:l 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 . wc /9asn(wmsassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolut lz6ov4t4xi+r ions as the car reduces its speed uniformly fro+toi x 6rzl4v4m 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s