A bicycle odometer ((6zqtjcfut6i7 m7p) t which measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you ut(c) qf6ztp 7tij 7um6se it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim gc+w5 (w:v rhuj-sm 7yckfyr*(xb0 q/ have radial and/or tangential acceleration? If the disk’s a- mxu+q (:b hrcfc/ ky(y*5jw7swgr0v ngular 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 be described by a single value of the angulare-b* 8 2pk wb/af/2ykn /slrdt velocity $\omega$ Explain.

Can a small force ever mk-ua z8:wnbi0g48pu5 ch.sd exert a greater torque 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 your hands behind your head than wh9ofw fmd3uj7a.s f0d 8en your arms ar7 fwua jo03 fd.9fm8sde stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and rg9(5q fkl t0npaw:s0three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large reaqfl9:k (r 0s5tawn0p gr sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower leguu7ld2se u4pw5y i-c 5s with flesh and muscle concentrated high, close to the body (Fig.u-d5p 5sli2uc4ew7u y 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 logewa/j - (/oovng, narrow beam?

If the net force on a system is zero, is the net torque also z(0a jbaf4)giwbg7 4 bhero? If the net torque on a system is zebb4) gaaghb( j47i0wfro, is the net force zero?

Two inclines have the same height but make different angles with thehefw yd,)3q2v horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explai)3d ,qyw fhve2n.

Two solid spheres simultaneously start rolling (from rest)vo 90smff4jj 1 down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has th 9v sj4o0fjmf1e 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 masz n ry;pt(qn0j4su1b5yif b4*s. 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 tosnypb *q1;(utzb44 irf 5n0y jtal kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. 1( *dsoz),xe0jt nj z;kamho+a ; t3niYet most moving or rotating objects eventually slow down and stopkn1 ti( ma+h*e3)jxtno,sjozd;za0;. Explain.

If there were a great migration of pw2g9e4uecg(sy j .9h people toward the Earth’s equator, how would this affectc.wgeu2 p9eh9(j 4ysg the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotat w+m(qym9iy.c+ c 1iluion when she yiwm+(yuc1q cl9+m i.leaves the board?

The moment of inertia of a rotgble2 t r;7fh:ating solid disk about an axis through its center of mt 7hb; g:ef2rlass 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 holding a 2-kg mass in each :x d3ufn iu yy.-)yqu/outstretched hand. If you suddenly drop the masses, will your angular velocity incrui/.:nd )yq3f-yuxy uease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, ldb bma* 0.d gi7+6jvoone is hollow and the other is solid. Demab ogddv6.7i+j b*l0scribe an experiment to determine which is which.

The angular velocity of a wheel r3l e/cixlpi/bh4 i,vsy45 r4 rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. iycr4i5l/hse,x4irpb 4l3 /vIs the angular speed increasing or decreasing?

Suppose you are standing on thu 6llrt :)v t/;jf1xpze edge of a large freely rotating turntable. What happens if y 1tx)/j :;vfluzltp r6ou walk toward the center?

A shortstop may leap* +ib ;+s n6c+js8 auy;woxtah into the air to catch a ball and throw it quickly. As he throws the ball, the+bcyj ws8o+n6 ;* sxu+ait;ha upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of an;qrr mt.9lyi qlgq z-a86x0c 0gular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operatem.lic6g009rzqlr ;a8 tqx -qy to keep the helicopter stable.

  Express the following angles in ra: vp7rs ar5,adll(4lw dians: (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. Calculate, usin8;oh)dn;2( micg. refb +cdh jg the information inside the Front Cover, the angular diameters (in radians) of the h;mc hj;dobnfr2(d. g8ce)i+Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moo rta51fb9q 4urn, 380,000 km from Earth. The beam diverges at an anarfqb9ur 1 t45gle $\theta$ (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 5(33jcgpvtb0 i0fqh ua rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as theb5 j00i gup3t3 c(qfhv blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. I5 ,6on3kakd b(odky t+f the ball makes 15.0 revolutions, what is its diametka(b6d+ oy5 n3dkkot,er?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionx vh694llu n(w( okb3re*a, abs do the wheels 3*b(nvr6 ao(xlk9a ,4lheubwmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500bnj u ;0y*w*ekhxe3 /k rpm. Calculate its angular velocy3xw0*kbn k /eue h*;jity 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 revolutit ud4boh c1:b;on in 4.0 s (Fig. 8–38). (a) boc ud:41t;hb What is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocitf 1kuutef,iy3.k d ;2oy of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of)yzx:ojk */:4yh wtas 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 783),zxhry6esw1xu d.4 l*wj;qg zadz .0 cm from the axis of raj3;dy 41 udwxl,gqxeh*sw)zz r8.6 zotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1htkrng g )rjcu y/q; v,w;o5*)30 rpm to 280qwytoj) h*gknr/ rc5,u)v ; g; 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 radius49uffwq4ovi 7k1v/n u $R_1$ 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 th0mu. b om(4wkze 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 . mmwb u0(4kozrotation 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 accelerafn u me)xm22sup2iv e75nw5;ztes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutu2 xni ;mfs)5ve25 nepu7 2wzmions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 120zz pln m)apxs kso1( q( /3pxvfq95-y4*rht,q 0 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 stresses of fly.pxuhe3h3s-uzh6fsw + r ;k: fing highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its x 6.rwes-+:uh z k f3uh3;sphffinal 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 frome2h (8nw8 sfa-e rbqk2 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? rhf8-b8 2kesa2w enq(    m

  A cooling fan is turned off when it is r zty.nss)tl2/ unning at 850rev/min It turns 1500 revolsl/n2.zst y) tutions 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 makq8e eyif ,fpl4casp 192t7 k/oe 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a l 1iecf ty p4f28o7k/p9qse,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 makhby:*qzlhhfiud :t (;u/1f3h0 ntw;we 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0h: ;nw u t/l tzby3di:w0qh(ff1hhu;*.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 allzw4ur1 z; rfk(84mv ir her weight on each pedal when climbing a hill. The pedals rotate in a circlrru;mr 1f w(4zz8i kv4e 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 o,r;f3gi94lmt x1r cy j/r /pw zxar2(74 cm wide. What is the magnitude of the torque ipgmo/xfi4rc1r2r;9 zj/w(yal3, r txf the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque aboutv vyqc;6re,8/aib3 vv zj-i,z the axle of the wheel shown in Fig. 8–39. Assume ev;v-jrv ibai6yzvz/c8 , 3q ,that a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mab3 q )2onk6 lrzw.z9dwlu l;;e x(rd-oss m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magni bqx69o()23zke udl- ond;zww. ;lr lrtude and direction of the net torque on this system.

  The bolts on the cylinder heaq9o j,snxvx 71d of an engine require tightening to a torque of 38o,xvx7 s19nj q $m \cdot N$ 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 0.64+6fc32snbu,hh mq brm1 52ki*p- daol8 m when the axis,a il op3rhqucf65+ mbd sh*k -n1m2b2 of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bien 3sw7(:b+nvm ubie3 cycle wheel 66.7 cm in diameter. The rim andnb7+n:v( biws3me3e u tire have a combined mass of 1.25 kg. The 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 in a horizontk1:)uf ipx on2al circle of radius )kipfox:21un1.2 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 .f +q:skdfsg* a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N d.k*qs f:sgf+ 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 point objects shown in k, wu l,*hmd+7djlkq5Fig. 8–43 ab5h,7km*q wdjll duk,+ out
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose totvai m9iub thgie/j8:ya y9)-0 al 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 cylindriuzxpu 3*6rzx5 cal satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellit5ruu xz* 63pxze has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm 9zyuh3knb k st5w.q/: and a mass of 0.580 kg. Calqntkyz/h3:sb w. u59k culate
(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 from res/+*or 3pf gwest 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 tangeijmlf8.l x87j ntially on 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 isl 7i8l8fmjjx . 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm isd**amsj b64srpd rnc:* :i b(x shut off and is eventually brought unifora bd 4ns r**6s pbm::cdi*j(xrmly 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. 8–45 accelerates a 3.6-kg ball at 7 xz (:pswfsx c 17c1(rv$m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of thedrq -uk9 9-cbg forearm, which rotates about the elbow jcrud9 9g -qb-koint under the action of the triceps muscle, 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 sh/, irpta:(lkt own in Fig. 8–46., rl( /kt:tpia
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two massezh5y 5uhz :no us p :ggqrxr4et*.9s24s, $m_1$ 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 fro0pyd+ny91dk ox2e g3 i+nc :+fj(c9v 5o ktfilm rest within four full turns (revolutions) and rel eo0+: nikgf tc f2+dvc1 kyl(i+djpnxy3959oeases 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 izd5 o twi7 6ct-:d4mcsnertia 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 aa 8mwrs),dsgi 5 n;b4rsc7;;wt(ykymz;di 7 torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and:*q+s;sl5cg a uz-tx*.gob s vo9d )) sd1akpw radius 9.0 cm rolls without slipping down a lane a uva 5dwas;gtbs9 ldpkxz))-* g o*: .sqos1c+t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of thew(r mhibr6 (ba(w gr6b8 1+ijx Earth with respect to the Sun as the sum of two t1(bxbrwgrb iwmr(+j6 h(8 i a6erms,
(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 r,q j6r 8achf s8syq.7yadius of 7.50 m. How much net work is required to accelerate it frq8h src7q 8y,fjs.6 ayom rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest xr:eh-r2q/ng and rolls without slipping dxhn2r-/q r: egown 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 mjqs-j saycc+ u.ur1:v;t7/cand its lower end does not sl7. ucjajvys mcu r -1+q;/ts:cip. 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-k*y1mn wa*v0nj6 coq: kg ball rotating on the end of a thin striqac* 6mkn:o*1v wy0njng in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum ofgsppzr;i 3,bw)i2 7sp a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatingr;) sibpps2g7zwp, 3 i 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 his0d4sfg:4ry( v q xdod. side, 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 4y( xsr dqf0.vdd4g :orotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one o,tbeiz61-9qlv,.zz 7n ul rk shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight 6rzz 9-7.ltlv,inkz1u e,oqbposition to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rospc g);, x kpv;*ht)axtation rate from an initial rate of 1.0 rev every 2.0 s to a ) )v*akxsgtc; h,p;pxfinal 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 v phk jqzh- 98 o4cq,;x;)eogt qfi7pp3ertical axis through its center at a freq;p7,eg zqo;h qi-pqf xp9otjk84ch3 )uency 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 figure skatepcj9ce31c7 g 7 imd:zarz) 8lur spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eartpc*sf5d1s, l uh
(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 momn pl pqq b+0h1pw7kz1b(nsc(-ent of inertia I is dropped onto an identical disk rotating at angular speed 0kchws (qz 1(-l bqpb71+nppn$\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at one7if n;y(;pv( d6k b nl.7ki6voz7g2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round plaa9:j*ls6zlr w.g 6rh;quefn - tformuz .jn*e6wrfsg rha9l: q6 l-; 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- q(7wy-l dxbd(b+ kj)bround is rotating freely with an angular velocity of 0q +ydbwld( 7bb )jk(x-.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 qd tm at8cl7lkx/qs suo/ k;mv706:m0 about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass c k/tx87kuql/670qa;sm0t m c :mo lsvdarries 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 excessx6li p6 hnlz54+wf rk; ( avz8oj90edg 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 lp0l83hf9;q8m1 v pd hnzzd(p$ 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 freely w 9zs- g-6 h,nk(dr3ufbhi 4iyrithout frih3(4-srg9f ,i6- dyz rkuhib nction. 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+i*q 7 +ih3z)hsqkxtn a 6.5-m diameter merry-go-round turntable that is mounted on frictionleki n3+hti)sq+z q* h7xss 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 cv f1s0- qk/ooof the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding osko qoc-v /f01nto 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 side always faces the Earth. De87- lrjwp vt1rtermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital artw-l8jpv1 7 rngular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest atqmc+omb q.lrx 0,z8 5w a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius37bq 9 p0z7vqa .fy5g4itefig 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelera0ig 3fb 7.qpt4evqyi5 f9 g7zation. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two 0 bp734j.*pul l-avxe vryu*hsolid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculaauhv byr*xev*3lplp4j .7 - 0ute 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 speezm+o k*io5w z (taqc;:d 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 x,( vqij gc s),g(db0q.x wt-e8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentu0g x .jc,di,q t) ((bevg-sqwxm.    $\times10^{9 }$ $rev/day$

  One possibility for ae.huy +(:jis vdj k72z low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cysuyi v+k7.d 2:h jjz(elindrical 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 illustradx1gss0b fda-y+g-zy ui3z) 8tes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speeo/z 1k-ihplcq:t z4w* d 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 an6bda3: rjnre nl s./,kt )gat9d 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 o:lnag9dt) b,6r /knes 3 jt.arf 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 standing verti3e 53;kuplxz ocally 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. 8z 3o3;u pxk5le–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a fmlwop2* n a:ly-)rz/p gbft .3lat road is making a turn with a radius The forces acting on the cyclist and cycle are the normapnmy*-:3o bgzl /aw) .lt2r pfl 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 length 1bqi g4j0:krm .k6 i(ru.5 m and begins whirling the rock in a nearly horizont:q4r ujkb (gi.rkm0 i6al 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, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a s1zm5*htd21m r fvc* s.3kmdx xoj 2p1golid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a* k1.c x* mps1h5xjm3gdftd1rzv2mo 2 spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a cluwf,nk76mkqll4c0 n +jpx.hh 8tch assembly which consists of two cylindrical plates, of massk kh6w qm70nl.8l4 hnf, j+cxp $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough track o- ice:z2gi8ent .r8e vf 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 w2i8 .re-evnzgc8: eti ithout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do ng8e.wfq z4oe2ot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the c:dl w yk28b:ngar reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eg:k2ndlb:w y 8ach 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