A bicycle odometer (which mjx8pqx li74swk aw6 aaaybo +2) q,x;;easures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What;i),aqa7ojx24y6 la ;+8xw kwp qx sba happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular veloci ec*;7 jf3lbxb68c cyxty. 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 an87f y *bxclec;3cjx6b d/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bodg:) vbcyzxk)ormzz xu3 -o) -bs3 fi-h;c87pg y be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explq pom0y;3y1nmdv 2 6zsain.

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 he 8/.m wjjrfp)rad than when your arms are stretched out in front of you? A diam.p j8j)r/r wfgram may help you to answer this.

A 21-speed bicycle has seveh3 7v.bv,bbv, lumcf9 n sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pe 9,fhmbv.cu vlbv37b, dal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on4k 7j rle2vcf46t37pbl 2nlmz being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is adv6j47k3t e2cb lmpn7 rz 42fvllantageous.

Why do tightrope walkers (Fig. 8–35) caens383 rx ;spt /qi.wvrry a long, narrow beam?

If the net force on a system is zero, is the nl/bore,-s5*or dzt3m )qddy 9et torque also zero? If the net torque on a system is zero, is theyzdb9 3r-l)oom/ r 5s*q,ddet net force zero?

Two inclines have the same heig j53wi3s ih6cydhxv96ht but make different angles with the horizontal. The same steel ball is rolled down each inclin3jyhxishi 6 3 9wd5v6ce. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One-8wu 5nj7m p3jxjd/l, 5gyuyt sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? /7-yju3lt my5x upjn5dwj 8g,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 (da ec.ggd+/k and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greatcd g.g(a/kde+er total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving hvk-5lq4cqjga7 lyc*n iyx l.b4):,aor rotating objects eventually slow down and stop. Expl cg4qhqk-)7v n al* cbjiy5:ly,alx.4ain.

If there were a great )ksjr31x q0jaro q(xpp *n0ei wgo):9migration of people toward the Earth’s equator, how would this affect the length of s1)) 03e(jqwjn pix*gpqookrx: r a90the day?

Can the diver of Fig. 8–29 do a s9,cxard8e 9 z(n9yy *nu/csrfomersault without having any initial rotation when she leaves the board?(xzyu 9a cnr*9c 8erdf/,sy9 n

The moment of inertia of a rotnuqt + -t+eu5mating solid disk about an axis through its center of mass is +qu+- e5mntt u$\frac{1}{2}WR^2$ (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-kgxn w *f(a )tt/*lxkp01ob ;ify mass in each outstretched h/ x(;k)ta btfxi*l 0 opyf1w*nand. 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. Howeverz7 k8utbc*ng ://cq q vt+2wul, one is hollow and the ouqnv+tgucbkq / /zw 728: ctl*ther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating edh60i*8jd x wkz4.s zon a horizontal axle points west. In what direction is the linear velocity of a point on the x*0s k d. 8eizz4d6hjwtop 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 the edge of a large freely rotyjou w 4:eyqjxc (4q73ating turntable. What happensj:(y4 7jx4oe 3yuq cqw if you walk toward the center?

A shortstop may leap into the ain;t ft ;nhiu15r to catch a ball and 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 opposite direction (Fig. 8–36hfuni ;1nt;t 5). Explain.

On the basis of the law of conservaw*to9w(-9:k zd smlymtion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopt:lmo (ykmzd9 *w-s 9wter stable.

  Express the following angles in radians: (a) 3kyii/dp;y 9xm8o+ :3z aql zin,ec31j0 $^{\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, us dx28fdo qrvymq mx, c66jc u+;+/c2kwing the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as sdwo/cd +u x6qfkcqm8mvjry;2 x,c6 +2een on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at tt0d0 hfkb+q/d3r3o bw3; gp cthe Moon, 380,000 km from Earth. The beam diverges ath3gd0twbr+bq d0p3 k t3/;cfo an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate atq d gyl zt:j6di7,fjbdm gf/l60.2.en a 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 aszl/2je6 6 l.q:dtmig,. yg0fnfd bdj7 the blades slow down?    $rad/s^2$

  A child rolls a ball on fvcb (fxs5 z0xp,yc k-/n3qw2a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diametef3bxkvn w / s cq0c52pyfxz-,(r?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revoldb*fc8z1e/hux /4 9vqcf)nbeutions do the wheels maken1/9 )v4xbcfuhbz c* e8/fd qe?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculatezj91d:-hde,;m :k ji 7dof. rhje8z ie its angular vejdm:dh efkj; 1z.eeh9:d7 jori8-i,z locity 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-6 i,( lqdddqg 4.0 s (Fig. 8–38). (a) Wh- qd6(g ,iddqlat 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 velocity of the Earth (ay,l w k00ve ssguzwtw70 r;(+a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speetp s54hz+s--k xzpx o40c(a exd 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 pa fdx:,g0p5m ulrticle 7.0 cm from the axis of rotation 5fdl 0ux:mpg,is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cen9v7hx kv,w7 rak :ae5pter from 130 rpm to 280 rpm inwhr7e9pax:5 v k,vak 7 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 radiusz(1w6qzq p,c g )tl6cb $R_1$ 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 Apollo+gxp ,f*xbm ;8 mmtiw)al:e-w spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotewa lpmbi;m-f:tg+x, *)wxm8ation 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 acceler/ rrb9k-vc)7gjfqb cz9(l 4fk ates uniformly from rest to 15,000 rpm in 220 s. Through how many vck9)lfbgqjfr c94zr-b(k7/ revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcul kleh+av 7mxz04hj8q5l; yhc2ate
(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 of9 o/sj +vcwwk/ flying highspeed jets in a whirling “human centrifuge,” which o+wwk //9csj vtakes 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 rpm to 360 rpm v j6 7q)7qz4 d(tnvv,y: zikaein 6.5 s. How far will a point on the edge of the wheelq j zz7vyeak6(4: )7nvd,vt qi have traveled in this time?    m

  A cooling fan is turned off when it is running at 8;abr-07c-m z/ ungett50rev/min It turns 1500 revolutions before it com ; gtbuazr7etc0/ nm--es 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 t8+c wl di4z:uyhe car reduces its speed uniformly from 95kmzl: i+ ucyw8d4/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduc8ec6b/ x r7oj7tlgx6tit c )0hes its speed uniformly from 9)7j 6xrlt oih7/86ct 0 xcgetb5km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her: mpm( )etg2em weight on each pedal when climbing a hill. The pedals rotate2te:mgme m)(p 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 the end b /bcwjcxu +1s c7h+2lof a door 74 cm wide. What is the magnitude of the torque if the forcxc b+27c+lc1b/hwj use is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig.9m jmawc igd 36et4(j4 8–39. Assume that a friction torque of jgcm(i3em9t44 ad6jw 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to tjp/kprg 6h/; rhe 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 magnitude and direction of the net torque o;jp // g6rhrpkn this system.

  The bolts on the cylxjor/gfh x b/.)3c*qc inder head of an engine require tightening to a torque of 38 xjf/go*)/bc c 3rhq .x$m \cdot N$ 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 0.648 m when thi n,tqu*lwy7m1be 8tnq91*gf e axis of rotation is throughw bl71 tmqn1 ye gi9qu*nt8f*, its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyc 1g0gv ioa(jrr/t0ww(le wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub c rig/(wtov(wg01r0 j aan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotatentv ldi-t.xqa42rm j*d :6f*3+it mskd in a horizontal circtstmkx-i3i+a *.d4*n2vq f dr:jmt l 6le 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 p5i -nh*a5e) cc (cbmivotter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the cla i( ch5vnam-5c*ebc)i y 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 point objecsz(5x k0b brl,ts shown in Fig. 8–43 z5sblr0k(,bx about
(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 w9 h l+ *lhqlf6ou/u4gihose 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 satellirc( ib-01 pfnwz ,/wgfte spinning at the correct 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 (wr gcfb0n/wf z, i1p-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 unifox6u 4o,xsu.ovrm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calx xu v,4.u6osoculate
(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 bac ,j)-:atl ze-mhr2*l2hxr zvd-t f,ct, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a smallvt ;6lt8tjz(4c d7mfv 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-rount64m7vtvj8ct z ; f(ldd 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatina / crpu22thtn)8(etvg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional to r/unt8 ph2ca) v(2tterque 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– j47jm b9tc/6,r8xs e4pqihw w45 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 thrown solely by the action of the forearm,f7w)b3xk l(. s9 b w,t-rbkdct which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 tbkcwwrsd() t3 9 .,x7b kfb-l$m/s$ 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 omr/.p d0 ke.drod, as shown in Fig. 8–4e./dr0p kd .om6.
(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 consists5.ewwkl fh h;k2on6/ k,q cd6s of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full+h p-9oo l4yh+rzzmis *aik12 turns (revolutions) and releases it at a speeiz p4aoos 2*+ lzy+ihk -rm1h9d 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 ikp ysr.+zg9d9yoz( p+ nertia 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 tor zor90..wx0 n:djbzwp que 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 rad,5qo4*up5fd : i kdxedius 9.0 cm rolls without slipping down a lane at 3.*edo 4u5,f dpqkd5i:x3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to zt (dpw1fi4.j/ x ss3lthe Sun as the sum of ttsx/ 4w(.ij 31dflzp swo 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 os0znjz0xlq49 f 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume z9x0s4q lznj0 it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolpsqkl2nul,,qs 2dx*2)e: laxls without slippinn:lk*2 s)qdlxaup, 2l2 ex,sqg down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to falli0 g q80v7(r+ efsd m/cxvxnt; and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservat8;dqv v+t7ern 0sf( /x0mgxicion of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bqjus a.w/d.b0 -nzkf )all rotating on the end of a thin string in a cdu/ kza)jn.-0bqf s.wircle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whpua :5p4,w 4 mso9otqvb 44bhgeel of radiuo ust aow,m4b vbph94qp5g44 :s 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, hanyaw*3k -/clb0ttkveo -r h.7rds at his 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 rotation decreases to 0.ak -30v/ker7c-ty o.*lwrh tb8 $rev/s$ (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 motjgx(r;: 80 )at 1ncg7oop0mxw*uchement of inertia by a factor of about 3.5 when changing from the str0jmp) (urtxg t8g;:n7xch *oa 1e co0waight position 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 a rf9ops dz4ep9stls+7l*l61 spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a lsozf7 1tp6ser4 a+*l9 pd 9slfinal 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 +c: x4fdkqo zd 86tm8wits center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clax+do8k68z4t:c dw q mfy sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 z l96rivp:;kuwqx*d e; z47)wkus ul9$rev/s$ 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 h;024qt w0)d-w6e hnb j.wocia(im qpEarth
(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 momen0mb*j c+ixh,dt of inertia I is dropped onto an identical disk rotating at m+,cid* hbx0j angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.s0ler+4( 0w itv1exy d4 $rev/s$ 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 merr fdu /6vz+c vvq-h8tg+y-go-round platform of radius 3.0 m and m+h8d/ctvz+-6vf g uqvoment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round ikctv32an up2* s rotating freely with an angular velocity of 0v2kna 2c3*tpu.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 eventz mh2v(s vg10ry2s d7g/3qpe yually collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries a1(vsqpzg2/730yvhsrd m 2 yegway 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 12cjnsz 2lf -4k60 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass x x0l)-enipql8 -sw9g9 )7o5 dpelhica.zl3b$ 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 cany(a v.m t+0lao rotate freely without friction. The moment of inertia of the perso (a y+lmot0va.n 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 diameter merry-go-r/5u.hp2 hvc gv lnw+lf7o4vx:ound turntable that is mounted on frictionless g.lfx4 wl ho5+:27pvcnvuh/ vbearings 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 t-u:,6 qhcbse;a+hk* jcq gbj854lk hzhe ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls hj, 6h;-ccahk4q+ gqbk js eu:zb8*5lbehind 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 thbpf7 i d*da j j)ho0fq;.(qn*ee same 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 particle of.*jdjhn ;e(0bp)qiq fda7o* rbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frw-ch 5j.fvma 9lua)vif/ -x k4h;-khe om rest at 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 un)-btt cwluee0++wj5hofo/7+ /dwign iform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular ac i0ge)ohbljtowfu/w5n d7 w+-/+ec+ tceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass (e y 26csrc/n k,blxq4fy13er 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 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 rny4c613xlrs/e e bq2r, yfk(cest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is thoflbyi 7 t.,b7k6bgx0e angular 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. /(zq(l,vgf sdc(c/on 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, losc /o, qsz(f dl((ngvc/ing 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 automo rzhvbdi8*-f/+ zh q(tbile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinu8d-zihvz+t fbqr/( h*p.”
(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 illustraii(b 8jwf2iz 1tes 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 surfav6 xjbhnn6c-5 ce 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 cana:qlw p0p.td pb 6m ;8jc0mus+ 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 p0t :.awmc+qm 6p;pl8dbs0uj 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 standingq(a h3h;3j*b lle)csc vertically on the floor, and we want to exert a horizontal force F h)c3e;bjl3a( qc*sh lat its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is dfiyuxxkwd*)c3 n03ivz9)( h making a turn with a radius The forces actik9xh w)( )zi0ic3 *yvndxfd3ung on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a rda.tyx5 zxc*g.s9 *wsling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a ra srycdg*95w*tx x.. zate 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 cylinder and her arms as thin row1*; xrccvi n;68 saubds, making reasonable estimates for the dimensions. Theirvc6 n;sa;*x wu cb18n calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly wn ua80;cy9j pz+v98lx:if21en mw edz hich consists of two cylindrical plates, of +u c9;el ne x:vdifz120yzm9p8j8wna 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 radius r rolls along the looped rouge3 3eq(ht ds rckykrb*xi:h9,d p64/gh track of Fig. 8–58. What is the minimuegsq:dbkrc/i6,3 (* y thped43r xk9hm value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu0a kkxp 93owf4tj4mt2me $r\ll R$ h =    (R-r)

  The tires of a car mabmm8, p67rdtk ke 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) ,kbmmr87 6 dtpWhat 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