A bicycle odometer (which measures dist7.by0+yfpz96 pnqp. zvfv+ mpance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 246m f07z+9nfp .qpbyvvyzp+. p-inch wheels?

Suppose a disk rotates at constant angular velocitzmezl3nb;/8 )zk h- wry. 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 tanznmb/3zek r;l) -zh8wgential 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 t9*wds, 8w*j7zre bhi6 p)2e0irehxqj he angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expl *t9--by.19 sopr5enhsn*vi kg 5qqde ain.

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 ww jv+cnou48(w.5 c; /ocqvhxa sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer t4+ x5quj ocnv/w8hc(vowc .w;his.

A 21-speed bicycle has se fivq9;o*9i mqven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sp9o*i qm 9vfq;irocket or a large front sprocket? Why?

Mammals that depend on being able a;w: ow5s5vfhf ( 8uuato run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of r u:8a;5h v5af owf(suwotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a3 uxra62k -qr.bv v3ib long, narrow beam?

If the net force on a system i./ kejbf kehx.w s.)8o7b o9gas zero, is the net torque also zero? If the net torque on a system is zero, is the ne. kaeh.xj9 )ks.eob 87/g wofbt force zero?

Two inclines have the same height but make different angles wiw (2rfv1jp x)ith the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball ax1j( wif2 )rvpt the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from reste-o :dh8n(tq3kodn ,f) down an incline. One sphere has twice the radius and twoeft:h ,8qn ddk-o3(nice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start frot 8i9ff2u.o3cp ru1azm 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 rotationalriut c uffo2.a3p19z8 KE?

We claim that momentum and angular momentum are conserved. Yet most mox 0wcv .2 r 2;jj36dwzdqwvpw7ving or rotating objects wwcjj0. dw7;w r6pv223zdqxveventually slow down and stop. Explain.

If there were a great mq,hz -gg 3l+-phh2ydmigration of people toward the Earth’s equator, how would this affect the lehq y-h-gdpmlh2 z 3+,gngth of the day?

Can the diver of Fig. 8–29 do a somersault without having any initiazg .s+(vm5vt* *fmcgr qc;zq6l rotation when she leaves the bogm.z*v+t c r;mcg(fsq6zv* 5qard?

The moment of inertia of a rotd4r0*jg yg3c u*1dwuk ating solid disk about an axis through its center ofgwuyd40*d* gc1kj3 ur mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holdiyeg3vo:v( ,p yu 3rgfbkj* r*+ng a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wil3*v:(vyuyg+rpr j3f *b,og kel your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is+ lwz,e hmzepy;j-j27 hollow and the other is solid. Describe an ex-jjew+zl yzh ,7e2;mp periment to determine which is which.

The angular velocity of a ov kxwb/5eiq22np59r csf*,x wheel 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. Is the angular spee k/c q 9 rp5sbwo5i,f2vnx2xe*d increasing or decreasing?

Suppose you are standing on the edge of a large p.aqr.lk phz 4c;ki4. freely rotating turntable. What happens if you walk toward the.;qkh a .kr. pp4li4cz center?

A shortstop may leap into the air to catch a ball and throw issl j+bsrn2;ad : jg27t 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. 8–36) bs j:nlg+s; 7rasjd22. Explain.

On the basis of the law of conservation qo zbzt*0) q:nof angular momentum, discuss why a helicopter must have more than one rotoqqz:0) n zbo*tr (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a9t bci2/jiy6y,abtf nye:5 ,cv5 jd/t ) 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 )w:wbl0pn pq qwlnxi+-, 2 9fian amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, awwpxi0fllq wi- p b),2 +nnq:9s seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380y scuesni q62k*(f9 j-lpxax2 uv(c;*,000 km from Earth. The beam diverges at an angle pcy sf (u-ks x92a*;xvj c2 6en(iul*q$\theta$ (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 turnedbyq )zymx2m-xexsj)0mnc/ 2/0hbu8 j off duriyyuqmbb8xnxm2e 2)- )0hjz s m/xj0/c ng operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to ab g+tvljc +o96i)z/1 bthvb l3nother child. If the ball makes 15.0 revol3/vb)+ 6 o1zbbj+vchi9 lttglutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter tra1zmwpvs7zbi+ 4en i 1gtv)e3 *vels 8.0 km. How many revolutions do the wheels makgi)e +zn v 4mz3v17ewib ts*p1e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 q:( kjslqpo+,r u) p,r:9lfesrpm. Calculate its angular velocity u+),o q eq:lp9,(lr:r sfpjskin $rad/s$ $\omega$ =    $rad/sec$
(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.zq kg03voo k;0-sk( ck0 s (Fig. 8–38). (a) What is the linear speed of kgkc03oo( sqkv-;zk0 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 (a) in its orbit around the Suq)mw),widh /rn    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 2h:qqu5ky be5of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axi;6qsi :z8kno s0el)un s of rotation is to expernzsuik) q68eln o0:s; ience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1ft97ugbk + 6c.tx od80 kcj3oh30 rpm to 280 rpm inuk7o8f9x .ctgcto kj6d 3 b+0h 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 radiu5vz7jcm 81 dp/rao/cl s $R_1$ 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 7 htcklweomht50 kme y)oa98s:o -/8 raboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time intervalwol)09 o yt-ck: eekhats/5rm87 o 8hm. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2 4h 9/0f zc3;ufsgj 9jxkfs;k .,gszep20 s. Through how many revolutions x j f/cuh3skz0ge;ff gs4sjk,.z p99;did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to(8xeer 5aq /tn 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 stresses of flying highspeed jets ifn.z 9e:8tzn 9jpf b7in a whirling “human centrifuge,” which takes 1.0 min to nt7 9ijfn9fz:.bzp8 e 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 rpm0o. nxf3o fbbfi;z *2j to 360 rpm in 6.5 s. How far will a point on the edge of th;fonx* f0j3.2bizbofe wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It tur(8 x,.c eccux4via qr8ns 1500 revolutions before it comes to a st88u a, crxeiqv.4cxc(op.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uni ti+ ullyk 2y,ew: *crz;51aobformly from 95km/h to 4 oyu1* 2,cely:lkbw ai+zr5;t5km/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 a 9u*d+puanj y0s the car reduces its speed uniformly from 95km/h to 45km/h The tiresd*0j y+uu9apn 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 p/gv mx1 )qshd*:v mkm uf8 -x9t7z*clauts all her weight on each pedal when climbing a hill. The pedals rotate in a 9*mvxucsm qh-:xt zlf*v 17 m8d/)gka circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a qfdutyd;u;txd+gh fl5z-.)y8 (1ck pdoor 74 cm wide. What is the magnitude of the torq 8ffdqz-k;c) 15u+u;.lt( hyxygt ddpue if 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 torqueg 2ttc - pcs:/hea,i7d about the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of:, cd2is/ t7p-atcehg 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachfv.lc,tp.s0 gyg g/ 2red to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positiotgvpfgsr. lc,0y 2g/ .n and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder hea- o(qp6ijvc0k9wko d6d of an engine require tightening to a torque of 38 wq9di 6kc (kp0-ov6jo $m \cdot N$ 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-kgkzufhfic7l1 ) vr9upa8*x7 n9x;3 gvz sphere of radius 0.648 m when the axis of*c9 lpa)8i f7uxh z1nvk 39; uvf7grxz rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inghm/hl+ y+ n6aertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?). lh +mg+yah/n6    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated r+ s) 5dmdslg7ryi*j 2in a horizontal circ*mls2dj7r+g5 si)y rdle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rodllba3jog*n hctt1/ uz p( 8b) *)x3lqtating at constant angular speed (Fig. 88*1t(d x3)lt l j boaugb)hzpc*l/3nq –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 point objects shown in Fig. 8–49,xkrm sm*2df3 about fm*9 ,skxdr2 m
(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 total mass isxa2hbmv07k gc2clhxu e4;)t5 7;mo uj $5.3 \times10^{ -26}$ 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 correjcshj.vt* )wq+ y5v )cct rate, engineers fire four tangential rockets as shown in Fi jy.v)cw5jtv)hq+*c sg. 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 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 withq c .k4w2kcv9g.( 1c qn wpa,7ri9hgrd a radius of 8.50 cm and a mass of 0.580 ghw9( 4gc,k.kc .apnivq c27 qrd1wr9kg. Calculate
(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, accelx*v x- p7 jr8ed cz3udsjr4q4:ljna3( erating 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 smalilue f.g)j,a 5eli8i4l 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 5,.el)eu iialf4j8ig (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 is shut off anfkcdhb m .c ;s35 8z,vek9ub(gd is eventually brought uniformly to resu;b,k (ec9m 5bg v3.f8kzd csht 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. 8–8l lk afbqd.j3yo.d-k3:, rn g45 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 solx.ad .9i r2kf2 mls0jqely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–4. q2l0rif 9xj.makds25. 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 consid pigcttdsx7. 8,in-xt4q ,a/ hered a long thin rod, as shown in Fig. 8–46.d i,tpgxs .4 i tqx/7c,hn8t-a
(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 mas5t9*/0aw 3y xkri/spl :u, eyk tjm;bxses, $m_1$ 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 fulci8d s-df)3bxv7 8wral turns (revolutions) andsdwx 8r b83)f-id7vc a releases 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 inertia of lgh1w*) 0 iyip$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280ms6/l:, zdrx-h+zop15l; 7zac 8or+v kxbfd a $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slippinb58h*l7x re6aau / :hqxel6ecg down a lane at b/7hx: xl65 e qece*ul8ara6h3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to8btpi suhr +(* the Sun as the sum of tw+hpr 8 *iubs(to 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 rad)l bjp7fmr6:wius of 7.50 m. How much net work is required to accelerate it :l6pbmfwjr7 ) from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm a*wlwcp w)-vx 4rm/j4rv- kkr7nd mass 1.80 kg starts from rest and rolls without slippin c-rkv* ) lrw-44prw7wjx/vkm g 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 t.r e(s; ,skqdjo fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the gro. d,eqssrk(j ;und? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the enrx- ov/ u*;*idc; o*q(eugx tkd of a thin string in a circle of radius 1.10 m at an angular speed of 10 o;*igt /-; xqd* eruo(k*vucx.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentuml-:xm wfoqw64 of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating o-6m 4fqlwxw:at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a plasb ;8ys,5rarf+t((ii3 jym zetform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48,(+br5yyzstm8j e3;r ai(f,is the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her ,er59e*if bidb (k qus;by/j7moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in d i; rk9 *f/q5y7(e uiebbsj,bthe 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 fua o.3 aw:id;2wyk tq1qg)bj; rom an initial rate of 1.0 rev every 2.0 s tq;o1t waaikqg;2jdw3 . : )ybuo a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its o-xjb u6./ib4wd9xo va1f/ owcenter 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 vaxf6.-x woi uwoj/o/9b1d 4b. 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 spinning at r- zmd cdxr2r*f,z*/r66l hiu3.5 $rev/s$ 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*iwc intbasxk c3/88* 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 of inertia 51a cf-yka;/w+d 3aac m8acf5fyc sz*I is dropped onto an identical disk ;53*k5awcyadm8 ccac1-/ az f+ y fsfarotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at35bf*kqy4an :jrq se - 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platf4f(n(nmy .q bcorm of radius nm.( nbc4(yfq 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-gol .9-4zd/s ,esmia4 mdp8ipbc-round is rotating freely with an angular velocity of 0.c4d-pa8lzbdmss.e / 4i9ip,m 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 about half its (c n8ew2bwdjbnm; wo8/7fs kh)s8kb1mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momebdenh) /cjn;w s 7b8k s(18owfw2b8mk ntum, 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 win.i h5 7+aqcabrds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 5fuqwi tt).81 gq;kds $ 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 platfor gx5 e*a1osve7m, initially at rest, that can rotate freely without friction. The moment of inertia of the pers7oex5* va1 sgeon 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-round tuty9 m-+e +wivp,dy;qbrntable that is mounted on frictionlessy+ vepqyd;m,w -b9+it 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 9*/wo1fin qwv of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holdingqfnowv w1 /*i9 onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always fac9i)l /, s*gtuvcqw0wtes 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 partw ltg )v/,9 utwsi*qc0icle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ofe:rvm b o7+3 f5hb 9k0/l ge3jnsm;koh 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.hz/w6p:hxu2q kn b+t of radius 0.20 m acquires a rotationab/2z6n.huqkx+p wh:tl rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each/ebl1rq - ep-lxh 1ic: 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 conservati xe/1l e-i:hpcblrq-1on 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 olj9uy q1qn +n:as.iwzwx84xr n0j x;1f the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, b1x r4y2h5eebkgre43vr/2zwrt r0j 4 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 br 14z30/vxbw44yhg tjerr52 reker 2process, 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 fordyix/vzd6 /a.c9i:jt6jq3q r 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 x3jidz tjqcydi/9 6/.v a6:rqof 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 illustratlkez.a+60bg *ul* v aoes 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 zsl 3mcv2 b)5 ms:kb ; (otkb2x*ga5xbspeed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., w3m3: ctxktfziej 2 89ce ignore friction) about a hinge attached to c 3ktxm 9ject:zif3 28a 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 f uaxin8v h.4tyn3*i)standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has heig3if* .uv n)4y8xhnitaht h, where h

  A bicyclist traveling with speed v=4.2m/s on a fla1/l8u sj y;.b u,sghztt road is making a turn with a radius The forces acting on the cyclist and tju h; z8bu,.gsy1ls/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 sling of length 1.,gc um4*lh;n8q9rglj(v vu 0c5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the tor g(u qng;cl4,8hvrvujl *mc9 0que come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, m bus(3g)ph4tv/sl 1bz aking reasonable estimates for the dimensions. Then calcb l4 u 1vb/s3)ths(zgpulate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platftg)pw8z ( z9zes, of9zfz)(g8w p tz 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 loope6t 73ht8u mgxfd rough track of Fig. 8–58. What is the minimum value of the vertical xgfh3mu 786tt 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, bud0m pdt ri;3)tt do not assume $r\ll R$ h =    (R-r)

  The tires of a car ma:z *k1( m himj6kf4ctzke 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) What was kk6mz: (hc t4fz*ij m1the 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