A bicycle odometer (which measures distance tra 1 5t+tby4j+sodwkb6wveled) is attached near the wheel hub and is designed for 27-inch wheels. Whtb yo4w6ks++ d5b1jwtat happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinmv*njaq, t a18t on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cjmav 1a*n,8tqases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describedi pjf wj2;zp6g2f5,bf by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a large dmb3tx;t7jc y0i ,)ot05etyv r 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 ywm5jias ;pm)ll if*w8dq 5.u5 our head than when your arms are stretched out in front of you? A diagram may help you to anlsi;.5m w j u5pm )qd*8fi5awlswer this.

A 21-speed bicycle has seven sprockets at the rearjz pkstn5s+-4ex)2u xaqho d9vh;( 2f 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 s-5qhh 2kt n p9u+zeoj(;xxa2f )4s dsvmall front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower )+t.9)m.byf+ rkwciuinds q6 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 advantageouink .ydi)q wfu+ 6c+.9smb)trs.

Why do tightrope walkers (Fig. 8–35+dgp /v -gx)sr) carry a long, narrow beam?

If the net force on a system is zero 1-9-t cxfk57q;u e7t) uznzyjjivih2 , is the net torque also zero? If the net torque on a system is-cu )q27f eniz1kux ijvy75z9ht; t-j zero, is the net force zero?

Two inclines have the same height but make; -yb .l*uvhae different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of *huay;e-l.bv the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start ui g*w (gt(t0kl6*xs3(ut e h:arah 0urolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other.t x au(ultshtue*r0:h((6*agi 0 3kgw 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 startia,yiuwpbp7 r--xf *h648sop from rest at the-uiwh8f7rsiyp,a6x -p o p b*4 top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular(* cep,ppk,-xt 9 o6 fk)hghpt momentum are conserved. Yet most moving or rotating objects eventually slow doopthck g -fpe)kx*h tpp,96,(wn and stop. Explain.

If there were a great migration of people2u e.)nf c;gowsqd)h- toward the Earth’s equator, how would this affect the length sq gf-u)n. h)cw;oed2of the day?

Can the diver of Fig. 8–29 doly k826 op4e3/n6cy kqgnbo2e a somersault without having any initial rotation when she leave3 no6 k2kbgco6p lye/q82 e4yns the board?

The moment of inertia of a rotating solid disk about an axis9 )u .(vcvu6vz 8lmfml through its center of mass is89 uuvm m)lfv.z6c(lv $\frac{1}{2}WR^2$ (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 p -k/dlrw)a;6tvi j0zon a rotating stool holding a 2-kg mass in each outstretchedv jwap zk )ld6t;-/r0i hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and h e:r d4krie.pq.65rl7zejdt n )3:kgmave the same mass. However, one is hollow and the other is solid. Describe an experiment7m. .rt jk:4eqe: 3 gr56z)p kerdilnd to determine which is which.

The angular velocity of a wheel rotating on a iuq vnd zj4,*79sj+qj horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acq*jnzj vd 4,su9qi7 j+celeration 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 on3:hv-- xk1lm matz ua( the edge of a large freely rotating turntable. What happens if you walk toward the centermxu3 :- hz1 ktvla-am(?

A shortstop may leap into the air to catch a ball and throfbaefw 0 h+-oa9b7 pwt(:s4aew it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice tha:b0abwtease h a4wff7 o+p-9(t his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a he zn.l ;eyt.i qs3f0ob)licopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller ctolyb3ie;n0fs.qz .)an operate to keep the helicopter stable.

  Express the following angles in r+ du tsq:siasil-:y 2/adians: (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, using the7i+ z. vtv1tau information inside the Front Cover, the angular diameters (in radians) oftvtz+.vi7 1 ua the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mu(5y4:y d6*aawhdeq q oon, 380,000 km from Earth. The beam diverges at ya4dh:e* 6qdw5a( qy uan 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 at a rate of 6500 rpm. 7wytofq8q:v 3When the motor is turned off during operatfq8:q w3o7t vyion, 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 ddqgllm)z; g w1vfln) 9z/7)qm to another child. If the ball makes 15.0 revolut ndg9qv) )7qfl z1zgw) l/lm;dions, what is its diameter?    m

  A bicycle with tires 68 l( 4byf-exu1f cm in diameter travels 8.0 km. How many revolutions do th-e lybuxff1 4(e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500uzuw;x 0 1mx wil*m4n8 rpm. Calculate its angular velxm*z 04lunu im81;wxwocity 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 on ej3mt(ejw16 je complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m jj3te6 wm1(ej 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 the1u7mqznnty e ,53a3bz Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speelv+t2b*9u9eub5)kzf h j2o oxd 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 par*p2fp :ltfs,pticle 7.0 cm from the axis of rotation2l s:*t ,fppfp is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformla b5u 3pyxxh)5y about its center from 130 rpm to 280 rpm inuy3b h xa5xp)5 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 radius pdpa2i/ajx 4i6( pyh; $R_1$ 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, astronautli5/cs nkg+x. s aboard the Apollo spacecraft put themselves int5.+cskxi g l/no 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 interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from b 4zijd /3jlq7la .af,rest to 15,000 rpm in 220 s. Through how many revolutions did it turn l/4q 7. dlj fa3ibja,zin this time?    $rev$

  An automobile engine slows down from 42h7q(3i em 0rhuns **/ fy+o)yms rqvw500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying h; :f,arpbqyt 5ighspeed jets in a whirling “human centrq trfp,b y;:a5ifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly f gi80gcv y)c8from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travel cgc 0y)f8vgi8ed in this time?    m

  A cooling fan is turned off when it is running at 850rev0 s2w2i-xxt kc/min It turns 1500 revolutions c0 2wsxktix -2before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its st:osw08 bt vw6kl6+ fm16wyc od9 r(kupeed uniformly from 95km/h to 45km/h The tires :u1+oby(w6d smw6tckl 6 8o9 kvfr0twhave a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its spew-dbc++ ibrxe/-om1 r ,c5kdc ed uniformly from 95km/h to 45km/h The tmb dx cck+ bo+crw-i-dr/51,eires 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 weiqa:q i cw,mu( ho5b59r.p:i- )gptgk dght on each pedal when climbing a hill. The pedals rotat(b qwd9q mao. -gp55p, h:cit )gukr:ie 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 of a domgz .3+zjeq c)ho.eq1or 74 cm wide. What is the magnitude of the tor cq 3h)1. zzgqjmeo+e.que 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 torqu:v1awhpy // h1d) aikme about the axle of the wheel shown in Fig. 8–39. Assume that h)yw1p /1am/ adhv: ika friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endjw m:)qk3ai0ez0 cs ,ls of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held sw) z30lcea:m ,0j ikqin the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of3 6i;tduy dq8vqk6k )d 38qd6qt iud)kvdk 6y8 ;3 $m \cdot N$ 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 4:ad8wdbmn) ert wf93inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is t39d fn:ametd4r)wb 8whrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamebdu3i a6+-9 ;bnam xyzter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored+6axadybnzm9; ub -i3 (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is/sp,/9 k*o ks4yd4 n8vgugl cn rotated in a horizontal circle of radius 1.2 m. u cdps,8o/k4ns/4y n*kgvgl 9Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spmj,4o ni*dl 3vy6dpf )eed (Fig. 8–42). The friction force between her hands and the cl, )dniy6o*fd3j mpl v4ay 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 oy )71vli:j zxrf point objects shown in Fig. 8–43 a7xrz v1lijy): bout
(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 condoi(0 dc:y;w hsists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the corr- l rfkjtej*u:1 ;3hmrect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellituej;:l- *j1 rt3krfmhe is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a lvqgncl i :i(/4je.p fa8nlwcu; 2b(*mass of 0.580 kg c leb ang2.f;jpi4:(*wq u8 v(llinc/. 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, accelerating it flm+;m vkq:bj99dvq+1 oqgvy9rom 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 -0 dlaq6s6uem a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. u0l-ms6q6ead$\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and h0r 6dj4em.ml is eventually brought uniformly to rest by a frictionmjr 6e0 .dmh4lal 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 b h2xg-0vs)w,zc 1+t ejxtzs s6all 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 forearmdy7 q s nty:ish6-:en5mc;0 qe, which rotates about the elbow joint under the action of tht nd7 50q :yy6ses;h:me-incqe 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 shown in 3 arr+t +li:c: pk 4gsk,jc,ycFig. 8–4rc,:lk 3s+ty,c:4 kgcji rpa+6.
(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 consists23-u,vc)gvn yfe b6at 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 wzwx2f xby0 vsx3+fdp0.ccexi+..8j rest within four full turns (revolutiex0v x.c+x0z i2.8bydx3 +w.jfp wfsc ons) and 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 bm29qyq th4e m:p -y.cmoment of inertia 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 torqum 8in,:qbuo1 p(c+bp he of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without 2 d0w ji8t5y ukrlpxdix77xk82 wz86 aslipping down a lane at 3.3 d 805wpy2tdj8 z uix x78 ir6kklaw7x2$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy;xfce5 j)09frh.ehk.1. kz)hjyfwsc of the Earth with respect to the Sun as the sum of two tezch 5 hcr;).9k..se ekfy 0wj1ffj)hxrms,
(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 15gg2 w2m b-cfyxl )g1fd rwlf43:l5un640 kg and a radius of 7.50 m. How much net work is required-fgg 2)ry llgx512n4wbcdl f5fw: um3 to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1n6z68nfiok7i(7 n aiw.80 kg starts from rest and rolls without slipping down a 30.0nw 7z8a6fionk n i7i6( $^{\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 faqu2tw0di4ci6 ;woh 3 fll 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 consew02h6wiq f4td; 3cuoirvation of energy.]    $m/s$

  What is the angular momentum of a 0.210-k ; (9afd qv3ves)i+jvbfc6.ngg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed oq f+gisf 3 v)e9.bvd;an vc6(jf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheelhlrx)h3 kym j, )p4pm3eo/ cb0 of ra, m3orhemk/c h3p bx)j)l 4py0dius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at rkfqh0j 7a+ w5his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arm7w h 0qkjrf+a5s to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8a )wjl1tbb5i fz(: zm2–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angulaz1w: mlzfa)ij25(bbtr speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incre0ix:nf/qa.eh ase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 .fea 0h:nqx/ i$rev/s$ 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 aroun8pn5.7fu:9v txo2j)vpi 0 g bdlra.fhd a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter the5.f va piu hlg.t rbx0)j7:98vo d2pfnn 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 skater spinni.1 zmuldb sn(14(o ehsng 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 mo2800bauoh lnfl 9*wpomentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is droppewevxridq74j.b;fmo,p)a i yj 0v 2; p1d onto an identical diiopi41f0 yp7 w2 bavmj.xrq),;jve ;d sk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns aefer ,im4bnu6t yq 12;t 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-gpr/uy:nr,ncq s a*82 lo-round platform of radius 3.0 m and moment of i pr:arn/8s n, 2l*cyqunertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rota9m4mhi,we q4 yfo e w1+n5w,pvting freely with an angular velocity of 0.mei1hq+ mop,5,9we4wf4nvw y8 $rad/s$ 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 whie*p/ ymon,:za te 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 away no angular momentum, what would the Sun’s new rotation raz:o*,pye /am nte 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 windsow0ba0:ko -aj 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 8s 1o(ew harif+4tvw) $ 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, initiallyn- a x(cuf)/xj at rest, that can rotate freely without friction. The moment of iner n-fu)xja/ xc(tia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry zf83 iui2.epq-go-round turntable that is mounteq fi.zp3ui8 2ed on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the ends )p96o, 0b0l xewmuootqj63x 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 behind the person without slipping.03 tjs,6e x)ooxlob06p9m wuq 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 face gys yt-j3;z7not5p;d s the Earth. Determine the ratio of the Moon’s spin angular momentu -ytg sdjop3;;yz nt57m (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/cw os:,bii5zo++e , mo$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m w m)daf *p,5ioacquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the m*foidm 5w ),apotor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.05vw6w(3 osdq)9 (jssnn:y ,myy0 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m.,owy (nm:v( yd3ysssj q)n6w9 Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the anauibq4 p5 n,1cgular 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 drno-93 o xsx1hn,7jqof our Sun, but with mass 8.0 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 atx1-n ,hqr9o7o xjns3d all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use eqks /lpyzopiq t -/o/. w:yw9;nergy 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,.qwl p/osip 9y:/ t q/z;k-oyw 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 illustratest /-11v2 j7nwxh,ajy2f(ea 0g*kr. pt bvhzun 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) r acrw7g vsbd0w6(6cmvi) twr6x)70pis rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pi53 62.a.rgmml nldce bvot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21gmer3 .cl6 nabmg 5dl2..]

A wheel of mass M has radius R. It is sta,/6q)ve/6wmvq o glwq nding vertically on the floor, and we want to exert a horizontal force F at its axle so oe,mw6/qvq gw)/v q6l 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 making a tuu f83mi2k+dlv rn with a radius The forces acting on the cyclist and cyk38d+i2 lmuv fcle 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-kd . *rlic)s0lj-ihv1jjz7ia .s -c0lwg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat1jilw-ah . *j7d-0ilcvics) rs l .jz0, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinderf8 kr:)3 fpve5w4m,oac7jsne in x. c) and her arms as thin rods, making reasonable estimates for the dimensions. The:e8r,3kfmpn5 47 f.ewsa)jv)ox c icn n 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 which consists of two cylindricaq );wo i:ee4q.bro y+al plates, of mass i br4qa.ee)+ ooq :w;y$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roll *2qw7 x9no;3hz orzbls along the looped rough track of Fig. 8–58.x3oz 7nzwb;hl92 or q* What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dou*jroi pglwwj;i(i gy 7 3k-/9 not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed u:/lkh2tap3 x vniformly from 90km/h to 60km/h The tires 3xt: hk/pav 2lhave a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s