A bicycle odometer (which mead 3r,:j8b lp ejv*oq*8mvfa,usures distance traveled) is attached near the wheel hub and is designed for 27-inchrajjq8 ob u*3m,p,8ev*d vlf: wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the s t.x-l2l 3lh6g2llgg rim have radial and/or tangential acceleration? If the disk’s angular velocity increg3hgs 2lx.gl 2l -ltl6ases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velkkii -y6.r 1qvocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expln+-f nbym1 2 dmk,z-hoain.

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 do7wsg-c;f 3q2n:nad rt a sit-up with your hands behind your head than when yourn2twr ga;:- sncdq37 f arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tha 1gv6 nm*,lq:n guf.we 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 spg1ml wf,:u6 .qna*ngvrocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slendewhw63d6p ls*+ xt mg:)v; ynnlr lower legs with flesh and muscle conce tg)slv+xmn;wyd3pwlh6:6* nntrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow be gxn q1mn573rn1kv6sml- fvq5am?

If the net force on a system is zero, is the net torque alr0czqmz3 dgf1.i jy ca z/+)j6so zero? If the net torque on a system is zero, is the ngi. c f3zz z)6yr0jcq1a d/j+met force zero?

Two inclines have the same height but make different t3d7gbg2dns 5*ah0gw angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be73ggwb hg5tnsa d 0d*2 greater? Explain.

Two solid spheres simultaneously st wyv1 1ocesn(j.gx) 6sart rolling (from rest) down an incline. One y( osvsc xw6ng.e) 1j1sphere has twice the radius and twice 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 s fmbq2c 6p6vv:/b;rzc,.jdkoame 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 greater total kinetic env2 dckm q 6 o/cb:.r6b,vjzf;pergy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or kgz8ryo1 6t;go h 0+bjrotating objects eventuall zg6 yrht+jg0ob18o;ky slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equa 6hbh (0n+y gthubm2,+ohf.kutor, how would this affect.n2 hbuf h h +ok+6mh,b(g0yut the length of the day?

Can the diver of Fig. 8–29 do a.g1 et,7l dqst somersault without having any initial rotation when she leaves the board?tsg q7 ,t.d1le

The moment of inertia of a rotating solid disk about an axis through its cente ph0vj:q)ko ;br ry+4xr of mass is jbror0p:yv h +)q;4xk$\frac{1}{2}WR^2$ (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 cd4m.iybnuq8j f/pl:3 tvd92-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same d p9juvtlimf2/38y.dq nc4b:? Explain.

Two spheres look identical and have the same maewz dvc)8b)3obg(l qut*x2h,ss. However, one is hollow and the other is solid. Describe an experiment to determine whic(cbqeouwl2,tg)vd z h )*3xb 8h is which.

The angular velocity of a wheel rotating on a ho uvx )omci*e70rizontal 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 speed increasing *ux 0ovc) i7meor decreasing?

Suppose you are standing on the edge of a largvu, 5:) iesdokrno,kq-*w,q7g hak n7e freely rotating turntable. What happens if you walk toward hw:ak7i),vs-,kqr7qoeo *knd gu5 ,n the center?

A shortstop may leap into the air to catch a ball and throw it quickv.irt6 yan *9c+fn 4hj1gc3ayly. As he throws the ball, the upper part of his body rotates. If you loo.6a9+jyv43h* ifrtay n 1cn gck quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservationhki- duf5cynvf+d o4iw:29 e5 of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can koid4yi +d9v nf5w5cuf h2-e:operate to keep the helicopter stable.

  Express the following angles in 3 ky9+0t.9vxzljyqweyr5 2k lradians: (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, j (vl;jb1*x1 huzuicu-e2, cxusing the information inside the Fronte1u2v 1xl zic-( *cujx ju,hb; Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Thebeu2vz bc/xtwawsi 0 yf 9d 51h/9t9k+ beam diverges at an ang9/ yc uhids/a0 zxb1e bk592w9vf+t wtle $\theta$ (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 tq finf *;qt(r,vv9h)zhe motor is turned off during operation, the blades slow to rest in 3.0 s. What is theqq* )v vffin(9ztr, h; angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level fr4r1, uvc* jhx ;yqdb+loor 3.5 m to another child. If the ball makes 15.0,rhv;ub+rqc4y * djx1 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many9p aq /s/3.:/th pohtphv co-w revolutions do the wheels make?/:cph- 9 owpp/.q3oatthh v/s    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 ky1f(d146 tdyftqm1u rpm. Calculate its angular vt4 y tky1 df6mu1dq1f(elocity 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-roub .5vcbbqp**vnd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the ce*vq*vbb. p bc5nter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular wb kio qp3g)a4;i8pir:a 54 hrvelocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed fa(-k cg ar91nof 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 nz. orkhjcuhyu;,.f9e 6.mr-1 mu*alcentrifuge rotate if a particle 7.0 cm from the axis of rotation is to,;1n.c6r j om9u-yf.larz mkuu*e hh. experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 28xvpo(/qa ph4 -;unv+ rg-+yjk qoz1g10 rpm in 4.0 s. Determinzvuvny gk4- 11qrq;+jh-ppgox(o+a/ e
(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 radiuxulu; vm) v98is $R_1$ 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, astronau 0bq6ji na 12wir*:qk.tfx6vl ts aboard 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 interval. The spacecraft can be thoughti rb i* qq1n0:vl2akxf 6w.6jt 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 accelerat-imlj)k4u*q:1e k nguz tb. 1ces uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time?jltk* :u-ukmg4.izce1)n q 1b    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm isdobadm9i0v2 q,d8ha4i e+(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 in a whir n60p ,hr9bbgr0dkk /uling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.bkd/u6g09pb0nkr h r,
(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 in xph;8;ilzb4 k:xhk;lqo+)r k 6.5 s. How far will a point on the edge of the wheel have traveled in this timb 8z+ik: ; h o)klpxqhxr;l;4ke?    m

  A cooling fan is turned off when it is runni da,2/khn 5v sc/j9r4jes0cming at 850rev/min It turns 1500 revolutions before it comes to a svcjd 9j 4esakr5 /,i2n c/mh0stop.
(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 i(u6 ngp oisn57 53-ttwy, rvc65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The ti3n6 ygu,ro(5i 5sntt ipwvc7 -res have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces itwz9lr)h u9pg k:mbr2w9)y 6e.a- mzpfs speed uniformly from 95km/h to 45km/h The tires have a diameter of 09uk2gme)yr.b) a zzl:pw pw9r6m9h -f.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climb ;tgai rsjh,xk*1 ;eh2j-m1uming a hilkh*m-su a1,ej;jih1x ;2 m grtl. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cmigh f6)z;d /xeyery1; ,0(v0 izhmryq wide. What is the magnitude of the torq mix( ;yh0efze1dvyi;,y60) h/rr qzgue 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 torque abou gi/yw:tn1 z,l uu() :h8tlmymx/g -slt the axle of the wheel shown in Fig. 8–39. Assume thatmznlhulxgty / gl1uyt8 : mi: )-w/s(, a 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 ends of a massless rod which pu-l+n+witj *r.bov +)hm;mv* ua r*anivots as shown in Fig. 8–40. Initially the rod is held in the )auom;h- nni++ raru+vmj l *w .*vt*bhorizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an enginez( dbr1(jo ;fe require tightening to a torque of 38fo j( (erdz;b1 $m \cdot N$ 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 0.64nd/e9zjfie9 ;9r o(o4gir0xr 8 m when the axis of rotation is 4rjr; re/9dgo9zo9i 0f(en i xthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diam 9 y8govxrocd*+-y g:heter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub *dg oovg -c98x+: hyrycan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball 0e wu*4fb86xx pklxd,on the end of a thin, light rod is rotated in a horizontal ci6 x*8xpu ldek4,bf0xwrcle 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 w)/,jzlhk 1gqro/g/cvheel rotating at constant angular speed (Fig. 8–42). The friction force bethr /,k1/ )jggzclovq/ween 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 ofwb 2 q3kx(w*yk the array of point objects shown in Fig. 8–43 y*qxkw2k wb( 3about
(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 oxygpz. .nna,wy1r en 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 cylindrq9y9kiiy )gf q,wz85e ical satellite spinning at the correct rate, engineers fir)y9,q 8fq iei 5kz9gwye 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 satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cw9mbha azq+bz6a0h ),bw2s 2em and a mass of 0.58em) z9 ,sb+ zhaawqb hb6w0a220 kg. 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,sj /6ves)ehfd ) 1h2rn 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 small hand-driven merry-go-round and is ablezwky tm8bz03 : to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-gow30:k8bmzy tz-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. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off anb ub6kf:ygj :3d is eventually brought uniformly to rest by6:b:u3 j yfbkg a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 acc5,nztm9+r1 whrm vrc1elerates 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 actioq38y/ca( xu( 1wnyxk fn of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball iscx3nyyq( ka(x u fw1/8 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 considerede3 30,u, ibel- -tqycbptgk1a a long thin rod, as shown in Fig. 8–46, a,iu0-13 tg3qpclty ebb -ek.
(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 conn dq (0/goyc(x.gz/ p.u7m eb5-apjnxsists 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 wdan hti4kv8-cr/eb-x 3vx g1 k7ht7-tithin four full turns (revolutions) and releases it at a speed ofbtxh- 77- 1/xvt8vk ihcrk4en ta3 d-g 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 mi/5t 4/ zusrts5xqz zb4kn.w7 oment 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 torque of 280 w.x0;n w)p9aiv7 al; ebk,mi q.elg7d $m \cdot N$ 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 rof/m;g ai4 :gb- v0bugills without slipping down a lane ba ;vgimbg0fg :/i- u4at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enerv8+ xz,-udmiqgy of the Earth with respect to the Sun as the sum of two term, i8-v duqxz+ms,
(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 m ..( rto8i +ah3e rcscqy(p4jtass of 1640 kg and a radius of 7.50 m. How much net work is required to a t.r +3htj(ap. (yi8sroce qc4ccelerate 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 1.80 kg starts si .w1t; 7m3j jsc*l6j3gnfszfrom rest and rolls without slipping down a 30.w*njc3tj; msg3l1 i.67s sz fj0 $^{\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 balanar1ga ,x0m(as ced vertically on its tip. It starts to fall and its lower end does n ar1mgaa(x ,s0ot slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bal*qsm 2 .j8amg9gx f7del rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4m7g8 q9xaf .mgj*d es2 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-k1swqe twyn un1;ns-2 -g uniform cylindrical grinding wheel of radius 18 cm when rotatin-n q2uywsnew ;s 1t-1ng 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 platform that is rotating )dm g* d56v xqxa8t3t8x jzmg5at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed oxm 56a5xdmz *tg8jx38tqgd)v f 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 momen d8tuvm 4zlpuq0;ty,0g5pl7 rt of inertia by a factor of about 3.5 when changing from the straight positio 7l0z,4tm0ur85;qp l dpyvg utn to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fromenp ord-u0t; , ,4dnvk an initial rate of 1.0 rev every 2.0 s to a final rate of 3keu ,rdn-v4;otn0 dp, $rev/s$ 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 center at a flm 6sc /i-xf2y)q/tfq requency 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 rots-mxy6tq f /c/q i2l)fating 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 spinning at (3k wwu9e+5d pzqlk8m1tt9wx3.5 $rev/s$ 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 angularzos e nwz u;ec (r(5npa5;-l-e momentum 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 o 6 1b. 2+oq(zspobzvwbf inertia I is dropped onto an identical disk rotating at aboqsb21.bzpowz +v6 ( ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.8r(kydo7tucwyg v; p mjex 94(3*snt;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 atbt-a vum kq +8a*(v6xq the center of a rotating merry-go-round platform of b aqax+tmk v8(qu-v6* radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-roun u(r26fak-o86qvf gl nd is rotating freely with an angular velocity of 0.rfgvku q68l6-n 2ao f(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 dwaru f:dcf*d*pusws 1set3 z++a 6f, 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 w* s+fucz6d sadeu 3p1tf*s+: 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 exce 3gsi2sj-gw4z ss 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 rwy*2,/pxr utml; yr0$ 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 resmj(af yof 84bp/e9sw+ t, that can rotate freely without frictie8+4w/ 9foyj ba sp(fmon. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diampn 2yo(8yw f(3st8dg ueter merry-go-round turntyuytf gpd8w38 (n(o2sable that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rol/)5* qmbzri u u*fv4pwls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of theu/4* * wpu)fivrzmq5b rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the sameaa6k0iut5z96 bcqg k) 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)5q9u6k bgaaz0k t c6i as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest adqcjbdgr 8: 9r078iio t a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radiusr84 e q2 -p -3msl8.hhvua1u;q,ilmyb hlex7m 0.20 m acquires a rotation -ay2mh 8l7s-mih8uhlqq,le ;x4umb1e .pv3ral 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, eac psybyi bl+02g6 h66xfko. ttaaz;- m6h of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical huby0 y+x. s626;oahpmlb6 b6t af gzikt- 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 rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whegdf 44bx+ gmo95q)j eeel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotyhu3f1 qjq*x(k5mj9 1f2 fp 5j fijx7hating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational coll*f1 5 q2phqfhji3u xfjy(m kj719 j5xfapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to un z 0g:qm5ct:ise energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses :: 5 gmztc0qnia uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustra;cpsisksjef v(y132rl) x 9 5qtes 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 rollinmu0;xl mi9m(eg0j r.d9rt +izg on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we io 69vzjnk 25xrgnore 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 the52v9zrjx 6nko force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertica l+d0upv gvwb31. ew.frc5gjd(c vq09lly on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against wvvdc + g .591vpcwj30flg (q.bud r0wehich 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 uuiz 3: eae0 tk7,*pczmaking a turn with a radius ic ke*:u,t37p zez a0u The forces acting 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 sling of lenext9;o dkr0-k4rc3z: o.l((vv zzl wlgth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from r.v(:9lt3zl vcz( -kew; 4k0o rzlxrdoest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms azn2,h). y,a x fnqk9kms thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against hernqa ,nmzk2x)h.y 9 fk, body.   

  You are designing a clutch assembly which consists of two cylindrical plasmg2mz,,0kyd0 kxpi 0 tes, of massy0kp,d 2xms0i gmk0z , $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track ath/0 (wvn1ik of Fig. 8–58. What is the m kh w(0vi/1atninimum 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 o+0p,zcp0d *iniq cz9assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the k v7** zqcrj3vcar reduces its speed uniformly from 90km/h to c v3kzv7 *q*jr60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s