A bicycle odometer (which measures distance traveled)bvx qonc--j9 7 is attached near the wheelq-c7 xj9o-v bn hub and is designed for 27-inch 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 theqbc vu,fk9,i/yjof* * 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 cases would the magnitude of either component of linear acceleration chanbcqi*,*,yukf 9jv/of ge?

Could a nonrigid body be described by a single value of the angular v6 yevf-fgnw:6 elocity $\omega$ Explain.

Can a small force ever exert a greater torque th-9e i(mjlb-h 34lmc;+h5r: hpmn wjv gan a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up wiu * ag2*khn5jzth your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thi2*a * 5zukgjnhs.

A 21-speed bicycle has seven sprockets at the rear wheel and thrkq; g9vu:33 )ray5 d azh9ezqj c-sj,ree 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 sprocket or a large front sprocket? Why? 39 e,zdrs)- hav jqkyqc9zj;5gr:u3 a

Mammals that depend on being able to run fast have n vdxekrg 1+-tzw3 x50slender lower legs with flesh anknr- dzx+t 3gx v0e51wd muscle concentrated 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. 8–35dr-u*n*p pt,oh5 ,zz c) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also g 2erlh0)t3jnzero? If the net torque on a system is zero, is the neg0jrtnhe) l32t force zero?

Two inclines have the same height but make differehn5) 7 i3jei+5sgs dbpnpm(q9pict+ ,nt 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 be gnep7pi 535q,nsc djphg +s(9ti+bmi )reater? Explain.

Two solid spheres simultaneously start rolling (from rest) doqkdo o-s u)4i)ynsg/vws7pg8 32dr:ywn an incline. One sphere has twice the radius and twice the mass of the oign /4k2s y-8s)) y :vpwru7 sdgqo3dother. 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 hav8moimqc.)v-bqj,00 pfed ya2 e the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has bqm0ofpj. m 8yd ,)ae 0q2-vcithe greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mr02h u2n),ev -or ajaioving or rotating objects eventually slow down and stop. Ene v2haj0uo)rir 2 ,a-xplain.

If there were a great migration of people towm/lm)ghxp:( oard the Earth’s equator, how would thim/mho(xp g):l s affect the length of the day?

Can the diver of Fig. 8–29 do a somersault witpm c3v;z z9)fhmw1;rm hout having any initial rotation when she leaves the boarmm9cp3; fvzh1rz; m) wd?

The moment of inertia of a rotating solid disk a)ut+ ml hy)gphje-c 0ig2 u*b9bout an axis through its center of mas0*uuh i) phj9gc e2)-bgmy+tls is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstret6z+wz yvs wdfsa)6ki,0 vh(u*ched hand. If you suddenly drop the masses, will your angular velocity increase, deczsav*u ds 6viw)(h6y w,fk0z+ rease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is h* 8q iut/ mok2.ouv(lwollow and the other is solid. Describe an k/8o(l .2u tq*vomiwu experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points lrqsa+ph5 od/ (e( s4ywest. In what direction is the linear velocityh4qa+y dpssl 5(/(roe 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 or decreasing?

Suppose you are standingkqk+-r2cl 4qn on the edge of a large freely rotating turntable. What happens if you walqkk +2rc -ql4nk toward the center?

A shortstop may leap into the air to catchm)9 m z vz .t:yufwh ac;1zw*n)df7zu9 a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you lz:7f*v1.mn )wwcyz f u)9zd;tmh auz9ook quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helbbrzi4 1;bw:y8j:w isicopter must have more than one rotor (or propeller). Discuss one or m:jb rw;wy4s8 b:i1ibzore ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: 7 cqc339cx* vlkdp.tv(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 Eabwfusy36zkh:8;wex3 wn .f+j rth because of an amazing coincidence. Calculate, using the information inside the 3wx +k;s by: 6wf8n uwz3e.fjhFront 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. The beam j3 m.tfrklx e7et p+ (l02fhc/diverges at an angle el/273j.el fhk mxt0 +(ftrpc$\theta$ (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 ofcquf.wmy x (9+qgt, n 2zk0:tk 6500 rpm. When the motor is turned ofg,tw.zny+uk9tx :cf 0(qk 2qmf during 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 another child+u, - js1kqlxx. If the ball makes 15.0 revolutions, what is its diamskujl,q x -x+1eter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.m,ecy (*t fbip2e;)l b How many revolutions do the whbeicbm ( t,le;f* 2)ypeels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rot6smi)yjtjv2d d93e6 sates at 2500 rpm. Calculate its angular velocity it3 m)jd6ye26vdjs9isn $rad/s$ $\omega$ =    $rad/sec$
(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 4.0 sk(uoyp qb)qs; y1a/q3 (Fig. 8–38). (a) What is the linear spee 1ayq/qpoq;(ky sbu 3)d of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earthpa lng5r:+x: *;jqerw (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point*7f.+bn8 s vqfqludc4hvm*5 h
(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 froma828ekv,qe q bis22rz the axis of rotation is to experience an acceleration of 102bie2s,kq8a 28zrevq 0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abolol j-)u,r-(r,ttj x iut its center from 130 rpm to 280 rpm in 4.0 s. Deterti llr o,)(-xuj- j,trmine
(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 radiu/fyof042flw n 1hc1kxs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecroxags u)s(:ci4,l g* 6rd5r tjaft 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 rrc 6si5gs)* g a(:ltx,u4 jdo12-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 fiw1 r c29u8w d7lxh diif2d0j-rom rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time82 j1x7wud -h 9r w2fdicl0idi?    $rev$

  An automobile engine slows down from 4500 rpm6 prm9lf5hel :wmaie0gm9: 1c 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 stres m,mlp8i 6sa c*1vc,ms e;k3iiku au6.iu7 5oases of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min7lk,u5 63o a6 mas.ui;1*kvuci, ai8eismc mp 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 fromj(/noau+fs 0c8dxy4gy7.f q- ezlzh 5 240 rpm to 360 rpm in 6.5 s. Hon04lh(o sf zd+8.y jag/-c qf7eux5yzw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/msw r56b).x wt6f6hmeqin It turns 1500 revolutiont f 5mexr66)h6bwq .sws before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutionsvur*ywch gg4w 2.-6pe as the car reduces its speed uniformly from 95km/2 p- ugwc64hy*gw r.veh to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reducesg0*tv1h h2o m6yo 4dot its speed uniformly from 95km/h to 45km/h The tires have aoood0ym6gt4 tv2hh1* 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 ald t:h.aj 0m0c:2x7 rcufk 1cmpl her weight on each pedal when climbing a hill. The pedals ro1chcr:.d2mump t0ca 7:0fx k jtate 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 forcek k6j,8l c;r,)5jydpbz )dmrx of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the fox p8);lm,5d)kjc kzb,d6yjrr rce is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel (q)-+/n mld hiofoy9vshown in Fig. 8–39. Assume h/ fnl+qood v -my)9(ithat 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 o11a:7 fbw btpr crte+5f a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this cat5:rbtw+ 71p re 1bfsystem.

  The bolts on the cylindero5fqdxk18o *if*du. r head of an engine require tightening to a torque of 38*oridq*fdf. u1k 8x5 o $m \cdot N$ 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 0.6 8 0 f9r6cmq8wd/x 9fhh.ncpou48 m when the axis of rotation is througp6qcf cun./hh0o8w9 98rmdf xh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a b qcku1li b6+z5 bhdgr69 05bfjicycle 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 (wh6i+655 f91 glbqkudzbh r0bcjy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hij *xzfaj i lmst/- o:k(pk;:4orizontal circle *ii m s:o f(j;kzjpx- l/at:k4of 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 potter7 vm2;ug4 ehjm’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total;hg v27e mmju4.
(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 theh(5l( gnizp rbke:n+ 2.jpoh9 array of point objects shown in Fig. 8–43 aboutok2l hp+(ni9:brn(hzgj.p 5e
(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 )b*i+/jww8i vc) t cb)kfsngqt27y+rof 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 cylindral9b)u8d2vvm cv d.+mical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 360c82bdmv.)v9 dmuav+ l0 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 5 awjybhtf(c..chx0h9r5 qa, with a radius of 8.50 cm and a mass of 0.580 kg. Calcua 5qx.0c ,5ab9t crwyf(hh.jh late
(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, acceleratiyw 3ida*koe.i 9scj;/ng 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 tangentiallw:tw( ,yzax )sy on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round 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 kazw:(ws, ) tyxg) 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 vu- jd-(mi*uo*t o5pr off and is eventually brought uniformly to rest by a tm(rdvp j5*o- -ui*o ufrictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball a b hrag:f f5*;-nydwq/.wx ky:t 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 bal dtbw+;6*pvmnbu j kz+8f5if6l is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fro*+midn5tbwu b6p ;ffkz8 +6jvm 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 ,+r+ v oc)uis 9jxp4zjrod, as shown in Fig. 8–46.s)9pz jc+u 4vxr,o+ij
(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 tw)y xy/b6m19onccm ub /o masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (r uacy9n1x13r, ztsba7 evolutioysatn b1zux 1397,ra cns) 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 moment of irlpgb am13/+ i)j,nmdnertia 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 to ;* nt. kcp:x3yuojd)crque 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 wit,doj 21s( hypajcw9w7 hout slipping down a lane atwjohwa scd(9jp7 12, y 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sur *7t)4gsu ;4fz jygowm of two terms7o rys w*j 4g4g)fzt;u,
(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 1w9w0-;g9kgn +qrgb ei640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest tok9 9wg rge+nq0w -b;gi a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cw j10nlkbabaoqp31 1 0m and mass 1.80 kg starts from rest and rolls without slipping down a 30.0a3 j b1bowlkp0a qn101 $^{\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 t hxvawf7ok)ce af;9 s(yrrv 9b-- +9phip. It starts to 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 ground? [Hint: Use conservatiyxa ; f7 e+9pfvr )r9-(9khas v-wbochon of energy.]    $m/s$

  What is the angular momentum v-arh: fd d+yg;0mzw;of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an anhdywd+0zv ;rfga;: - mgular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg-xr3mg 4(moj h uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rr mxhg(mj4-3 opm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, ow :y8frjnkwh 1a2sw -2svu7b4n a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, 1 ww:j8y2na u2ws s7fhv4-bkr 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 xd:ylxgxxm,8* sk 3x c)k9)ey shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to txd:8xe,symg xx)yx* )93ck lk he 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 2f4,sd;qhqtp rate from an initial rate of 1.0 rev every 2.0 ,2hspqftq d4;s to 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 center at a f s90;n h-tgtbz:yhb;r 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 rotating wheel. What is the frequencyz0r9s:tn gbtbh;;y - h of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinniz: v8uw m4p23 8rhg:grfu,dxd ng at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of t aiw k(cjj c*b42+h/( wjomfm4he 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 o *u un12dp5stdropped onto an identical ditp 5odu2su *n1sk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns / nmkazic)a)h1xj/ 7 gpt/+nmat 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 platfor0tp u+:t(ue 0sg 8mkmym of radius 3.0 m and moment of inertia 920 ts: ymu+0k0 ( pge8umt$kg \cdot m^2$ 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 rotating freely with an angular velocity 6h u;fahh9,1 djje*osof 0.8 ae9;,1 j*ds oh hjhfu6$rad/s$ 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 dwarfv:kxypj1o;yq5d b+rnr /b :)oed 6i5g, 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 momen;jdo1nyvy5)ib p e qg5 kr/6b:xo+ :rdtum, 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 ztxxr*.8j ypt p/zf;mr+0 0.x7st lgb winds 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 7 d0a oo)ow9ga$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate fro v e6.k1ymd0peely without friction. The moment of inertia of the persoe.omdkvy 10 6pn 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- reb.)pq,.audc,3y k sgo-round turntable that is mount)s.qrkyc ,e3dab ,.uped 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 end of:5 x,ykmd;uyo 5;hxz)n s hv/l the rope lying on the top edge of the spool. A person grabs the en;; zosx 5kh/v5m:n lhy)uyxd,d of the 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 same side always facx ni*f0(-/9 zajsjrnq es the Earth. Determin ri/sqnja9-fx( *n0zje the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest gxua lhn(exy1 (;w/ootin4 ;4 at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder o,j(m 9f(zejkmf radius 0.20 m acquires a rotational rate of from rest mjzek(f ,mj( 9over 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 of mass 0.050 hr qv1 p. 4xsrwk28do8kg and diamete qd2hv.os8 18wxrprk4r 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is gl6mc/gv6 sy *the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotatp;m; r0yw bx5r4o8 wmying at a speed of 1xmw8 ;m5yr0o 4rp;byw.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stolj c xr6kpmr -0j81d-pred in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spi8xjj0drlp-m1-rk 6 pcnup.”
(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 illustrates anaxya zrp,6;ofsd 0// y $H_2O$ 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 sc *ct 0z0mof (/)c7 .f9jngh9.ljtnri ,a ugwon 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 ignore friction)sjpbq k7y/f5n- y3(i t 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 (7qst jp 3yni5kyb/-fshown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, atp.(c,9v otgf1 dd n0 uuon)b)nd we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–), oc(p0t uovbdugnd)9 .tn1f55). The step has height h, where h

  A bicyclist traveling a1uolzt;b owc+a m84 5with speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normazw8lbom 4;1t+uao ac5 l 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 lengtmx k,6pp 7p-ki/(x srgh 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to xk gppp-(krsi,/6mx 7 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 as t)s u;epqpz9jk :s ac++hin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular spze +qj9u): spck+;sa peeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which fl 9b,mw1xwj9consists of two cylindrical plates, of mas9f1mw xj9w, lbs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tbjiro ql4ev) r1j(/dkdxw(p7i -q1:che looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if ibj pqr7 o4 we):/(i1 rq(ddv1ji l-cxkt 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 aulo ird4 23+t(hkn jx*ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces it mv,a.cu8a 1uws speed uniformly from 90km/h to 60km/h The tires have . u c,maua1vw8a 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