A bicycle odometer (which measures distance traveled) is attacb 8 p82*zqddg r2e mnyn0v+/arhed near the wheel hub and is designed for 27-inch wheels. What happens if you /2n+ yb2 az0m dgrd 8vnrqep8*use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hanp6d7lt v1s :dj(k;j zve 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 magnj:1 dkj6z;pvls d(nt7 itude of either component of linear acceleration change?

Could a nonrigid body be described j z /w,stb2n0a3kohy8jg ma42by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than ah wj(y st bj+;2f27jmx 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 3/v;htltv prc)1q/vc )4i3w;umi v uwsit-up with your hands behind your head than when your arms ariv4pvhw/;q l3 w);tc1v 3iu )vcu mrt/e stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sevety5j3l niy u .u.se6s vqt+6 g5c)f/oon sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear spsu etu.3jovsgy5iy 6 q + )/nc6o5t.lfrocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wbg:5zlx y9:k38 zxs tqith flesh and muscle concentrated high, close to the bod qx:zl5bg z3y:tx 89ksy (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, nyi,uhh1;ixn4lvb;zf b b b2, 2agh.g9arrow beam?

If the net force on a system is zero, is the net torque also zero? If the net to9nvyn12zu* w*4zeosh ew0 3en rque on a system is zero, is the ne30ensnwo z1 h*v2 zuewe4* n9yt force zero?

Two inclines have the same heightjz dy 5 (6o7c56tmcaky3 .tqpqnow(3z but make different angles with the horizontal. The same steel ball is y to3atpk6o73.q5nydzw q6j 5czm((crolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously staran m 8vy :r.u6fp1i;kht rolling (from rest) down an incline. One sphere 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 greatef.ih;81au k:rpmv 6n yr total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the samer5d p-(i7yvh k-c 9bey 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 energyp 7 v-ibcy9k5ehdr (-y at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conservev/aaf) xh1 v*vk j-9lqd. Yet most moving or rotating objects eventually slow down and stop. Expla-1k/*vfvl hxaqj)9av in.

If there were a great migration of j**0y*u ,)awsvkkb :oiyk w w70pxb-qpeople toward the Earth’s equator, how would this affect the oqk*ybw: u0wp yajsw7x- ,iv **0kkb)length of the day?

Can the diver of Fig. 8–29 do a somersvsvm 3jm-:ved9c e9(h ault without having any initial rotation when shed (meshvvm3c 9e9v- :j leaves the board?

The moment of inertia of a zv:lzu4 pky94rotating solid disk about an axis through its center of 4kvz:l4z 9pu ymass 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 mztzzs +pht5.ve8 zvc;1fa/0 uass in each outstretched hand. If you suddenly drop the mass/vu1;vsa8pt+ 0hf5z.zctzez es, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and )c.auhcbj q kk0dih; hb/( r*zb0y8e0 have the same mass. However, one is hollow and the other is solid. Describe an experiment cb(.b h k0 )8/rk hbiy*djqza0uhe0; cto determine which is which.

The angular velocity of a wheel rotnzud2lg ):bdd hl s5knv423o -2 ke)iyating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the topuo:yd2nl2id5dg)2sn vb-4h3) z lk ek of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whr-g, g gmkuen +8/j,m dw-jq8hat happens if + ,gj8g-/dnjg8, m mewkrh-q uyou walk toward the center?

A shortstop may leap into the air to catchsexqp )94d 8p(fqfejbr.+reb- /nq5k/jn9n w a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite directb 4nejfr-kswjebd/8 (pf)np rq9n./e+x 9q5q ion (Fig. 8–36). Explain.

On the basis of the law of cons g(-brcajk:l2nl agg7 3/mj;wervation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stan2j lc3agm :jkwg( bl a-rg;/7ble.

  Express the following ))fhmtv ,ufq2angles in radians: (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 anywl;i4wtf4 1ig:h-:+c qff2llfg n4o amazing coincidence. Calculate, using the informa4ycwfng+ l gf12qfh:4 il-4wot :l;fition inside the Front 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. Thry/yvhe+j mb- k :.mz7e beam diverges at an anglee. jv/-rhzy +7kmb ym: $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blende(khdtx xula0. .wvf:o 3 - *g7(bmaatpr rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as -l bxm0ah.t xktf(p g(a*d7a u .:wvo3the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chzw ov3re 0mj+tww6 2b.ild. If the ball makes 15.0 revolutions, what is its diameter 6o2w tw 0e+b3j.vmwrz?    m

  A bicycle with tires 68 cm votue)kep6+d:ub 7x0 in diameter travels 8.0 km. How many revolutions do the wheels make?vbexp:7o6etu du0) +k    $rev$

  (a) A grinding wheel 0.35 m in diat/ge 384)e9 6iihbbw7d6xnnulpjd k2meter rotates at 2500 rpm. Calculate its angular velb96je k6dl4tg3h e)xniib n8 7w/u2 dpocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38).t.k0zl lb/ih *v+gg+o/0r68c ahs qti (a) What is the linear speed of a child8 kqt+i0c0g+/t. hbhir6vzal o/gs l * 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 thu4ek rexvo// dtf 8 p0ia/v(-fe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s cd7h-s*g*1ks/i p slbi of0r1peed 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) mustn.r ab ,gud9j, a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelend,, rj. 9ubagration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uqgovqi6 fyj07, ,s1mfniformly about its center from 130 rpm to 280 rpm i fsfgvq,7jy,imq 01o 6n 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 radiukl(fill 4l m *gsmk145s $R_1$ 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 spacecra qssfd;ts+n0st0z8b(r ,t 6 e s:8undtft 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 duri sd 6,;0(tdtns rt 8sq0e8 f:bztsu+nsng 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 rest to 15,* 4/ ha 3uy 26b*c pjqb8u*vjbqvtqt7d000 rpm in 220 s. Through how many revolutions did it turn in thiy6 tb q/pqt3bvuuj7c j*bq48h**dva2s time?    $rev$

  An automobile engine slows down from 456 j8siqj: g:3zs8hey x00 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 th+xk7 q+ zb(wzie stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching izkiz b7x(qw++ ts final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 36h ifx;9 m,1vpu1r doj00 rpm in 6.5 s. How jm 9di1;fx0pv ho1u r,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/min It turns 1500 revdq*(ljgno92 d olutions befor*(d l2djn9qgoe 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 rv bp;tm /8y+5z5e kkhgeduces its speed uniformly from 95km/h to 45kmekkv8gp5m5b hyt+ ;z //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 cr5gs l2e.8+hog*u 5hfedg/e ear reduces its speed uniformly from 95km/h to 45km/h The tiresdr/2uehslg 5eg*h +o.gfe 85e 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 weight on each pedal whnh 4(jjq9cmlt6mvk5 gt +*n4v en climbing a hill. The pedals rotate in a circle of tcm* n9qjhgtm4v+j (5 vl64n kradius 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 t2jy:td8 ep8xu0l g1mi 7gqxt; he end of a door 74 cm wide. What is the magnit et qipy288ujtdxx g0g:7m;l1ude of the torque 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 about tjx6tmlmyu6 yr(b4 y- yo 8cj23he axle of the wheel shown in Fig. 8–39. Assume that a friction ty- t6u(2rmy4 c jlyo3j x86mbyorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacqy 3kn* spk w50q+csow,)wng- hed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rodw5 ) wp*q+sq0g-n,3kcysown k is held in 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 idv4a)i 0;v anto a torque of 384i 0vi);aand v $m \cdot N$ 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-iiyl920n mph 3kg sphere of radius 0.648 m when the axis of rotation is through its centeyi932npih l0mr.    $kg \cdot m^2$

  Calculate the moment of inertia of a bich+pxe l dv67y6ycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub cly76hedv + x6pan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizwk z4x+iqn1 -g:gd;fvy( pk; zontal circle ovw1g;-ipy :g;(kk+4qxz fn d zf 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 k 37ti xn-l-aoa potter’s wheel rotating at constant angular speed (Fig. 8–42).iax3-t n -kl7o The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fi8c n3rji:z6c rg. 8–43ic r6nr8j: 3zc about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose totalq3 x79u) xu/on 5k;kuv*ycnos 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 cox qenz zte-nn0)bhw4w b*+i(.rrect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a4we0+ nqz b.extb*w i-nn()zh 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.gze hois2 q/2egi70kt yw5 j/150 cm and a mass of 0.5go 52/0etii2q1/ kjzewh 7gys80 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, accjti yq i-356beelerating 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 ;s koqipf+/5e zi8zd1 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 th +pkq fsedz;1/5o 8ziie 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 r1puazpw2fcdrdr/ rvs*z;( 85pm is shut off and is eventually brought uniformly to rest by a frictional rc;5wdza *r u8 /dpsrpz1v2(ftorque 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*htlb; k ;hmx2all 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 kf l) a5x eoiy13vogw-y4du)1 58ikbf of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest tk 4k35aul 1)b 15f)xiy- owvgf8 doyieo 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 catv1 c 6o7xvrs/n be considered a long thin rod, as shown in Fig. 8–46 t167vsc x/ovr.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two massexc:k :tugr57os, $m_1$ 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 t cx9l2-zxgg)ohe hammer from rest within four full turns (revolutions) l9c -gxg)oxz2 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 ( pyjotcbc *2mu+l60nof 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 developsx+3l,m snnd/l a torque 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 w/a/+ 8q+tmft )by*j0npisj fgithout slipping down a lane at 3.++f is8mj *0jt/nga /pyqb) ft3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as th)l7hlw oq.5qv e sum of two t)75l. qoqhvl werms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.5p) yt-1z th5o6)zm5rp ngooy70 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? 71)-ztp p y5)om5zoyhgotr6 n Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest ancn jvo5,2t5qzptqn;8 d rolls without slippin5 qn2n, t 5j8toqp;czvg down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It iofyai5u+22 sblpijd , *y66(o9ysfk starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just up6y9(2yf62a , i5i o*+slj fsyikdob before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a th/r 3yo 2v5cjmi9sybl ,in string is, b2 3mv9lcjy /5oiyrn a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2,xy*v 5vqsq .eq0h38juc i8bj.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 053q8bq ju. * eh vjx8syvqci,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 atrxp;-noi dt(m 1c nh(i(j- zq:(zg. tu a rate of 1.3re1n ;p t.-txii zr-hgd(ozjqn u m(((:cv/s If he raises his arms 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. 8–29) ca1av (mq2cmsq )x np07ln 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 i) sx cv am2n7plq0(1mqs her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an iniauj*.qgfa 8rf43 wn-xtial rate of 1.0 rev every 2.0 s to a finalra.4jg nu x-*fw83f qa 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 it 8,vyi7/4sb1i 4qvanpwr* acfs center at a frequency of 1.5rev/s The whvn,avi4*/r4i sq b py7c8waf1eel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of u5f,eym-zk/ e7s(qwh cqz 0r0 a figure skater spinning 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 angula.v63gmku ab y.r 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 vl+sb/w.ccu9*j4 zvkof inertia I is dropped onto an identical d/zj.slvb* wck94+ uvc isk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns s h1d45xevtuilzumt 48e1bb 4d/vn+. at 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 thfdnk vf tz607 3pnu*s(e center of a rotating merry-go-round platform of ra 6 sffv73tpn 0du(z*nkdius 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-round is rotating freel( +xfxvra;ki, v)7z vmy with an angular velocity of 0.8vv)xm;rz7vxi a ,fk(+ $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing4) mam-bwh*t h about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass ca-m *)bmh htw4arries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve ,+;qpp( ;mpx j-vgv-r q)s+ tqkz0d viwinds 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 nj/3/z- yml8gwv vo*gb ;v4/z ci busf*e+d( r$ 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 :3 vg x9 vukjrc;0je1d7dp ew:2ulvs8freely without friction. The moment of inertia of the person 2;ws r lvc7keud:9d 03jp:uv8j 1vegxplus 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 5g.k2j3z ufdp 5n)ig j b/)fctdiameter merry-go-round turntable that is mounted on frictionless bearings and hasig jjc)3./fz52 ug pbk)t5dnf 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 the8gq m :*te l*/df2,ytni;d.eol xll.x rope lying on the top edge of the spool. A e/g llln ed2 tx*;t*q.ilfyx.d m,o:8 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. 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 sid (bctz q*cq-j52 it5e qw 61u47wqczdde always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular mometz u q-je4idt17*wqqbc5dwc5zq6 c2( ntum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest atp,rp) )h 2wz*qozv;k74 l zzqe 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 uy6nf2 : uklkz(2:;wzj:xjsweniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the kyj uz2:k( 2xjeslzw6 wn;::fmotor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, ewd;bo 6sn8r. hach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin sonbso hw8 6.;rdlid 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 the angular snwgzune vn y;j)f7:;8u5z q 3gd*nf5qpeed 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 max(w)9msxe1k eoh7 qs 4ss 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 he (4x7sqwe) smx91okradius 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 isr+9:a.+x g lb6szbbnl for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should sb+a : 9xnglzl.+rb 6bbe 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 illustrates anwin(+g jcxq, x;pq,v+ $H_2O$ 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 rol+gzonu6a;k4q lymkg/ i x41 vl)bc0;sling 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 lenbvm8i swr- sczw,(p1.gx5g7 ngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume tha-1s,8 w g gp .xcmrvin5wz7b(st the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and wwr; u +7; elzq*0 rzh1+ixufnoe want to exert a hori1 zrz* onxlf7ue; u wh+;+ri0qzontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road isyux.hogek2137w qai.jwyna2h 6zz),4zi5 q f making a turn with a radius The forces acting on the cyclist and cycle are the no zif. ,ea 2qzx5w34g q)6y.a7jhuwzk1oi2n h yrmal 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 okpco as0d9*w c d)e-:uf length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, acceleratd:0*p-ucscd)ka9o e wing it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin roxwc30 nr+ik 5zlf.s m8ds, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spilci8 r5 ksz3n .0mx+fwnning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutcs1:);1ge6qo(a6h jgofcu ej0cxy h,xh assembly which consists of two cylindrical plates, of masag 6s )hgex 1yfcuo16x,j(c0q:o;hje s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 of Fig. 8–czdl5bp5sj;: dfde1g+m+s472 ql ukp58. What is the minimum val4lzgkdcfld qs :m;p5 deps12ujb+ +5 7ue 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 v60ek* ir3i0 mv8c7oj cj axh)do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifor38e8yva clc w8mly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angu8 vcyl3 c8w8aelar 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