A bicycle odometer (whe vd(wgmqf6; yl aa9:)ich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happmwvldq( )9ye:;aa6gf ens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinkrh :ecpn2g(j1 rc )-st on the rim have radia reg )p c-cns12k(hrj:l 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 change?

Could a nonrigid body be described b1kef3 w tiv;x3y a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greuhx9hlf+67x 2par z1xpa p/0later torque than 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 with your hands behind your h ; y3pf6:gf ;h/7z5sfqls5gl9ccguj b ead than when your arms are stretched ou5c9bu/ lhyzg f5:glfgcf;jp; q 7s3s6t in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threequ-pirag kp0 8rl/ b31 at the pedal cranks. In which gear is it harde uqiar-br gp1pk 3/l08r 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?

Mammals that depend on being able to run fast have slende2+c45f,lw mktd i3ems 7cy*ner lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this imwedn53 ety2f,+ lk m7s4*ccdistribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrowlr3e/y 8nuqdpl;px4( beam?

If the net force on a system is zero, is the net torque also zero? Ifw5hd /ra:d g-t.a cvd+3qeol; the net torque onhdo:qdv 5cd.e wa+g t;r3-l/a a system is zero, is the net force zero?

Two inclines have the samc36hzwx: 0lj3 pzf b+w7l xv:xe height but make different 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 greater? Explain.0blh+f6 3:wpxw vxz 7z3l:cxj

Two solid spheres simultaneously start rolling (from rest) down an inclinz.) w.3d1vbnmnz m hy*e. One sphere has twice the radius and t.b1y*)nn m.zz3wv mhdwice 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 t -mvwttl62o1gi3 hpg.he same radius and the same mass. They start from rest at the tophog-vm 1.ig 3wt2lt6p of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or r0 m )qrwil0a*wotating objects 0mqw0w l)rai* eventually slow down and stop. Explain.

If there were a greatqct/, 6hflm )z migration of people toward the Earth’s equator, how would this affect the length of themtq,6lzc )hf/ day?

Can the diver of Fig. 8–29 do a somersault without havi3ee20g xvt9ixng any initial rotation when she leaves the be2xe vtix9 g03oard?

The moment of inertia of a rot hgsnag, yt;(t0q.;4zl 0c gsvating solid disk about an axis through its center 0,c4gy;h zs a;sqltg(g0 nt.vof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotajxnl 37.8g.udu p3x vwting stool holding a 2-kg mass in each outstretched hand. If yn8d p3lx3vuux .7 .wjgou suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same x h) 50vecar5jr (ejf8mass. However, one is hollow and the other is solid. Describe an experiment to determine wa hc5er8 r5ev0)(xfj jhich is which.

The angular velocity of a wheel rotating ovmh ju+z4 /d 490jbqvin 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, describei9 qvvj d/ub0h44mzj+ the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the e uzrwuf (-h.+ege9r*+(sgbup j6a ( vgdge of a large freely rotating turntable. What happens if you wue.su+gw-ag9* h( vruz(e (gfrjbp+6 alk toward the center?

A shortstop may leap intoktivjzua53u sg6t:wz3) -e w(6je / xa the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quug-u5:)zk z/w(6a6 jxei e 3at3 swtvjickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of consewsi73llssjgrb lxm- 59 +3+jo /aipr+rvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or b3 9jr jo5sila/+rx-+wsl+sl7gp3m imore ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radj5ui7 dnido1 vi:m; /nians: (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 beca/7bgd:emyd-xzus q7 kl3*lk3 use of an amazing coincidence. Calculate, using the informaty7sgmkq-*eld: u7dz3 x /3l kbion 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, 380,0000 e vf*6*lhs53waqx4g3qokx c km from Earth. The beam diverges at an anglec* * l4hw5kso6va3e3qf0x q xg $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is tu 6v/rkq9s8c*mhzcf)w +/wqnw rned off during operation, the blades slow to rest in 3.0 s. What is the an6)/wmqkcqsh98 +f n/vc*zrwwgular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If pxi22/qp g/srb*))b8mat 9, upoldahthe ball makes 15.0 revolutions, what is its diamx sb8dq)l 2*mptop 9uap ab /hrgi),2/eter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolut9:k(+aq3s1rtjv1d0v1 tqbbp 8 hctpb ions do the:cppv+b tr3q1dsk1ta10(t9b q8 vjh b wheels make?    $rev$

  (a) A grinding wheel 0.35/ze5 igr;3wwfy3 9+ zlhtp0u i m in diameter rotates at 2500 rpm. Calculate its angular veloc3p;w+0w ii5z9utgef h/zyr3 lity 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 on1 :vt rv4nvgm6y/h0+ 6htcecw e complete revolution in 4.0 s (Fig. 8–38). (ac6chv y6tmw 4 e+nr:h 0/vtv1g) What is the linear speed 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 Earth (a) yag s2pf5w q/ br:9*qgin its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s 03i7d6 xzkj5d/txq bipeed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from * ycd jd8gnm0;the axis of rotation is to experience an acceleration of 100,00d08jdcy m g;n*0 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1vjeh, mm,9x0-atug x 130 rpm to 280 rpm in 4.0 s. Determu,xm - 10jehagm,tx9vine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius o. :h28cvemo (f:fysb $R_1$ 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 sp .qv.,eh9+qxmdl4 gc nacecraft 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 thought of as a cylinder witml.q.v ch+x,94dnq egh 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,grq nt2fit pw f8iyv1g5edjw2./,(q0/a 3em z000 rpm in 220 s. Through how many revolutions did i( e,mq2if/gd2. yij01evtqgw/wr 5zn38f ptat turn in this time?    $rev$

  An automobile engine 8tp)fhq -z k-*n+zqs8vx k 8qxslows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stre,esl)v 4zedeh*0o)/ ztf4es c sses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tur4)l,e*so0t evzf c z/ehe4ds)n 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 fr4zsj/4 hx-sc zom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this 4c h zssz/jx-4time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns ngr)9sn- ab c,uik: n,1500 revoluts ungb-) knirn:,9ac ,ions 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 revo9( t ms r/fgry,7xdj+ulutions as the car reduces its speed uniformly from 95km/h tom y9( gjtrd7x f/r,+su 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 r99dk k 8inbl(:t/xli ji(q9q geduces its speed uniformly from 95km/h to 45km/h The tire nt xkl(ikil99(iqg9bj qd8:/s 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 when clav dcah .6)nvgd/m- )mimbing a hill. The pedals rot/)vn dag6vmm-ah.)cd ate 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 cm wide. What /x-mr4muo7 +bfy(diz is the magnitude of the torque if the force is exerted mf4(rmu-o7yxi/ d+bz
(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 shown in Fig. 8–39. Assumg-d4l ftd;9 yrm2uij1 e that a friction torqyltgjmd 4riu2f9- 1d;ue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached lwk:9r/p8r(h xq-6q+ ltauu t to the ends of 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 pktuq l :-+/ rrthwx8l9(aqu 6system.

  The bolts on the cylinder head cyk:5w;33hk7bxw,r h;oj is u of an engine require tightening to a torque of 38 xiujy357 crk; so :;bhw3hw,k$m \cdot N$ 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-pz (ef )i+sb(;puw7nekg sphere of radius 0.648 m when the axis of rotation is(); 7bezpw(ue+fp s in through its center.    $kg \cdot m^2$

  Calculate the moment of inertia ub z)0, j)a6usgczq 2kof a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined maj)2 , z subcz)0qu6kagss of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in )q6gtr84oqqpn 4 (1tis(lh oum-v8p4 t aglp6a horizontal circle of radius 1.2 m. Compp4go 1 6q(tphv8l)gira6(utlnst 4q48 q -alculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel ro(1tv2o:9c vr a668 j hameqwcjtating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N totch j8o: a2jear(6c69twv mq 1val.
(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 t2)kq(fyk 1ej of inertia of the array of point objects shown in Fig. 8–43 at2)( f1jk kqeybout
(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 atobvcb; ql*a1put( l (;pms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engw 0oupr,7*zdolzx/+;o5 xmhe ineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a m/e;lo7*x zrhuw p,m0d ooxz+5ass 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 8x4w-2c) nbpl0m 1dlow7h4 xxw.50 cm and a mass of 0.7w44d)n0 -b hw cpll1o2xxxwm 580 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 ba w.gz-k,)3jauy k7tsqgj. :h ct, 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 gp m6:b, rycur36j m:uis 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 opposi,j g3uyb:pmu 6m:r 6rcte 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 and is eventuall)v;;vt hxz0 sgy brought un)0txzs;h v ;vgiformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a h9dewb2c)h 2-lnamk, 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 action of thz/+dnz r.dn+ qe forearm, which rotates about thn+. rdz/z ndq+e elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a lont d,n1;y(eb1jlojcse;6 nn +vg thin rod, as shown in Fig. 8–46.n,j se 6 on( +etbv11;dyljnc;
(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 masses, lfu13+d l +yqtf;ca)j$m_1$ 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 r 63xb/oph8euc bap3611 vqkqug( vd e5qmg7 3full turns (revolutions) and releases1h3eq 6kmb 1u3e8 5qogcbxg37d(pr6 uqvp/va 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 inertimw:+npqo.f8f )a ua h8a 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 d/6wfou 2 rm g*)wxwrz3evelops 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. 1tho 2en6u6hv3 kg and radius 9.0 cm rolls without slipping down a lane atth 6nov1 hue62 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Etuj xflip h1+ s2;z6zdcr6p 0+arth with respect to the Sun as the sum of two t16jrc2 f;+pzdu6s zxlh i0p +terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mus(ljmi: iqi (0;rf- jach net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? j;flqa-0iij (s(m ir: Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withouv3kevx:hp ay3h)-q n;t sliqx)y3: v ph;vk3-eha npping 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. Ip/ he7)a gf(c0d4lyd st starts to fall and its lower end does not slip. What will be the speed of the upper syh)alp0c 4 fd7(de/gend 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 ball rotating on the end o) mcf ;8o.gt:97 xcnbl 0cqadjf a thin string in a circle of radius 1.10 m at an cjfax.:;moc d tb0cngl )9q78angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheeem5qzlvlw mc*zj++ x,qnf3; 6l of radius 18 cm when rotating atn emqvmzz *+ljx+;f5c3 w,lq6 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 rotat 4f:ozn6iqp. -,u csjfing at a rate of 1.3rev/s If he raises his arms 6o ji sfu,zcp. 4f-nq: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 ae9 x8q3hi)dl one shown in Fig. 8–29) can reduce her moment of inertia by a factor of abouth) 8il9qxdae3 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an in)kt20v qid grq77/tvaitial rate of 1.0 rev every 2.0 s to a final rate tqq/ vg)27i atdv70krof 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 vertic1dl *3puitk m6al axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center il 6k1pm *ut3dof the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.1s2f ptgr -g2i5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the E )hmss8w2z+o 7a x7mwsarth
(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 cylindri g)df.b o/2z54zdz6dvvdae r .cal disk of moment of inertia I is dropped onto an identical disk rotating dbd24/rz6dvf g).vz zad .oe5at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2jhpvd8th0 5h(g ) 9xph.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 rota;qk d:,cqfg;a/cr jwezj/ y*1ting merry-go-round platform of radius,jk wq:;gc/e yfd ;*/cqrzaj1 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 rotatin qi hh qa567ux;;5qcyqg freely with an angular velocity of 0.8yi;;ah5 75cuqhx6q qq $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing cz/8tsht kw30about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest intw/ h ks0ct3tz8eger)$\approx$    $rad/s$ (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 infbq72-hl b g;j 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 bb8b-n7pgf 4j$ 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 7 xv ne0c6 *ioy)xe3yzfreely without yxveey )60xnc oz*i37friction. 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 stk z8xraw,vj 4-ands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frk,vja4xw- rz 8ictionless 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 drf ./ci+(: s/bci-hvvoe r 6cthe end of the rope lying on the top edge of the spool. A person grabs the end of the rorio6c bc: ve f di+.v-rh(//scpe 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 faces the Earth. Detv+f)wi;y xl*g ermine the ratio of the Moon’s spin angular momentum (about its lw * vig;)yx+fown 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 rw6, ) pax3cd:lwqkt.west 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 ep eg(1fy48 pkl*4 ywtmpi3o-in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant a 3yt*y1g4ip o (p4e8 kfewlpm-ngular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of tp3l+ xyloa3xo 63(qfwtpkf6( 3+aj lwwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long6a 3lw3xjt++k(olf( wo6x qa3 3lppy f 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 sp66j lq t0td 1raizr-2feed 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 gre6aomfgnoybwq,s6 7x 730k vp 8at, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collfq p7,gymn 6skaobxwo 8036v7 apse 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-pollu/ y -5rxifwb*ftion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a y-ix5b*/ffrw 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 “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 an7:d;m5 kdjcsh $H_2O$ 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 onxey;9 x gnr/w4 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 fric l no4wd tb7hy*-m-pi88n sq(otion) 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, po7-whbnod 8 i-tq(4ynl *8msas shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It i 1() 2 i6v7d0ytw,+izetriiqigd( e mws standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will w26ieer+md(t1i,q w i(z)i7 g0t vdyiclimb 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 s/gwlgz9gn9y9o f fl9;+l: sa 1b trt0is making a turn with a radius The forces acting on the cyclist and cycle are the nor9olf tb ;1tn0af+ s:lsgr yl/9g z9gw9mal 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 i:;h(-gjcdstd q.d h;dccqp7 2q9qn6:vp s v-gnto a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required 7p; -qp hh2 ;s(: qd 6d:c.vdvqc9jdqtcsggn- 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 a1(p xiv unp+q4rms as thin rods, making reasonaqnv u +x4ip(1pble 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 her body.   

  You are designing a clutch assembly which consists of two cylindricpa(bs-ne e-lkn8 sj4 /al plates, of (8a/le-p4ss bn- kjen mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r k mxi)xf;ub)) rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point ofku)i xmfbx;) ) the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, buakff9wodqxca(5;z- m9k 04 b ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduce;ai p x/.h424spnvras d2v4bw s its speed uniformly from 90km/h to4dp.sibnr4 sa 42;a2 hx vvw/p 60km/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