A bicycle odometer (which measures distanct.yeu.nh9aa-t mng. 5d.ci n1e traveled) is attached near the wheel hub c1 an hin.mt.u.n5ygeadt .-9and 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*u.cu.mlrz / lehz75 r velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which czru5.cl7eh muz ./*rlases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the an d75i2qqtf gg)gular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a la-p -socij0 /avrger 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 behgn/b m5hfg,9an , . l0td(pyi5yup)gz++t aypind your head than when your arms are stretched out in front of you? A diagram may help you to answer tt z5.(gt+nd9,l 0pyb5)upihyyfggaam/n+ p ,his.

A 21-speed bicycle has seven sprockets at the re,w j9txa5vn)o7.f(ng3 pn m h1 lfcbe+ar wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or f+xbe7p,)nl hw5 gna. n fcmtv9(1o3 ja large front sprocket? Why?

Mammals that depend on being able to run fast have slender 1fnr ;e8vub(i lower legs with flesh and muscle concentrated high, close tob81(eivf nu;r the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope wal:rj1zvp,jf0: e:v:ey sk a9r ok(jov( kers (Fig. 8–35) carry a long, narrow beam?

If the net force on a syso- t knt *+i;pzq/t ygm2ef:p2;+x xyttem is zero, is the net torque also zero? If the net torque on a sysqxyptt-tng +mke2: o;fz/ *xpt2y; +i tem is zero, is the net force zero?

Two inclines have the same height but make different angles with./bix6dsavpl3 p *9v j the horizontal. The sam3 x .6ldapbvvps *i9j/e steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inh3 *9tnzzv2, skhlkh1cline. One sphere has twice the radius and twice thevzs*kh 39hz n h,1tk2l 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 tho k) p2klq jct,p**u,be same radius and the same mass. They start from rest at the top of an incline.pk,*2) bj,ocp ulqtk * 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 :rz4cf nimy43e:mv a.angular momentum are conserved. Yet most moving or rotating objects eventually slow down and sto fmeycn3a4:v m4zr:.ip. Explain.

If there were a great migration of people toward the Eanz,8c1dmd co+rth’s equator, how would this affect the length of t8 n1zd+do ,mcche day?

Can the diver of Fig. 8–29 do a somersault without her;)wox0e :5tq 0aaj having any initial rotation when she leaves the board eh:a0rt0oxeq5 ;j w)a?

The moment of inertia of a rotating solid disk about an axis through its cenrv2l58y rgz2 v p;1t-cdwe, pater of mass isv1e vd;5w,ptapr2y8c-z r2 lg $\frac{1}{2}WR^2$ (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 az)ez4 6 jh,p-mcp1tx j 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or sp zxzpmcj-6 ,41 t)ehjtay the same? Explain.

Two spheres look identical and have the same mass. However, onehba*ocn 4+ tyq/p7j 9e is hollow and the other is solid. Describe an experiment7pcbje9 o*/ t4aynh+ q to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In 7eo p)j0nk2*kjctfcs qflpo* 4f7i46eqvz53 what direction is the linear velocity of a point on the jckqsfj6503*pt)4 f74*vk el f2 7zicoeonqp 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 standing on the edge of a large freely rotati8e-)h1mu3hec h3v usf/ :cncd ng turntable. What happenm-he3)hn/ufd c8u ch3 :1vec ss if you walk toward the center?

A shortstop may leap +4p yhi4age+y into 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 quickly you will notice that his hips a +4+ga yiyeph4nd legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of coa2z5qt0u,7xdod znc,2uk 5 q4zsr) winservation of angular momentum, discuss why a helicopter must have more 57w2,qaodzdc0tq z) s5 rkz24uiu,nx than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles ixdg. 9l8l. 8kpt u2hsnbn 4*bi0)nxc on 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 ancamt0n f0;m:1 jv s)rh amazing coincidence. Calculate, using the information inside the Front Cover, the anm: h0ran c;s t)vj1f0mgular 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, bmup*pq. l :9kj-ja :x380,000 km from Earth. The beam diverges at an angljx:k*p:mp au -bq.lj9e $\theta$ (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 civ.ptg9,n kn58 e kj+k7, hxjthe motor is turned ofk.gnkn,7v k+ixh5jj8c et ,9pf 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 le5x(qhygmqmp8m ;v3lw * l)dl0vel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diametelwmmvdlm8*l)y p;3( gq0 h 5xqr?    m

  A bicycle with tires 68 cgc+(kwcf3uaohc+m88ho5 sg1 m in diameter travels 8.0 km. How many revolutions do the wheelsw a5h81 f+ouskmccg(8oc +g 3h make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anguljni9- pso8oe0y ixl96 ar veny 6xs-9 8e0j9plooiilocity 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 clz3sz1y1r n 4pomplete revolution in 4.0 s (Fig. 8–38). (a) What is the linln31y1 4zp rszear 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 velo/ 1hib: anzmacf.)wqd ss3k44city of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 8akwa6 gx1 2ra8gpg0 jof 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 cen--zmh7 9p:mel5 zq xu/docw3etrifuge rotate if a particle 7.0 cm from the axis of rotation is to experie-5dzmw -q7lx/e 3zouem9hp: cnce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itsg. c(t3qodq 3u center from 130 rpm to 280 rpm in 4.0 s. Degd3o .qqu t(c3termine
(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 radiuvzv pfcc16( i(6gn9y.(blypvs $R_1$ 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 spacecraft put themse 67hae*gp0z dq h/:gzplves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, ad*06qp: hgze7 phz/g they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates lxbyh;m2rz;ljbj*72hm1 l1 z uniformly from rest to 15,000 rpm in 220 s. Through how many revolut2 z 2by*l1hrjxzm1 ;7lhl ;bjmions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcu dtb fg5 m/xdykfqb4c-h4mzy2. )v38o late
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “cf1.p. hu/ zgqhuman centrifuge,” which takes 1.0 min to turn through 20 complete rev1z.h p/ gfcqu.olutions 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 accelerate jexbl-56lxwl ; ys14ps uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have-16bj ; 45lw pslxyexl traveled in this time?    m

  A cooling fan is turned off r4l*2(2q6 uvixy43e3m ngkxilumc8o when it is running at 850rev/min It turns 1500 revolutions before it comes to a stoulx2 yn4 qi*8ol( e3 mi3vr4g2 u6mxckp.
(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 revolutionsvqxcuexvs+0 *1-a2a d as the car reduces its speed uniformly from 95km/h toxca*uea 1+2sxdq -v0v 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 ma5f e;bx 6i1jzcke 65 revolutions as the car reduces its speed uniformly fre15x6fz;jbi com 95km/h 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

  A 55-kg person riding a bikc+knr2 xjltk cd21t(m/+ mc7 ze puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of r 2c jcdtrl1cmmn+/tk2 (x k+z7adius 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 xp 8u- sl nyc1*:lv1n+qtfdl6wide. What is the magnitude ofnq61 cxt8+ d-pf*l:ls u1ylvn 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 the axle of the wheel shown in Fig. 8–39. Assume g r)1si9az se8that a frictige8 r is1)a9szon torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacheh oujk6ct-msflziz19yc:s y* 2 (6.n qd to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position 9:k6h*1fiqs6 mz( uycnzsj. 2y oc-lt and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 38 4at/,zap r0xqp4ra 0at zxq/, $m \cdot N$ 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 ks-b ea*1ptc./ku 0jd sphere of radius 0.648 m when the axis of rotation is through itpcd/ j 01e* t.uk-skabs center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rrk4 rj(k-e)+nu7jb h8z z b2knim ah)2 j nbz +k-r(bkr47uz ne8kjnd tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the env.)zig -n3s; oym+ /71t2ws gsrtpbx n2o+mzld of a thin, light rod is rotated in a horizontal circle of radius sw3z;psmi2-x g /t1. 7n y+st olonb)gr2v+zm1.2 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 potterrwd(q h;:qj +b z vxbcb3 s6sr-.;g;nj’s wheel rotating at constant angular speed (Fig-;zjr.s;rhg xcq 6;b3vj+ snb:bd q(w. 8–42). 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 inx1syij * va;dx 2z.w0fertia of the array of point objects shown in Fig. 8–43 abouts.zj* fvx 0;1dw a2yxi
(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 total mass is8 k;o*is0bedsh6wf 7 j $5.3 \times10^{ -26}$ 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 ratepifadvpfu fe/-9c66d 1 5f +oa, engineers fire four tangential roc6 - d+p dfu6vapc/ofe51f afi9kets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a rad8x.d6o e/+as)kz moudius of 8.50 cm and a mass of 0.580 kg. Calcul xom.oaed)6/sk u +d8zate
(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, acceleratil*vtbv1k9/ily;8x px 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 tangentially on a smzj237+ta cv b)tox81p w2 avwkall 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 2xbvwpv j) 31o+7 82ck2a ztawt.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off an zicevk90i a27d is eventually brought uniformly to reseva02k 9iz7 ict 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 ap; s.d qeqiq2 2.6oqovccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball ia8x1ey bjeb6+xm8ow j 89xf7l s 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 balmebwfaylo6 8 x8b17x9+x e8jjl is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown incyek;gl7 *i/b Fig. 8–46.c7kgiy /lb*e;
(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 *onizznre+t7qx lc2 8a- p3.ltwo 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 tur59djzwulyto 5m.lfa6-oc -8s ns (revolutions) and releases itmlydca85fuw.o9 zl-s- toj65 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 inef(z xo7 ru)ry.rtia 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 t hd54l/7nv qd0 uug;znorque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping do 3wx(v /hx:;t)lkudsgtp(l1 9f0b rqnwn a lane /xpq0u( xslt;k vbh3g r1tl d( f)9wn:at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun ya th085-e c)k7fz k/cd: erafesce0:as the sum of twoe 0c eh e7s)- kk:a/e:5c8rzfay0tfdc 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 apyc3h qiii9rl ,i2n au/3z ,6vnd a radius of 7.50 m. How much net work is required to accelerate it from rest rcu2i9i, ,i/33 qnlyv6p ihazto a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest a0 /9(obke9ol-rrgz s gx+apt -nd rolls without slipping down a 30.0 ge(lrkb-tro0xs+/zoa - p9g9 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts di. af t5utc51to 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 cct 5.iad 5fut1onservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the ens x+59sgdca3rw 4 ht7xd of a thin string in a circle of radius 1.10 c9gxah + 5sxtr4w37sd m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyli2u0,t2 pf.z zwz0hg jwi q,fx4ndrical grinding wheel of radius f zuf 0w0zh,j2t.2 wx,g4i pqz18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating )puabr,sj2u )at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, thea b)usrp),u2j 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) can reduce her momw9m:ug yzc-/ g3v;debo p6m1+jui6lb ent of inertia by a factor of about 3.5 when changing from the straight position to the t;b3z pcew+iy 9lgbmjuu /1d o6mvg:6-uck 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 incre:blgk )bjb ji v3y62d0ase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s t)b0ijy b 6l:kbgd23 vjo 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 freyz xtx-ujp w9 z((u,p8quency 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 frequency ou jy,9ux8w(t x(zppz- f the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular moz5p32025;*d0 :o5hx q jwf fct:xbfpllivmf dmentum of 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 angular mom hrwd :99sqygl04/bvhiv5rts5 j/kl )entum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dkb7x8kn*q4nk5 trg+;ffwlk ok- ::mlid- gi *ropped onto an identicalk;5 qkrg8k: io-l+4wk*fbng-m*7 tdkf:x nil disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 5nm,b+chqa p, $rev/s$ 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 tyn65xyio n04 :6mkinwhe center of a rotating merry-go-round platform of ry xwi4n0mi6 :n5yo6nkadius 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-roxru+)4 yq-hmnund is rotating freely with an angular velocity of 0-uh)mnq 4+xy r.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half4s(8m 9 g;5msjv f w(wc6bhhtp 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 neajs5;h 6 h(tw(g c fwp8b4s9mmvrest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excesz +o7(yo /eaj /n-f9x ,egceehs 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 *:w ifrid(;pwvaw1x 4 $ 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, iy:y ,w+y.excynitially at rest, that can rotate freely without friction. The momentyy ,x+ey:c.y w 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 stanyqcdj*ln522n7 ld 7ctx55tq 5yeyf . hds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on f.yl*yye2hld 5 jtqnqc7 72 555cdt nxfrictionless 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 the tje57 btfs1bcg j+;)e rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool r 57tbt;bj 1)jcfse+ge olls 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 Eart jhzu0ook2(yg4qm2:akh8z n; h. Determine the ratio of the Moon’s spinmq24az:kk2 oun; yj g0z(o8hh 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 fr9u3q7g r+aejwdb:xm pbk4 64vom rest 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 sfm(j7tiz 3/oj;sq *wn hape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleni* z/ j7(ftmo3;jsw qration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eachy dn)v n/3mx .8scij5v of mass 0.050 kg and di3x/vis j. nv)5dmcy8n ameter 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 the angular speed of the rear w6*cbe g n9n+ijheel ($\omega_R$) 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 qrh*/j*ycb) bigxk/ r *j*p b.with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km,.*b*q/y/jr r*x)cgkbbi hp j* 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 wt6;yv;*w6v xu en nf yul57g.stored in avnl7 f vw xuy*6w. 6ny;tu5ge; 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 “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 illustrat7qgaswmmzqc6o;.q:9f *b:nz h -7 zsfes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at )gggk(tv (txus0jlde5 et+73 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 frkgi/ bp:dh:kqqe8 j0)eely (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) th kkqd0h/q::i) 8ej pbge angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, an2o)0 w.hscz ts o05voh41xhadd we want to exert a horizontal force F at its axle so that it will climb a step against ho02oac hss)w4zv50 d1 .txohwhich it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with wfq(nbkc5: 6 4oooeq3qr. n(sspeed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are thq sw4qco oekr5qb(.fon3n(: 6e normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begin 2ao)9o-m)ho,k*lza25rn bfz, l pjsks whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does ths lj bkrf 2)*l9zpn -a,hz)m,a5oook2 e torque come from?    $m \cdot N$

  Model a figure skater’s body as a soqi.zmmsw0 54 olid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the a0. mm4iw qosz5ngular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists o r1o(iy9dl0x ef two cylindrical plates, of xryd (91l0 eiomass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rok bc)8aos760kf8m 1fca(md/ei )agch lls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop ic6scmofe /d8(1ck07 mfh8ak)ba ia g)f it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu *1edbo ghq49/lmgw1 eb g0k/ twl9w5sme $r\ll R$ h =    (R-r)

  The tires of a car makel*zli /kjn-l oi 3.rblox:+3w 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceler+ lrwl. : ionl/k*3x-jb iolz3ation 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