A bicycle odometer (which measures distance traveled) is 2;qtuk2k:jm wattached near the wheel hub and is designed for 27-inch wheels. Wh;qj2mk2u wt: kat happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angul.qv1ofe fny3vwf:+ 2lar 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 tavyq :n wff3.vo 1+l2fengential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular 5l ssc3v(3qh lvelocity $\omega$ Explain.

Can a small force ever exerw zl1e6 p 5(s)tydlig ;.sufm(t a greater 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 behindf8qvtd0pa6i)c +s zw*v(hl ;r your head than when your arms are stretched out in front of you? A diagram may help you to answparqtc06i(*+ v8lfw)d z ;hvser this.

A 21-speed bicycle has seven spr*p * ;,lhrfd8hlgby/cockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pe,8y *dpgfc ;hl/lh* rbdal, 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 u5s ck 57zdt x(r;fv c*prgkr;d 2(ip6being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics;g tur 5(dck 6(fi 7c;2vrpxp*zr5ksd, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow be.:wp)nncg7 jw xid -w:am?

If the net force on a system is zero,5be/d cvdsj ; dx;bo)za2ad), is the net torque also zero? If the net torqjd))/z,d v;; o sx5bd2 aeadcbue on a system is zero, is the net force zero?

Two inclines have the same height but make differeftez f,k;.kw67b 5y ovnt angles with the horizontal. The same steel ball is rolled down each incline. On which incline will tw kv o,.5b 7e;6ykfzfthe speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One,j,so t4dp8 bcf8s jlz(wci *9 sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incliptszbj,o8(89*,ifd c wjlc s4 ne first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the sx bi2uix7izz8v .9u. same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottoi uxxv.9 u7sz.z ib8i2m? Which has the greater rotational KE?

We claim that momentu l(3lmiimmwr)8uy-l0, r4q svm and angular momentum are conserved. Yet most moving or rotating obj4ivyl) m,lru m-3silm8w0 r (qects eventually slow down and stop. Explain.

If there were a great migration of peorcft*c sjb k lb1y3 c6l-slp4 a00g9r:ple toward the Earth’s equator, how would this affect the length of the bc t39y-splcrr s06:14 cbkj* 0allgf day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatishlffgp l2,j1 1)j g g.jiz76;g)qlej2a)sdfon when she leaves s g;1lsj)6g)a gefqlpghd,f.) j2j1 fzji27lthe board?

The moment of inertia of a rotating solid disk about an a+y1pe y rf7 1iu*h5xckxis through its center of xye1iyhu c15p* k+fr7 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 rotating stool holding a 2-kg mass in each ouctfwa0 d5zr5 8tstretched wf5t580r ca dzhand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one (r,9a3ejm46 qh qdwvyis hollow and the6e,dqq9 r a jhymv3(4w other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel b 9 i lit-)xvr++shhc*w4q9lfrotating on a horizontal axle points west. In what direction is the linbxshift9h r- il*v+w9l4 +) cqear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a lacxec 1x qg5czox)3( s/rge freely rotating turntable. What happens)scc eqx1x3g/zc (5ox if you walk toward the center?

A shortstop may leap into the air to catch a ball and thbet jq2u:+bg/ row it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice2u q/g :j+btbe that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angulaf o*m i.p-j ey1x7jgy7r 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 .xjy-ofmyg 1j*7 7eip stable.

  Express the following angles in radians: (a)7q xhcyysa*gul(t 8 h5 iq,i(z.1t 7rj 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 xn6i c5 dr67vlo rru)0because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen u)rnl7rx 0 c5v d6roi6on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges aez w+ 3x;vnd1p 2icg7yt an angd ;iz3xn+1yev7cwg2p le $\theta$ (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 a9ynslf0(ty(5owq::-kszol y t a rate of 6500 rpm. When the motor is turned off duri(qs(wyyl-ts:5y: nof klo9z 0 ng 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 0d 1 0d0v/j jgsqo5rfnon a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is gjdj5rs0 d/v f1q00onits diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How ma a;rxqe/a,)hpb)t,t ow rkfu9jg8h4 +ny revolutions do the whea+qogxj,kt) /ab; r,p4 fu8th9)her w els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angu ; tngo.y7wic,lar velocity ;oti. n7 ,wgcyin $rad/s$ $\omega$ =    $rad/sec$
(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 revolz0jjyqq, eh1b *k. fx2ution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cefz 0yxqe .j,bjk 1*2hqnter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the Sws+yvt7 8 u 1kvzak5/kun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of ku;m s0om).acz i/(m ;meox7ga 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 fb1 if0fpc8 :acrom the axis of rotation is top:0 c1b8fcifa experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130xe8 6zgvue3j 4 rpm to 280 rpm in 4.0 sjg84z xeuv63 e. 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 radius (9ql.hcuk +mbr(bi+c $R_1$ 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 tjewud;/:w ( 3ryl 3lhput themselves into a slow rotation to distribuhew lrjt/w 3d(:3 ;lyute 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 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 uniforml m:uf-k8tz aa be -8umj3jwr9*-fz ub-y from rest to 15,000 rpm in 220 s. Through how many revolutions did it au-t8b:bjz 9r- 3ue ffazm-*wu8j-kmturn in this time?    $rev$

  An automobile engine slows down from 4500 rpm9er gvjp8hbv 6d89s6jo))8oezf n z-k 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 stresses of flying highspeed jets in a whirling “hut8wqx z; v:9xkman centrifuge,” which takes 1.0 min to turn through 20 complete revoluti;z 9wkxx: tqv8ons 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 from 240 rpkaol3z:9br lwk83m -q m to 360 rpm in 6.5 s. How far will a point on 839lr 3: mw-klq zboakthe 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 1 pwz6 taj8 /+b6auxe*34 2v-wzjsilok500 revolutions before it4xl j wk6bwtszajo3ei p6zv u*a/+2-8 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 reduces its spe y,jp.i7s rpat89 uyljh8a l-*ed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 aajrhlj9lup py*t7i,- 8y.8s 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 reduce6 3 gfg6 :nqb6 a(tys/:klouhus its speed uniformly from 95km/h to 45km/h The tires ha66(yqh3a:/ubfgo: 6ts l ugnkve 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 pux/ 2,/wmuixv gts all her weight on each pedal when climbing a hill. The pedals r/x2,vwm xig/uotate 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 w hr.ew)zl +y-17b dz 4,/hxd nyawuli)ide. What is the magnitude n+bl7rie,xd.l1ydwhy u /4za) w )h-zof 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 ax*p l 3-i)zi ucw95(k7sev awdsle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 lsi kw3vd)9wi5ep-7* ucs(za$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod wxtb1 pimlc3g+ t, z,v:hich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction o+lzxg ,cim3,bvt p:t1 f the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 5f3d is5mth9w38 w 5sh3dif9t5 m$m \cdot N$ 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 oq0l0 fmx/7mtd f a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its cent m/l7x 0qf0mdter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamr*2ux5du s1 wel0r h;ueter. The rim and tire have a combined rhe dr1*uu ul2 ws5;x0mass 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 tm8 jx;r52ek te9gmo* rotated in a horizontal circle of radius 1.2 m8xgm2 t*em95r;ektoj . 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 podutj k, s*54p liqxq2.tter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her p 2d*q,qtsx.5u4kl ijhands 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 dt1+; fky/tfr5jj4 mm4kmeo4 shown in Fig. 8–43 abouyt jm kr1o/f4fme 4mdtk+j4;5t
(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 ofcf +rv-l:sh 5v fk-8yl two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical,m cah0 en0o:yaov +d5 satellite spinning at the correct rate, engineers fire four tangential rockets as shown+ ovomnc0a dae 5h0:,y in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and asf8:+u-;sa k)vi ddo rtvjt0:xk 32ytrjlx6 . mass of 0.580 kg. xto:taj 2rytr3j v6dx ;lsi0u +svk:8d.k)-fCalculate
(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, accelerating it from r0 oppc my (qy);rj 8mbf r2x)d7*l-oenest 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 smu6-tk k /avwarsk 7:u4 (u+zr,er5ycxall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm int65k 4vzu rxaw-ar(uu ck+,eysk 7r :/ 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 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 z5z)hc 8y j).fjwba i5y57bih10,300 rpm is shut off and is eventually brought uniformly to resc8w hj57ay.bz5)iif5h) zjybt 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 z *owa2-ovs+eaccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thmc3ewyb2 -+v1yq2 tperown solely by the action of the forearm, which rotates about the elbow jo+ -21 tpvq3 wem2cbyyeint 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 long th,0.5/der/x vfuv h 3k;arpsziin rod, as shown in Fig. 8–46.i r v3pxred;/h,/vzu.5 f0ask
(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,st8 k(izbm34 g;pss*bcw iv1 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 hamegxwem8xq+3j*cus 4;+u.bj5a o-. vxlom a4zmer from rest within four full turns (revoma+4 e3; 8-z juqjlx xcmw xg*o.v+ae.b4os5u lutions) 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-tra80+uyt)q2 z,dz rdc; o-evuod o. moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine deviadu2e69smv4 kv3 3y helops 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 without slipping down l, otqqlh dfqp:fnscw/)6j0a 0i5k)0 a la as),0ncf d5w6q :llf)o0kqp qj0th/ine at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resb6 +pm:vb16z*c jc lxrpect to the Sun as the sum of two te:l 6c1 mvjb6*pczxr+brms,
(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 radiit,,j ,ehwtp4-tv:rnnbx, q;lm n j :*us of 7.50 m. How much net work is requimx,vt,:e 4-q tbn , i ,whjnltpr*;:jnred to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.d2/qi - et/mkk -aid x-tc, kc9*mtnt30 cm and mass 1.80 kg starts from rest and rolls without sl-dnmkx,-dati3ctc k /*qikt-/ me2t 9 ipping 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 starts to fall andmg2r5i nh0 k 9qt,0ddl its lower end does not slip. What will b90,kt qldgrd0m 5 h2ine the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a sc *w ci8:y;rme.ye(b ta) wuew7g.l+ 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an a+(: m )suecerw.eictb8w . yg7y;a*lwngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a j8 air8uv scnkg6elek+ (l*)f j69lpg(zpa /*2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 15k)*v(n8c 8zsklfp9rjglu+(e6 *a ilj6 /gaep00 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 )wi2ca(q-s9a h2sbv s at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases tv -hasbwsc qa2s29)(io 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) 1an0r9o+wg e ycan reduce her moment of inertia by a factor of about 3.5en0r+w9g1 oya 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 initiasul-vma8 u 2i2ekyu9 9l rate of 1.0 rvylkme28i2 uau 9 su-9ev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical yq79 -+qryptpaxis 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 t9y7+pp - yqqr3.1-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 a figxiqd 4/nsfy/9 ure 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 momentum of the Earsu7f7 4za,/h(gau r ruth
(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 momen0pod;9bdu j 3tkvt3 +kt of inertia I is dropped onto an identical disk rotating at andt +; k djp03t9kou3bvgular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atz hl0 l8h18a,4qwciry 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-gog512o uuzra4k-round platform of radius 3.0 m and moment of inertiork14 u u25azga 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 m9e4f7l9dc sc b.9low rotating freely with an angular velocity of 0l9c4os7wd9f. cme9 b l.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, losindk*e3 lwej2ts g. y55vg about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new ry5s vk 2g5*.wletd3ejotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excessc 34vlsue; fmbsq :i1b,)u v5d 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 j/43(s q 1aiskg/dztu$ 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 gm 8 7:qf5drw)wok:8/fb t8lwi:bri2eglaa( rotate freely without friction. T mfw walg8ri:bt )2k8faro 7w8:qigl (d:/e 5bhe moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry0q 2.vym.ox p6)6wbv m: czmlq-go-round turntableqlzombwpm.0v x2 6 m.6cq :v)y that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope 3pvon:3q7l9g6rilq g rolls on the ground with the end of the 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 rolls behind the person without slipping. What length of rope unwindsri :3pgln qlo79v3q6g from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth su a*7vad v q5a4,xv*prfch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (a 4vvpfav*7*,a rq5 xadbout its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate o,(k /zgjjpcwq :v5h8 cf 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 6 1e yo 70 ddr7wgpi1w3z6yy5c9tarwu 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 angular acceleration. Calculate the torque delivered by the63i7rdeyruw6y1 pw91oyw7t5 0da zg c motor.    $m \cdot N$

  (a) A yo-yo is made of twmw- 6jga-c j7do 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 th aj 7-6-jdwmgce 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 speed1 ;jy; myyc; 9leypg0c p92le.qdtb8h 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 withe4/*4v7s nxphmr2p eg 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, losing three-quarters of its mass in the process, what would /m4nhs 2epr4pe7*vxg 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 mt./.cel2 e -y+vnsefit 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 be a/-t.2 . e ls+yveenmcfble 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 adok8)uqc v**dy/9 )xgnk cyg 4 gyw71tn $H_2O$ 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 speel0, s32/rmixnzf i1fvd 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 freel/ny utu-7/cinyjsa 01s 69 t 8odet :guvo11yjy (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 oea 1-0uot9u:d s yjj/tiu/cvy1 ny6 gt187s nof 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 a9 32bje0d2vi lng 9dlis standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig.v2e9ab29 3 lng dd0jil 8–55). The step has height h, where h

  A bicyclist travelingjfuxy2)cu* p 7 ujgq7+ with speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are tgju2fcj ) uu q77p+*xyhe 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 begins 9vd3d+t c4j ufwhirling the rock in a nearly horizontal circle above his heau9+c d 4jv3dtfd, 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 the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, maki6tln:kc- 1 cuqng reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstre6cltu- qnk1:c tched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly q-61or;ye litrk r7: cwhich consists of two cylindrical plates, of massey r c16rkiqto r7l:;- $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 trackfzad gx) z9sxat-1n jl0+-w 1t of Fig. 8–58. What is the minimum value of the vertical height h that the marble musdjzlw1n) + 1 ftaxz-ga x-9t0st 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 drdro7;3cp 1y6hw0ujw o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rgh. z:atc9x2fd (rwu)evolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tir(:xz uhc ta wdg.2fr9)es 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