A bicycle odometer (which measures distance trah :p g8mc)*dgqvdi) dn0gs1egz645 jxveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use 1 gjg:x* qdv5mgs z) p6cn04ihedg)d8 it on a bicycle with 24-inch wheels?

Suppose a disk rotates r+2 r(uce(phxd:j4ppt3k7l s at constant angular velocity. Does a point on the rim have radial and/or2sexr(j7 (k 3l 4chut:rp+p pd 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 by a single value of the angular velocity v g*r q(d 6h*wd 9k113eieaccz$\omega$ Explain.

Can a small force ever exert a gp/19ca7iot(.x dl.8gyfbvtr e vj u5 8reater 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 ov a:h)/ syru3hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thi/r vouah3:s) ys.

A 21-speed bicycle has seven sprockets at the rear wheel and three attc-5v0qvvo ms9 ej1i 8 the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large reare81-t v95m vov cjs0qi 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 slender lowe:rv i8o.gzh:suu)rl1r legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis 1hi8uo )svuz :rr.g: lof rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a loh rpuo.5-ln3rng, narrow beam?

If the net force on jtv. svay vbr5jrt30; e /ob2(a system is zero, is the net torque also zero? If the net torque on a sys2 (ea5;.vtbj3j/vvrt or 0ysbtem is zero, is the net force zero?

Two inclines have the same heigljf wt nf l*4t7 9my: oh3vm;fqw-;9ieht but make different angles with the horizontal. The same steel ball is roqf9nvo-3;m4ly7 : ifww tme9fh*jlt ;lled 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 incline. O hgdkk)-a+tog )ykqr .b)6j /hne sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fi ao+q))dj6.k/-hrkk )tbyhgg rst? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sta mg:)9hjq i:lhrt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Whicglq)h im9hj::h has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving o9z+i ;uo9;ty qymhtb qb; h9qb :+-6 xdia9easr rotating objects eventually slow qh;9s x;ue +69q+qtdb io:9 az ibh9ybya-tm;down and stop. Explain.

If there were a great migration of peopl av-iw7ap(cn8mrz 7h6e toward the Earth’s equator, how would this aff8cr6vnz 7(7m ahw-pi aect the length of the day?

Can the diver of Fig. 8–29 do a somersaulttr/n;jds :4b +tbfl d6 without having any initial rotation when she leaves the boarj4 t :nsbt6 /+df;dlbrd?

The moment of inertia of a rotating solid disk u 8 r2kwfjzoo0jn*z.: about an axis through its center ofj 0ouo .8*zrfkwnj:2 z 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 *v ac0xcpbbc9. h1jm7u: l/d trotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wi9ab*du . mhlc /v7jc c:1tp0bxll your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and y;pxg ecz12n )gvw,:pthe other is solid. Describe an experiment to determine which )yp,n xvz g;pweg :1c2is which.

The angular velocity of a wheel rotating on a horizontal axle points west. +fvkhc)s v ph8;5/rqfIn what direction is the linear velocity of a point on the /s+8r hvhc qf;)pf 5kvtop 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 rotating turntablf qh f34mtr)ayb;8y-h,h 7x afe. What ham -3 84x,; )bhtf a7yrfhafhqyppens if you walk toward the center?

A shortstop may leap into the air ty 4and6-hpf-xo catch a ball and throw it quickly. As he throws the ball, the upper-xhndpy-4 af6 part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of aoqr/3s t, qsocir+m5 ) )t:sgjngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can ojqscqt/3 r:5ts i) )roos ,+gmperate to keep the helicopter stable.

  Express the following ae xl3 j8m)bgt/ngles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calq .g3f8n5w*iexy .d22q hvqdp culate, using the information inside the Front Cover, the angula2. g5fqwdvpn2x ideq.y8q * h3r diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km mbl;ideb/.6efr x r9 /from Earth. The beam diverges at an a b/d;ef.9l r6mi reb/xngle $\theta$ (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 i nl:9g :pbn:gms turned off during opggn plb9m:n:: eration, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chil ja;8.,jytpco:+op yhd. If the ball makes 15.0; ,8oh jo .:pjpyya+tc revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in dihykis k .e j48u6vtq),ameter travels 8.0 km. How many revolutions do the wheels m .kkheu8qjy,is4 v6t)ake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its an*ekyvzjnf 5(w-. v)yp gular velocitypw-y 5vf(e n* j.y)kvz in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fih8t(k cowa s(8i8wck8g. 8–38). (a) What is t8cc(i8ks a(w howt8k 8he 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 Es+y iymalukn;qy+*h o3 rr5 3.arth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poir+hkts */pxo +bn72dj nt
(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) mustia9sir ow8ij(+4s9 kn a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 10s9+snkj ioiawi84r 9( 0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel at9n+gi -dek 3kp9i ph5ccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Ddikh- 395i nppk et9g+etermine
(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 radiusl7/ vjo/k gt1 vd+pzvlr,kb13 /me 5bw $R_1$ 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 snvc hoe;1..e ipn 6rd-pacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of thev1.ei; pc oh.rd6 e-nnir 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 uniformly from rest to 15,000 r+,c0dpp0w5 c t,nc(axxjh 6ns pm in 220 s. Through how many revolutions d tp jxn5c0a0s+dcpnh6, xw(,cid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate c8gq0o(r9gbfb sv)od6the(u1. 2h y a
(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 jet 3gl;nmc*cjmw .dit*+7tp-cg s in a whirling “human centrif3c -m pg+tn*icc lgd.j7*mwt; uge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240do . px02xoyma c2i2,t rpm to 360 rpm in 6.5 s. How far will a point on the edge of txx y0 ,ipco2t22o.d amhe wheel have traveled in this time?    m

  A cooling fan is turned off when it is running a 24 v c5lj8s 3+qc*reuc(gemgzt 850rev/min It turns 1500 revolutions before g(5rec* j 4cq u2vlze3c g8ms+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 revorsxh :r ha.2c4 b7uda9lutions as the car reduces its speed uniformly from 95km/h to 45km/h Therrs :a.cah92ubxd7 4h 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 revolutiosh*y1./v.obqg f:)r6rgd q *s p/w oidns as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.r*.q w1 /pf:s/6hro od *qdi)gsyvbg.
(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+-h , tvlm6rmw weight on each pedal when climbing a hill. The pedals rotate in a circle of + v m-mw,6tlrhradius 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 h j vb4dn87z8tys/gy *wide. What is the magnitude of the torque if the force vygh ny/bd zs* j84t87is 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 wheel4k.3go+ i s,i:rxa ytp shown in Fig. 8–39. Assume th: t4gso a i,i.y3x+krpat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod which s o:m;,ajx0ijf.z7 kz pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Casifjj ,xkz :oz07.;m alculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenin5z z;lih2mk4 og to a torque of 38 kmz25 holi ;4z$m \cdot N$ 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 spheri:k +9 q3wyrube of radius 0.648 m when the axis of 39u:+irwb yk qrotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in d j uys.a4lqc95iameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why.4s lu 5aqjc9y?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hor-7uy 4y,z uxflizontal circle of ra-7yy ,ul4fu zxdius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s uydzm2bk.m1*t 8tz( owheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.mm 8ot t bu(yzd2kz*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 jpmyp s3, tw5 rd(59zninertia of the array of point objects shown in Fig. 8–43 a (sry5w,d5p3n9mtzj p bout
(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 (b(fif+zcgv)dtl 9c6whose 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 satellls ck6s rbz7(6ite spinning at the correct rate, engineers fire four tangential rockets 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 tkl6s(z7c b6rs o 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 eb d;uhx/ve- .uqj+ c78.50 cm and a mass of 0.580 kg. Calculatuq/v;eu- xj ed.+7bche
(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, accelmcg9ca90q6-h erv *ua68sc ogerating 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 tangena q.6w.vift j e0duknx3jrk.w693uq 8tially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radi.w 68.kvqj uk3j9xtuie q 6rwa 0n3fd.us 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 10,300 rpm is shut off and is3 go)x j-4eck8dgyxl-c p4 z+j eventually brought uniformly to restx-3o4 jgcx)kj4cde8lp - gzy+ 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 3.6-kg bad x9:c(/eqxr(w ls)t ipbz/u.ll 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 the forearm, ss8y( viim 7nc8l/v(qwhich rotates a7(/vnmics8l iq v8y(sbout the 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 long thin rod, as shown iao4sdqo-b0u 3 j9(ce xn Fig. 8–4xc4e so3j9(ao 0bd-uq6.
(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 mass.(e m(h6dffbe es, $m_1$ 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 fo3fvqx/h ho+ mibovp1l:9 *tq: ur full turns (revolutions) and releases it at a speed of 28h1hmblof3p/ +vxov9qq i *::t $m/s$ 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 inertia of 3+73bds8izof;/m y 2 fxooa; 0 obhjyv$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a trs )iuvb-d 1/8.w mhbu) f1b3ez- rhdkorque 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 do3bsy j(d(rw/1hgrw7 fwn a lane1 rgr/wds 7hwy(jfb(3 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic8;cpnmoxz-*s q6tn/c energy of the Earth with respect to the Sun as the sum of two terms,mcxn8t6 / coqsp-n;*z
(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 xq;f ;q sc-4f4ss ket71640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a ;c4x ssqf; -47sktqf erotation 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 and rolls withoupc9ds9j)uxj iyj 3 86ot si6xj)p3o s9d8 9jyucj lipping 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 balan969cclqis,b.p+ swi //fl jj gced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed ,c bls cs+ljpq //.99ji6iwgfof the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentu7u e2ebhm */ey3msr9 bm 1t xpvegl2n2 :+5dvum of a 0.210-kg ball rotating on the end of a thin string s +td r2 3*/m9n7p1xlh yvu bmuv:e2eemg52bein a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular xhqdyl + ea)l-39ow*pmomentum of a 2.8-kg uniform cylindrical grinding wheel of radiusyq) o*ph d -lex9wl+3a 18 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 avboxfd -jo+-z4azl)4o ; zn ;st a rate of 1.3rev/s If he raises his arms to bzo;oo)x;sv ldf+-zanz44- ja horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig.c*vm;w0dn u4 l 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotation cu *dm4n;w0lvs 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 e8a )*hdcva3s, g jx.eher spin rotation rate from an initial rate of 1.0 rev every 2.0 shs*gjce,vedx3 ). a 8a 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 rota4 drw*03dtulwn kt*l ;ting around a vertical 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 of the rotating wheel. What is the freqd*d tl ;w4t30lnk *rwuuency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spicu1 -hb+uw8/y5qyd8 pg5as(.nfd nrinning 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 momen7 l8o;vb6*x s grw.sbptum 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 cylindri+cp25zg5o*ehbeegh 2 cal disk of moment of inertia I is dropped onto an identical disk rotating at angular speedozb 5*+h e52p cghge2e $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4dp.v; *nf zqri0h4 -yr4 l0xwg $rev/s$ 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 83 e(;c:yb fjwrsj0e5.r/ jmy ze ur5lrotating merry-go-round platform of radius 3.08/c5m(ejjbr;: elfr3w ryyu .0je5sz 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 /,i rjcs4gr u4rotating freely with an angular velocity of 0/s ur,4c4i gjr.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 collapu:l27dqdjz4 w:i9f m nses into a white dwarf, losing about half its mass in the process, and niw:du7 j2q :dmz9l4f 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 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 inl ecg:/ ;dzoo* 1(rplm 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 sjwt2mt,jk+;5 a py8e$ 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, initild4e.ad zflr*: xp-o(ally at rest, that can rotate freely without friction. The moment of inertia of the person plus the platforzll.od:*xrp d 4f(ae- m 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 on5 ubuo2df xd0ajr- 1jr(j0*yf a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and 0ujyo2an*r5djb(j 0x1r u-fdhas 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 of2ai eq+e e0-xf;u laggl0-wv0 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 unwinds from the spool? How far does the spo 00al;euv +g eq0--ag2xie wlfol’s center of mass move?

  The Moon orbits the Earth such that the same side always faces tt, u8.vh yb6kxhe Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Mo .h68vbtuxk y,on as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratesem e0 l2/s/ngr from 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 shape of a c ;qzv0yg/lv 5cl9g/ puniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor. 9g z/lgqvcvpl;0/ 5cy   $m \cdot N$

  (a) A yo-yo is made of two sv s- ioqoiqc0do6v96 ucy- .;hx5f5gtolid 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 y9cicgq 55.i6of6;toqo yv- -hv 0xsduo-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 a:exb,.gcpp 514v,pekw. y/ o4jhzeeo 7har )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 ofod *vt5;0oep- byc6ru our Sun, but 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, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the stp 5ovucyet -b*r;d60o ar 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 ab;fo6cl ux ildt8f;/3utomobile is for it to use energy stored in a heavy utl 6fx;/d;i8bo3 lcfrotating 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 illustratfd36**r s/vzx6dlv vf es 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) isx8iwzp ub3n z9*6pbhqqf/y.1 rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot frhm7 aoe2yql5)e 6 v+vomo 56yweely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizont5 h6lovyw+)5ovem7a oq6eym 2ally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floo:f1gimma3 eazq r6xp4+ , 4nztr, and we want to exert a horizontal force F at its axle so that it will climb a step against which it r6aax ginem34zmrt 1+q p:z f4,ests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flq:oqlrq19 ih5at road is making a turn with a radius The forces acting on the cyclist and cycle are the normal foq qrqi1l 9oh:5rce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 l3l 4cngn;dg4ci9 pmo8 ength 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 gicldn8 44gn9o3p cm;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 js;93 o zjy4weher arms as thin rods, making reasonable estimates for the dimej4yj;zso39 we nsions. 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 assemblyam 2-ab7*h sjf which consists of two cylindrical plates, of mass7asabhm*j-f2 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ahor0 z.bk(jk0 y7,/fcvhb7 tuj1ispz 3b4q ) vnd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that th bs03cjvk0 )otb(j1 y.ru7,4 qizzvhhkp 7/fb e marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nojyu .ue; (bm;ct assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces i;e5zz+ v ;xbhi b0+wjtts speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eavh;xi e+0b;+j5zztwbch 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