A bicycle odometer (which measures distance traveled) is attached near teh 9d wpw9h4*p x4k+pf)ja;vmhe wheel hub and is designed for 27-inch wheels. What ha)w p ha4vwph 4*k;pxdf9jme +9ppens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant anlds -hu*5+o3ngidg n9wiow0 n k69 l8pgular 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 cases would the magnitude of either component of linear acce od6i-08w3hlu gk99 o snnpw*+dg lin5leration change?

Could a nonrigid body be described by a single value of the angular va18u/hgzsm 6y elocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explaxa3 dy3wq agpygc60l 3lm)9m3in.

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 diffic:7 4(da l/wysxv3v ycjult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may helpd(y:x ja /sy34cl7 wvv you to answer this.

A 21-speed bicycle has seven sprockets a egtds8 *g3o*pt the rear wheel and three at the pedal cranks. In which gear is it h*p*8d 3oets ggarder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowere ulync)7e/2)ef v t0 rphg/2r legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis e ufet)2phc0/n gvry7r2/le) of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bew52 qpc00.gyhesnswh7vxmqe)s 6 62 oam?

If the net force on a system is zero, is the net torque also zero? If the net tuncj( le(pn eqp7y8w3 /up d:6orque on a system is zero, ip epn(/u6jlu:qc e 7py83 (wdns the net force zero?

Two inclines have the same height but make different angles with td-2er8z fnup520 orjz he horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? r jp8o5ud0ez2f - rzn2Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One r2fwsb ):nc0 fa b1e/rsphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the gr)cfb r: rwe0/s2bf1n aeater 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. Thn1. yzf cw3zl(*bkij7ey 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 ky7 jzil3k. znb1 (f*wcinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movi3f18 : a *,guq mwzt7gswq5ebtng or rotating objects eventually slow down andwq8 s7b:*mufwq153 zatte,gg stop. Explain.

If there were a great migration.h4zi u ex+m*4z v3ahod19gs x*idzh6uk :;tf of people toward the Earth’s equator, how would this affect td*hk ztvsf4 ui;gdx i+1 9xm3a. uh6z*z4o:h ehe length of the day?

Can the diver of Fig. 8–29 do a somersault without havingkn*mf fcsb 211 any initial rotation when she2c1fmk1b* sf n leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centerl4 /cv-zcbe ibs6nm,vqf+ k+4 of masiqbne4+ -v/sfvb km+6cz ,cl4s 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 hovyp +4y0zn 4) xevxj18h.xzholding a 2-kg mass in each outstretcpx zvx) y4x0h+.8v e z1hyo4jnhed hand. 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 mj 48csh2 (psc4t-geg p fb)2tblmiql5, xi-j7ass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.feip4t22 bs-7jgx84-) ltl ig(qsh cp c,jm b5

The angular velocity of awiyy6-m*+ pwzamss n0,) ( rzv wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the w,yrpmw mna*-zw)zi0 s+v6 (syheel? 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 freeh2f7rp+whh m6s n 7q,gly rotating turntable. What happens if you7q w2rh6s,mn+p ghf h7 walk toward the center?

A shortstop may leap into the air to catch a bag,. wjxz5o-hi h1-.j*ds lkj all and throw it quickly. As he throws the ball, the upper part .*dj jx lgj 5,1ka -.o-hhszwiof 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 conservat ipfpmsw.yc. b x)j nn8omwyl76* m:ks)/xw*-ion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or xm*m :i*6o)n.s./ wln8j7b xmp kwwfysp-c)ymore ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in ra1u,cyovq.0p v9( yj bqdians: (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 becausezfu2mc-l x :2+e5bcip of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular dcl: 2m +-2ixep zc5fbuiameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diver*q *.whe 95ohhl ngye2ges at an angle 5.l*yq wh *g9ehoeh 2n$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender ro5j9xpa /r8vn htate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerationa p8 rv9j/hnx5 as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If thezfdq*io;;zl/vm* :sbj-g t; y ball makes 15.0 revolutions, what is its: zg;jmifld* yzo*qt ;;b /vs- diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutio 0z+ 8xadu)3a/jkwl qjezf)p4ns do th +/ af keuaq)8)jw43jlxd0zpze wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cai. -08ztwxpslc.0 q,m gk hzz(lculate its angular vep0ihzs(cz k.80lm,.q-g txzwlocity 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 .x0ma)alfx5l in 4.0 s (Fig. 8–38). (a) What is the xma .l05x)afllinear 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 angulartmt1 5fe5 *n7fgbf9es velocity 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 slzhqn *9wj5q 1peed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm f)b228fmpzg/;uvv i aurom the axis of rotation is to experv/g2)2iub uz pvm; 8afience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformgp yh 19yw 4wz3bls +n1se(gx:ly about its center from 130 rpm to 280w9l +4(e3:nx h1zybgsyw 1p gs rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius f(dzy)) x46z hpxlh3z $R_1$ 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 fd40t 41 leohu87 sgif3v(fcg9p qmy4aboard the Apollo spacecraft put themselves into a slow t 4( e4lp1fgm8h7u 43v ydfoi09cg qsfrotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder 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 rpmaiu -zp9so7 /+ri4rqwh.f txubm c:15 in 220 s. Through how many revol+: 7.ub5 i19wxfpc/ tauhorsi qrz4m-utions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in b-x .j1w j7koc2.5 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. uzs1pq hb;)r a whirling “hu.z)hb; 1up srqman centrifuge,” 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 240 rpm to 360 rpm in 1fw/o1 ntrj 2d6.5 s. How far will a point on the edge of the wheel have travel /rjw tn1od1f2ed in this time?    m

  A cooling fan is turned off when l+t*w*s 8z ri uqh6pm6o .0kskit is running at 850rev/min It turns 1500 revolutions before it cops80+s ** owmukiqzk t6h r6.lmes 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 spz2 ptz4izt * u0-d:nem0er :zreed uniformly from 95km/h to 45km/h The tires have a diameter of 0.20ut 0:*-e tezizrpd n4mr: zz80 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 thca)grpf .zm)y 8(m5hve car reduces its speed uniformly from 95km/h to 45km/ha5(hfv.mz y)mp gc) 8r 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 azg n)f-/ymg1 j bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17jnfgz/ )-1mgy 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 do0gm 6++qxza:vd bmuodj63c :d or 74 cm wide. What is the magnitudd g3 06mmzx +j6:d c+voqab:ude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque(l 65a g.edwj)tb 7n /mes9wxi7-erxx about the axle of the wheel shown in Fig. 8–39. Assume that a friction torque o ldirmxs77.n 6ew5)(xbee /- ax9jgt wf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached tozz; yp1s( +wveqj, obn( 5pbvo8.r2sc the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rve2b+b.8n ;zpywpc5qrsoz o(s,(jv 1od is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylind5 fn;q0s o8ircer head of an engine require tightening to a torque of 38 rq 85n sfoi0;c$m \cdot N$ 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 sphere of radius 0.648 m whe j;+v+*7ftfu9wu/r :hapmwyk n the axis of rotation is through its center. hu f /pw+wa vk:t*r9f;my +uj7   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in a kcg0*(4qb8 -j:vczkg 6eqtediameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igga-0vtg qe (k46 :k8z* ccbqjenored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end0i9 : yru7nmmwhhc:i 4 of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculat7 wu0hihr:m : m9cn4yie
(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 onfc a40)zn :nely2u q0q a potter’s wheel rotating at constant angular speed (Fig. 8–42). Th04ql2 0:yeucqz na )nfe friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. qh3g efk5yu:/8–43 :5/kefyq3g huabout
(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 whose2q ue/g *r w*hop2lm-i total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, e gjhdvi52ru4-f7,yr ungineers 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 to ri-54d2huvf jrrgyu 7 ,each 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder w xvbj (k5o2nv/ith a radius of 8.50 cm and a mass of 0.580 kg k5ox jn2vb/(v. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, acc.(c is t9wgh ;8nrwm9belerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-rot/yl 0w: hdhh e78p(oxund and is able to accelerate it from rest ty07podxt h /h :leh8(wo a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate 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 9cg6vh je 2a5srpm is shut off and is eventually brought uniformly to res9 e j5gva2hsc6t 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 accelerated7b3e;j7k ghj s 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 thrown sole5*r p*rmgjnyz t/gm+9ly by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rz95/m y t*gp jg+*mrnrest 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 4/jg88*pscpdz(flw9 aba r o( be considered a long thin rod, as shown in Fig. 8–46 w pr/9z *l8 4oj(8adfsagb(cp.
(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 masse853l xd7bd n.1a/rjbvqih rg9s, $m_1$ 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 turns (r21p2:paiui h7v01c ,r ksygje h0mlr 8evolutions) and releases it at a speed of10 8lc ki2gpihej a1p2ur7 ,sy:v 0hmr 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 h5ad4 0wjr2u.x8 ao x)pwl,oefas a 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 develops a m (li4-oy2+v (wadscb 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 c/98,u qf5g4*g qr)ykvzotrwum rolls without slipping down a lan g*k4tuy9u8gwfzr,/5 q qrvo )e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ea :fs 8b-,fjy7dhnad o3rth with respect to the Sun as the sum of twoando f df8jh,y-:3b s7 terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How muczz(ti 0q ntfob+ l.m*fkt 1x-45o yl2mjni1k;h net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per m* oo.-ft1x(0t itln zz;j4m i+l byfk 2qn5k18.00 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 without .jb *5 g4qxzrnocv *)vslipping down a 30.04*g j 5xno.b*vcv zrq) $^{\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 verk(7z q7ajgt+ av1vla4tically on its tip. It starts to fall and its lower end does not slip. What will be the speed ov(4a 1azlav+ 77g qktjf 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 0.210-kg ball rotating on the enx qopa/g;:g;0-mix3viok+e zd of a thin string in a circle of radius 1.10gv-azox0;ope3:i/ x ;+i qmgk 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 cyli6rb c s4e .jk5 x0t p-aqc3nec-9qkh:jndrical grinding wheel of radius 18 cm rk.54 hc6qecp-k-n30 bt s:9xec jqja 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 plfrv . w1ee4n/tatform that is rotating at a rate of 1.3rev/s If he raises hif. 4nvwrt/1ees arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8n v7wlg2m4e p,51m(nz 9-k uush -cvxq–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 rotations in 1.5 s when in the tuckmn9w51v kq vcxe-uz(lg4mu-n, phs7 2 position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ro+o . k:wqrxy hnx.c1qet.6wb+tation rate from an initial rate of 1.0 rev every 2.0 s to a finalcn.wo rx1.qh.xt +6k+ :q bwey 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 qp/phsy(z ,u- 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 frequency of the wheel after the clay stiupy ( /-s,zphqcks to it?    $rev/s$

  (a) What is the angular 3( )kufc0mf dejdj1 .imomentum 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 momentum x(m3um q75qv -iswkmd918oos 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 (dseu v (rn+9o/ky tn2moment of inertia I is dropped onto an identical disk rotating au2(yskno(ntd e9+r/ vt angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atg2a.s)r,irqg c0uwul b,+pi / 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 st )yi li2wir-i 4kh56)rseh n0yands at the center of a rotating merry-go-round platform of radiusr)rl0neiyy)-wii6 hk5 4 ih2s 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with ans -8wheu8m1tk angular velocity of 0.8tew1um-8sh8 k $rad/s$ 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 whit ontwd:4k lw,8gcp*3txs/ zq) e dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assumingqc) 4 sw8:p,gtdlxnowz3k*t/ 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 lq tt: dnac-6qeu3t:bc: a7,e winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass iv(f f40jvdi3 ap(fr.9ov vk1kdod0 5$ 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, initiz,ny k(vhy17hl -lo3y ally at rest, that can rotate freely without friction. The moment of inertia of the person plus th lklhh3 - (nzv7o,1yyye 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 stz rro7+e.6e * 3lcpvpsmt0d8zands at the edge of a 6.5-m diameter merry-go-round turntable ttmr ds*pzrz7 v6.e83elpo+ c0hat 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 rolls on the ground with the end of the rope lying on us lcu wbn l1hvy**obl2 f)5,h5v5jn) the top edge of the spool. A person grabs the end of the rope and walks a distance L, ho1fnlb w)*j5hso u5,vc 2lyuhn5*)lbvlding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Deterf97dg,9 yxx6pfwtnl*mine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case,ldtf7nw9y* 6fpx9, gx treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f.,t . b-gjslqprom 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 uniform cylinder o ekk jn0:ke* xx/s4j;imse5nb 9erf*4f radius 0.20 m acquires a rotational rate of from reskn*;ei04j5j/ms xs n9kee: k*ebfrx4 t over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.0eg8gq n-uj2o6jh*3 jb 50 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 o3ho j6g8*uegbq j-n j2f 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, h3 cz1hn(gue,y6f 9keg ow is the angular speed 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 si.i+ 4/yn9hmg*)jntagma .:v ybpncn .ze of 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 ra)+yn4:mn/cg in*jyh. vb ta .ap.mg9n dius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for ac dh9(oc:)gyxt67dzx low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 24d6 7tczgxo9x :dch()y 0 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 illustratkj 4 54gd:.r2np dqhwz/ srrj.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) is rolling on a hg3ql. hsz*;ooh(v6ak 5s h1nmorizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i9(ubyh/t .h i,u rmt3gzn6 hl(.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as sho6ytnrh itg( . h3uz(/ ul,mbh9wn. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. v,k: i7 9f if-og-swumIt is 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. 8–55). The step hasm-ovs ik 7i:f-f, u9wg height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makuoml;.u )4fxdv,-8o7gf/ uo g 6i harbing a turn with a radius The forces acting on the cyclist and cycle abf6u/, 7-ah; duoi.lx8fgrm ug4 vo)ore the 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 py5yo,z:kguh7k* k5r n w6p lo;; 6gdnwhirling the rock in a nearly horizontal circl n5pwkrok ;p,k; y*5ggzlo:u6dyh7 n6e 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 the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin r (mirv z36kwt5ods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms h tivw m3r(kz56eld tightly against her body.   

  You are designing a clutch asmzvzd ao 92;sf9 76u9y.;agg6 djtruosembly which consists of two cylindrical plates, of m;6y;at6vzfs zd9 oudmr .92ao7ujg g9ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopeo *(vg sv4f ue9zyb++w pu+i8nd rough track of Fig. 8–58. What is the minimum value of the vertical height h that the + 4e(8zsp + 9uyw+nouvvb*figmarble 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;itbo h8f (7pkt8,gvu+m 5xq a not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduc +b ckp63h3zr*(pbm)l avc(bces its speed uniformly from 90kb3p c )(r lkvb6(*ac+pzb3mchm/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s