A bicycle odometer (which( zmme+ u6,- q dejjfy01e3ibve-xh, j measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. ev ,0jy b-uz jjexm, d 3eeh(1+mi-6fqWhat happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity1u j8t9(s4b6b *nfw f,eszok58rfygn qp:q4k. 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 linef5f,( tfkn *pbj8ks 94wybog6 sq un84zrq1:ear acceleration change?

Could a nonrigid body be described by a single value of the angulas/ y2wun1k i2u9glryf:xz *r9r velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forct5g*ks :voi 8 1ojw,eee? 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 difficiwgpf /y,xo9d-; l qa*ult to do a sit-up with your hands behind your head than when your arms are stretched outw a of ydpiq;,/g-l9*x in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at t6 ym1 4wqseza. h6gqgv+.w4sw he pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket org.a.h 4sw1vygw 6q4 sz6e+w qm a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowve1-qs h eml6.cth52exy 4ob+ yzf1 +qer legs with flesh andle hs4 tfmxzh.-+qb61+ 1ceevqyy25o muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers13*m ;v9;9z cnues 6oukqsmwp (Fig. 8–35) carry a long, narrow beam?

If the net force on a system ist/n .99n7q jaw*3lfajjwr: pi zero, is the net torque also zero? If the net torque on a system is zeroaj9*:p n j7j/3ir ww qtln.fa9, is the net force zero?

Two inclines have the same height but make different angle(r2xoxqhcpm 4*r v5 3hs with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at p*c3 42h5rrhm ( vxqoxthe bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) d-zhy) *-pf kmsown an incline. One sphere has twice the radius and twice the ma y-z pm-)*fhksss of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius anddx w -o7jw/wv-k(6sxa the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has k(-d vxxwwsja-w6 o/7the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angulaly)o3u t vdme)sln.h k)8:d6xr momentum are conserved. Yet most moving or rotating objects eventually slow m.dydnk3t8x) :lvu)e)hsl 6 o down and stop. Explain.

If there were a great migratio+7rdbi (t/ uj 6be.)id,wpqq un of people toward the Earth’s equator, how would this affect the(edbj+ i6 .iq),d7r u qbtpw/u length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial p63dk u xep1-te5qxn;)g0h z2p8kj7 rrgo;qtrotation when she leaves thqq 7ngt ek)3581xrr p -hg2 6k peuzxo;t;d0jpe board?

The moment of inertia of a rotating solid disk about an amy 03/nq;qikt xis through its center of mm/ny q;kq30 tiass 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 stoo/t r gdp07ztx4l holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreagtr d 470xt/pzse, or stay the same? Explain.

Two spheres look identical and have the 3f 5( 0xhem;monor av5same mass. However, one is hollow and the other is solid. Describe an experiment to determ(30o xov5rfh5mamne;ine which is which.

The angular velocity of a wheel rotating on a ,pom/y,vemm*ke 5w lyccx6,.horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the anguxv.yccm, 65w /l,e , *ypkmmoelar 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 rotatingf t yic/ha;7(j turntable. What happens if you walk toward the cef hy/t; ji(7canter?

A shortstop may leap into the air wx,dz :ml7fc.9 8 sqxrto catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate i97qs:,l cxdmxr .z8 fwn the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angu.lzhcs)x 9 +xrlar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways th9).s+x xlrhcze second propeller can operate to keep the helicopter stable.

  Express the following angles in radiansraej (0a/uop:: (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 ; 4tq-e)3yf- mney9xodx xu4hof an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) o-;eh)o4xm y3exydq4xn -u 9t ff 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 be7wn 2sbah dm pk(t;+ -ejn p.h4;ia9bxam diverges at aeb2(+ m7-9k nb j;nw. ax;pd hhia4stpn angle $\theta$ (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 twu/tk5w:g 7ois turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades/ wut:5ok7t gw slow down?    $rad/s^2$

  A child rolls a ball on a levh wxg5cl5j 1-neh9 f+av/qf:bel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its fhlfnqgjhw:a+ c xv5e1 b95-/ diameter?    m

  A bicycle with tires 68 cm in diameter travels 8j 4o- uo6:k*u:/hijrmyo2q mw.0 km. How many revolutions do thw::jihk*2oqj4m/ u m6-yo ruoe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 4ly/bmvb-wj * 2500 rpm. Calculate its angular vwb/-ly v m4bj*elocity 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-r jz6:k(af zbz9ound makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear szf9 6 jabz(z:kpeed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the Su 49+ pb.5 v:*fpamex9askkj kwn    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a por f0llko9n -rh3xb: f/int
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from tj/ ks ,xkt75ryhe axis of rotation is to experienckry/xk5j, 7t se an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uni+0kh i3 ,lonojformly about its center from 130 rpm to 280 rpm in 4.0 s. Deterok+, n0hoi j3lmine
(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 3 v(,djgg)q2f cw nvd2$R_1$ 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 aboarkt*w6jcjq cv0 sb twkna+-ef 5e255o3d the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every mi5t2b -se awv fjk+j6nc5ko5 wq*e t03cnute 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 rpm in 220 s. Tn3upe f+c:5hg q 1ax,rhrough how many revolutions did it turn :u13f 5n+hxgerpc, qa in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200o*y31 5 fogdd-zl;r ;lzgh;;m hts;/ erwaps; 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 stresgd*0d-ygnl6hzvzg( kvb v, ,v 1ln/7ases of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20dy-nvvgv (h1 /6a g0 zllgnb*zvd,,7 k 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 accelej72 vq/px/z9byqv s+d rates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a pox by7d//+v9 j2qvpszq int on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min Ig :kc4t4mj4kizz*j y)t turns 1500 revolutm*zk4 :)j j4 tiyz4kcgions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolzgj ew1/8x w 2fptf02outions as the car reduces its speed uniformly from 95km/h to 45kmop2f1ze/ gf xj0wt8w2 /h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car ) a wt:h w)*;lki pb)xjj 7mr33dqr3.g9dzgpbreduces its speed uniformly from 95km/p *t r;q3jab ljd 9md3bh)r: xz7kig3.)w)wpgh to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike pu49;lkz y d6hrvxt 3,lfw7mk zw)x. /ghts all her weight on each pedal when climbing a hill. The pedals rotate in,3 /thh.yx7;xzzk96m4 kg fld vw)rlw 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 vo97kmn(pae 9g 5we-i end of a door 74 cm wide. What is the magnitude of the(v7 m9iee-akng9 w5o p torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assucu) )lofgh.pjgb71y) me that a frictiong h))p)7l.fy gjcb uo1 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 yml72 wf3w 6diends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then releasedfdw7 mi62wl 3y. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head ofn5j0,eohb9b6 .lt jpp an engine require tightening to a torque of 38 j.9ebo ,j56pptl0 hnb$m \cdot N$ 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 inyxtfm et.e9 ;0ertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation;f.t9t0 myxe e is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamet c08o16sp d6s 50jedffjg l.jj4kdeh5er. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?). . h06e1 lpgj8fj 4dsdf05dj6jske c5o   $kg \cdot m^2$

  A small 650-gram ball on0l o7,.lnqbdr the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 ,qr l0.lbd7onm. 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 wheel rotating at constant angular smy28r-e7 q mwkpeed (Fig. 8–42). The friction force between hew2y-em7 kr qm8r 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 spkm rivk.8m:k1le4 ( v7.nnpbhown in Fig. 8–43 about .81pmekpv:nr7 k(i.vn4 kmlb
(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 wlcr .omzrvz1y x567y *hose 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 satelli1dg e sc k76fm l/kb1h)s4-oqste 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 to reach 32 rpm in 5.0 mi 7 ssfc1 kb)ksge/o 4dh16-mqln? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass oe-)jw-/1spo0 8t l ybq, d05zjnjwoehf 0.580 kg. wbjjo )ye-oenj z, st/10h0 -l5dpwq8Calculate
(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 fr9 qrlv;j.r n5nom 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(nhxu(es6g* 5t n/;dzjbao 7 b-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 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, negleubx5*e(sn(dnh ga7j bzto/6 ;cting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually broug 2c3i4eutxdhc7d t b);ht uniformly to rest by a huditc4 e)bc xd2; 3t7frictional 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 mht41rnga m:b0jp***lqc3fp 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 65eq.huwrb+ ui0 nv(ad(g;ao ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from resqd60 uvaw. u+;(bion5h arg( et 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 rox b)8onrflj0*/ :vqsrd, as shown in Fig. 8–468fln:j) r0xr* q/ vobs.
(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 +gz7r c+ao6civ:j:urof two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer y71z7d cld oc5 from rest within four full turns (revolutions) and7c y5 7d1zclod 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 moment of inertyq hs y94zkmg,+ 7cqx9ia 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 c:olxptgds:y 0if*64torque 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 ra7fu 5clnfo- q8c 4x/v aod7 65xwgx+xsdius 9.0 cm rolls without slipping down a lane at 3wl+7asxo7fg5fcx856x/o d qxv ncu4- .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ntu jfq,/b8-hpo9cn( of the Earth with respect to the Sun as the sum of two te-8obhp9,jqf/ unntc( rms,
(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 much net wor pr 5wh.ydndfq7u iv3o893fh3 k is reqnphv7ui53.3 3oqdhf8f 9rwdyuired 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 20.0 cm and mass 1.80 kg starts from rest and rolls with6i b s3- o54crs(uzfaxmn)n8s out slip (56urfxcia)on3s 4nmb-s z8sping 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 star9arxi*/:kr0qh jz.xzpx 58ba cuc 30o ts to fall and its low.9u jpkohx8rc/3r bx5z qaz a0x* :c0ier end does not slip. What will be 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 0.210-kg ball rotating on the end of a thi0kbx wh.*3g/ng.t v jon string in a circle of radius 1.10 m at an angular speed o*g0hjw3.b vno. x g/tkf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of *1nz++/jiy :bu qy svc y4uo.za 2.8-kg uniform cylindrical grinding wheel of radiusb*oyzni.vc4 uysy+ :j+q u1z/ 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 senx6 4cxv-k6m(pg6.l/mmr f i(mnn9, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–4p( s9n.lv(x46m6c nimrge6xk/m - mnf8, 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 show,ckba ca6 ;vw*n in Fig. 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 ac ;* v,wc6abk2.0 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 initial rate of 1 zeqqysx0,;u:w5s9k+ *mxgb m.0 rev every 2.0 s to umgw,+bq 9sq y; sxz0 ex5mk*:a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through6z+ du7ka)f dt 7bgxf3 its center at a freq)b67zax +gf7 tk ddfu3uency 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 sticks to it?    $rev/s$

  (a) What is the angular mom7tohn((4 qqd uentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular mom x:g(iy(m 7ruh/m rfi9entum 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 cylind( ul sb ryovx)k*if / j)rw232.p6lsngrical disk of moment of inertia I is dropped onto an identical disk rotatwslu23os*bj i(n)r gp2f.k6l v /xy)r ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 7(:sw/sm eiwwat 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 t58 fq 98-g4vsxqzmrn ihe center of a rotating merry-go-round platform of radius 3.0 m and moment of inert-gv rfq5inm4z8sxq 89ia 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 an angular velocityz;0cgw9nlc 2y of 0.yg2c9nl;0 z cw8 $rad/s$ 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, losin46wvh; zi.le1pzq +e bg 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 1 ei;zlpz+.46eqwvhb 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 ac-f1 y/dk e2pin 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 y 0tr (gh7ie 4wl8q8cx$ 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, tha,rit.sly (r 2st can rotate freely without friction. The moment of inert t,sl2rsr.yi (ia 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 persook:f 6u.gv4v.q;lex+, 6a fwxxorl)d n stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless b).:v6xo x,xlar6fvl 4+qf.wuedkg o;earings 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 grv jh6ah v,, vghg3;q-aound 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 6 gh;ajgv3vv-aq hh,,. 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. Determ lce/j; +2 bdhl3rsc8mine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angulr lc 3mlcjbe/;hd8s2+ar momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate g13n:;l kq3dazo-hox 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 3f0j+vzc w1l cuniform 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 ljw0vcc+f z31torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cygcgl*fvc(s 3y+b m(.slindrical 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 tsg3( b*y .csvf(gl+mche linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rearf /gy(r9ouuj5 rxg 5,p wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as gr+wwtv us. cv,u; gx9v2eat, were rotating at a speed of 1.; g2 9xuvvv+,wws uc.t0 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 star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy s4hv uvbpx;eiw8 a-qy7 j3p0fga8 *1nltored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrn1e ubqy7x8vflv;i 0a g*p3a4j hp 8-wical 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 illustrate p1 h4bk /n/v:j3fzkjve2k4wss 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 horizont5ucwvvxp8m77jq)e w*rr9 f-s al 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 le.gk7m;hpkfsqj j o;(4 ngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then re(jhkgjf7o pks. ;; qm4leased. 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 floor, and we kv i7b8a/lsg2/kif.hwant 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 has hei2 gk s/7h.bflk/i 8vaight h, where h

  A bicyclist traveling with speed v=4.2m/s on a fla,owkz5p,s6p 8p a el5o; mt- 1v6gq(eewr(ueyt road is making a turn with a radius5 vwa- es (;6,e(6 w8,y5zg lprmtuq1opeokep The forces acting on the cyclist and cycle are 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 )c4wey9(n23 p tor czym and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve thiyo94zry )ew n cc(pt32s feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s ;l/. t-ioubsx..haeo hf aq/)body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretchedaqx u.s/f)ao/eltbih..;h o- arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, o1 ynoef7yzo 69f mass o71f6 yzoyen 9$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fk61+/p rwvi- ci vly/eig. 8–58. What is the minimum value of the verti k6p-vvwi/r/ lec1+y ical height h that the 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 d-dgxd+whw *pbh97aj0r6e9 qme+;oknot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducx:hy/btj i;i i.-2hdl es its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wiht y:jxli db.-h2; i/as 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