A bicycle odometer (which measures distance tra10/8t e q,hkpuho;uod.n rdh*veled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it onh. t ,eh/*k o0uor8dh;p1dunq a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rimhc-snn6bg i-3 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 magnitudn g36i-hbs n-ce of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular ve6biz ntfb,s;7 cf5 ue2locity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcef2e* qa-p)l vf? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behinr tek2l+a9*gt7b 7 ucnd your head than when your arms are stretched out in front of you? A diagram may he9n+ rkba7 ectu2 gt7*llp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheep c.ccd212/w)2vnzb oesw vfj 0m-p2wl and three at the pedal cranks. In which gear is it harder to pedal, a)pv0jp 2b-n2o2.edv1/ wwzc fm2 cscw 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 slenderxjrjv r8h kimo/f:,72 lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of o2 mrv /7:rxj8kfh,jirotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) cxxpyf;s8 1dmn:mb3- zaob. h6arry a long, narrow beam?

If the net force on a system is zero, is the net -xibbb n)o 4x7m3kse 9qyn6t8 torque also zero? If the net torque on a system is zero, is the net force xmyenbqx3o )9bisbn6 7k- 48t zero?

Two inclines have the same height but make different angles with thnvm*-ri 0 4 acbo7q1wce horizontal. The same steel ball is rolled down each incline. On which inc0qmw- cr 71v4 aib*oncline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down )hxkv)z ,r(aoan incline. One sphere has twice the radius and twicer)axozh)v (,k the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sk593n pgpag, ftart from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has tpp3kg9 f5,n aghe greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentumjft1o2u0(zg( g5(n+4 r dpqaug fc47l 1glhh z are conserved. Yet most moving or ro74 1(fg(u2o qg4+tguf0hl (c1l g hjnzz5drpatating objects eventually slow down and stop. Explain.

If there were a great migration of people towar u;9ao7duaa*a d the Earth’s equator, how would tha a*u9ada; ou7is affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rota(f k1zz(z ,iwdtion when she leaves the boarzfz idk( wz,(1d?

The moment of inertia of a rot 8(j1gdtrrj 8hating solid disk about an axis through its center of 8d1g(rrjh8 j tmass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass inh6+wz k:yqdi-dbq:mu ;8v* i l(msxb. each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or swzkv8 * u qmybdbsqhid: -;xi.+6l(m:tay the same? Explain.

Two spheres look identical po+wd t470 maz1d8w92 z3wdie/s,dp-mb u ce aand have the same mass. However, one is hollow and the other is solid. Describee-4zewa9dzpdsw 138/m b +m0dpwo,7aud tc 2i an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. I : e)q-f;advlpqaf- 4xu3dj0hk lx(g4n what direction is 4ehfu3)0p ag(ax -q kdlqv :f;ljx -d4the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large f1l tq6scy08yg *tdiw)reely rotating turntable. What happens if i*q 0)6t ysylw8 1ctdgyou walk toward the center?

A shortstop may leap into thmn15 , d4gaqhgq(lxm0e air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direcx(0mqd agnl 41q5,gh mtion (Fig. 8–36). Explain.

On the basis of the law of conservatio sunb:ergif18 5opdgil;8,0 y n of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discu:; fin8ripe5d1g8uo 0 y lgsb,ss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following a+ fb3 hmknis.3ngles 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*tyca /wa q6)v coincidence. Calculate, using the information ins/awt6q y*)ca vide the Front Cover, the angular 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 from 35hfi2 l6zj6 f4zxsmv Earth. The beam diverges at an alfzhzj626i vsm 5fx34ngle $\theta$ (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;boip,ext. t : a rate of 6500 rpm. When the motor is turned off during operation, the blades slow tbt.:oei , p;txo 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 ano11oaezbb78 og hfx-k3seq224o8 ofk k ther child. If the ball makes 15.0 revolutionaos kkb-2h q kzo8fgeofoe7218 b134xs, what is its diameter?    m

  A bicycle with tires 68 cm in diameter tsrf0c+ /xxyuf ah1w 4(ravels 8.0 km. How many revolutions do t1hxw04 r/a uxfy+f(s che wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate it8fhj( 7 xmir) v gr*ol ,hkkjy9395hhmkjr(x6s angular 69m jr3fx h)hgk 9vo5yhim7 l8kjhk,rx*((r jvelocity 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 revr hpk3+ q.6p l/ehd,8do)hsc + y.dzjs )msg8aolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2khqd+ma8+3,s eh8zsd ygoc)dr6 pphl. s)./ j 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 veg nbux(,mqa6/locity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point12xi;pemp n3e p:d9slic5:+)qsj2 p tig 9y oe
(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 b*pf)6 ill0+vj7wej f7.0 cm from the axis of rotation is to experience an 0)vp6b7efj lwl+j if*acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its 5+/l- qrln f)gfi b*/0 iiwxjecenter from 130 rpm to 280 rpm inbi qwf-+lir*)i5/n0 x elgjf / 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 nyk7 laq66i.tkwl+p: tw 9773 vtdyl i$R_1$ 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 spacecrafte-9+;j5z3ufz zl dzy r 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 minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of ;3u +e9fz l-yzrzjdz58.5 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 rgr-w6 us4gkwne d,c) b+k46wwest to 15,000 rpm in 220 s. Through how many revolution d6nk- ugw)w4b6 swg ,+wr4kecs did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200gr4w q4p0*c rl rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirlingw b;0(4oh shtx1yi zuuj h9,r7 “human centrifuge,” which takes 1.0 min to turn throu,rs0ub7 x hzt 4y;jow(91ihhugh 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 uniform: mf4a8prt z+05ke t0em3jth cly from 240 rpm to 360 rpm in 6.5 s. How ftj:4 rpht0f0m et 5ca8zmk +e3ar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off whe1 zaq 5p+byzb3n it is running at 850rev/min It turns 1500 revolutions before it comes qy+abbz 15zp3 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 revolvrog73gcdt73lg+b)j u *i6iwh :w qk 0utions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 06:ibg3o0c d 3igl vtj7ww+uqgk 7*hr).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 rmm77k, rq t 2q6j:uspueduces its speed uniformly from 95km/h t:672uru p7kqj t,qm mso 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 puts all he*h0dr3j y2 uon,1gqc3agd 1 sxr weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 sy dgqud33ja 01rc,o * x1gnh2cm.
(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 wide. What is )0cgmxo 4 jr8:,rf*ogj(w k uqthe magnitude of the torque:u(gjcqxgwo0 )o ,m rk4fr*8j 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. Au9lb6p )i l)bhssume that a fricl6 bp)b uh9i)ltion 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 massu1+l6c8i 4- n q)brc ;t6qdmr c43k.nszictwgless rod which pivots as shown in Fig. 8–40. Initially r3tn swnt84cg6 lz u4.dk ;b1-r)iq c6c+icmqthe rod 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 cylinder head of an engine require tk99)oddy7sr f ightening to a torque of 38 d79ors)fd9yk $m \cdot N$ 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 sprky uxcx:0 r/3r6.w pohere of radius 0.648 m when the axis of pr x6/0xoyrwu r.:3 kcrotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 b*3yddu 4cc ,pcm in diameter. The rim and tir *pbddy,c c4u3e have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rota4wext5m ug3) k4z)ays ted in a horizontal circle of radius 1.2 m. Cal u4 )5agyke m)4sztw3xculate
(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 rotat *j,qqtfrp gjg46m(b9ing at constant angular speed (Fig. 8–42). The frictioqggfm* (p 9,br4jjt 6qn 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.2jkunc.w-e8 b 8–43j nb- .c2eku8w about
(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 tw,6wtub 4itq( z 1gu mw;mo1 hn(:xzno8o oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning auc+vjepo- :y 6l/; vgkt 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 invlvk-c :yug o;/+6pje 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cmb/ zz4x r*:28 hxde6g3chmtdd6 g6 hly and a mass of 0.3:2xe6 64ht6y/lrg*d8m bhd cz gdzh x580 kg. 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, accelerating it noefy 31)8hr67zb ko d9anfv 5from 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-round a0gjkoqd-9d y qp0,uce; z:pc +nd 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 to cdy z,kup00:-qd;9q ec+gpjhe 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 jhtrqo s1z, eu/qnt/8u 7h.7yand is eventually brought uniformly to rest by a frictional torquyt tj.8s,ehzqu71/hn/ 7o qr ue 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. 8bah hoks8i45nko ;qt- -j c6 2osej/z0r ezr04–45 accelerates 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 solely by the action of the fj/ epcd bs)isz514d2 porearm, which rotates about the elbow joint under the action o)z4 ce/dj dpps251 bsif 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 in Fig. 8–4)nxu7ir;qd: 3xj iwc9e h)hf46.; 4hj):fxuw)e9cnd q iix7r3h
(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 cg(d4*t r+ k-p xbr2(kkckl eo2onsists of 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 hammgt0,b,cb;f ot ,+bu,+ emwocn)(rrz ter from rest within four full turns (revolutions) and releases it at a speed of 28 t,m,rwz,bgotr ,cf; 0 +t+)boe(b unc$m/s$ 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 inertids aq8c3 0 l+1m+rh0wpjowai8 a 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 torque of 280 )8ebx q;icy8 i$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kee/;48e f+q gh: gohrdg and radius 9.0 cm rolls without slipping down a lane at r:fh/q 4gee; hed+og83.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect pf -fk wh)0/p0/uhqn d o p/)nusp2u+mto the Sun as the sum of t /0n / u/h0spmp o2pu+pq)fd)u wn-khfwo 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 7tw. o53 kbqo(.nzbjo3a(r ei:.50 m. How much net work is required to ai3on.5eb jawro : boq(3(k.ztccelerate 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 massm8q2oozy 1.1y94 pihq q1pz qr 1.80 kg starts from rest and rolls without s1qmr.i1hpozy1qy 48 o9q2p qz 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 balanced vertically on its tip. It starts to f o m0l:*-fp um5t pau3v)+kwnacxk-r:all and its lower end does not slip. What will be the speed of the upper end of the pole jt+-vmmfxluapp kk:0 * cwn5) ro-u3: aust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momenk7,is d;bhod1m9z)+wl7 jr-meiy 6 qftum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an ang,ij kq l bdwm;1 fyo7-)e67 z+hdrmis9ular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindi, d+bg6 g+mehqng wheel of radius 18 cm when rotating at bq+em d ,gg+h61500 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 v4 n-ejomb tjt0yb)9(side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotationn me vtbj-tbj0(y4 o9) 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. 82jrzgz/;lfv luo/r+ 0–29) can reduce her moment of inertia by a factor of about 3.5 when changing lzlrruj/o fg+;/0z2 vfrom the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of g8o(hch0 s0 xfja- *sm1.0 rev every 2m(fj hsoa8 c-*00xs hg.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis throumvqb*01yskh-:et , j pgh 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 frequency of the wheel after the yshk ve ,t:q 1b-jpm0*clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater 8 k; ytprho:z43+tdrjspinning 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 mn,g95(iv b-ioi 1)k xi1 yxqafomentum 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 of0+bqxa .d2ss k moment of inertia I is dropped onto an identical disk rotating at angular x sbsakq+2d.0 speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns qa3 :boihrp4i (q51lfat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating m o)wlr.v-t.ku ;x nps9erry-go-round platform of radius 3.0 m and moment of inertia 920 ; - lk)v.t uwor9pnxs.$kg \cdot m^2$ 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 wu)nw bhsw du 9 sxqt9-(-3z+hangular velocity of 0.dxsuu3+swz h()wh nb-q-w9 9t 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about halug; 3wivexb *1f its mass in the process, and winding up with a radius 1e1 ubxwvg*i3 ;.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 involvevak,4d 6xny g3 l/r, dnr(j2l eo2fvk4 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 q n38c p7+ br7pv-x 4tg4meypi$ 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, thatzqu noqws73(b v gl:9c nx8p5) can rotate freely without friction. The momew9 culx:3nzog5n)(87sq pvbq nt of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person staop 1oz cml ,merrs-14nu 03n2gnds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of zn c420u-or1, egromsm l n1p31700 $kg \cdot m^2$ 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 wlui o8y qh97tgfbn/i59) l-xzith 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 slipyghni/q8 obzt 5lx-)i7u lf99ping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earthde ;jbp3x2v5l such that the same side always faces the Earth. Determine the ratio of the M5bl ; x3vpd2ejoon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ra0qll(zo,h9 jite 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 uniforqi*k:b1*f k3h4l6d ..pjt4tw v jt. oxk3hgnbm cylinder of radius 0.20 m acquires a rotational rate of from resqh:gj n31lh64 wbdtk. 4*k .pvf*b.xjto k3tit 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 ci*r9 glclmh69 ylindrical 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 mr99igl* chml 6. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wy8e5q xdl46ac heel ($\omega_R$) 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 Sx9 kp1ui 1f1u1 s3;kebav h*vnyip0b3un, 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 r h f10bub 31vu avsnp9*ky11 xi3kpie;adius 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 ccsm2)xyu m42tk5sahr+ .b0gstored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, andastk.yb 5 mc g0+ru)x2 cms2h4 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 illustrates an +*y .adhri;xa $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal sur0zz;gm64t/khes 1r no face 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 (- :;5 n *z97rqon)wya btpgbosi.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 trazqt :-bp onb*gy5) 7on; sw9he center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M hasiytfn 8l3wlre2k/4 t2 radius R. It 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). rwl 8ye/lt3t24nif k2 The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roadqodrv9sr 70qfpdx+bh8+1 s 4 a is making a turn with a radius Th1q4xps7 d+rdafb0hs+vq8 9ore 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.:r bknp/+4 +evpqh tl)atp0a 450-kg rock into a sling of length 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 s. What is the torque required to achieve this feat, and where d+ n: 4abtr+v/0)ehtpp l 4qkapoes the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thw 5a1r9dt4lo;b7 ju9l .qd/a8nzxu9mjbns/ xin rods, making reasonable estimates for the dimensions. Then calculate the ra r8z79qso4abu a9b x5nlt91m/dw .xjn; /ljdutio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutcov9tjbpq1s1zrg6 7o . h assembly which consists of two cylindrical plates, of massjq7vs1boo 6g 1p .tr9z $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alonh5 fk)6yabljy*-u. r xg the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the tr)rjk5u-. *yly f6bh xaack? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu(j c.pocagklzn1s1f--2g 7h e,y:xi dme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformrgwptw; ev yz*e5)v)7ly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a7 ewgt)ep*rz;vv yw5) ) 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