A bicycle odometer (which measures distan49u: 3gwb.0l6bxa uho* vrpg wce traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wh4h0w:x * 6 gvbaw9bluop3ug.reels?

Suppose a disk rotates at constant 7d 2 n/ bm0rkrfnyq(t.angular velocity. Does a point on the rim have radial and/or tafqr y .b7t20/ (nmnrdkngential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veloci r5w , pz;)e,nraci /c9lldwa(ty $\omega$ Explain.

Can a small force ever exervim c+)21b atjt a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head than wz57k/za h9iw nhen your arms are stretched out in front of you? A diagram may help you hz/ wa9n7kz5 ito answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedalx0weuvnh7 o) 5nw5n;q 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 or a larg0)xoe ;nvw55whnn 7qu e front sprocket? Why?

Mammals that depend on being able to runx cb 7zgowv88w5t1o k, fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageowkg,b7oxzt v88ow 5c1 us.

Why do tightrope walkers (Fig. 8–35) carr+hzpebuf:3 h07or-ku y a long, narrow beam?

If the net force on a system is zero, is the net torque alj)gvl4v za :0zmx c8 daw.d39-di0ge 6fg( edbso zero? If the net torque on a system is zero, is the net fovi( ad-zcwg.l603dm)fddg 8zg b :j xe4e9v0arce zero?

Two inclines have the samt,qqbpi 7n 39ogj,q4x e height but make different angles with the horizontal. The same steel ball is rolled down each inclig, q i7nbjq4 3xqop9t,ne. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling s ts,9vjd xbue416jr1fj cma 3c-,fj: (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the great avc:ucm96,1brs,d 34je xjj-f1jf st er total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They startlhbhe v p5+--/ pbfhj2x.ojd , from rest at the top of an incline. Which reaches the bottom first? Which has the grefjbdv+ x,/bo2.5l -ejhph -ph ater 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 ango2p )7b(vnqiqx;u)b j ular momentum are conserved. Yet most moving or rotating objectsvbjx) no72p(b) u;qiq eventually slow down and stop. Explain.

If there were a great migration of people toward the ;ctwqn l+ nojzv8/7 4vEarth’s equator, how would this affect the length of t;/ q4oz8n vj+vlcw7nthe day?

Can the diver of Fig. 8–29 do a somersault wipqlfnk08d 6ip5mt4a.qc v-y0 thout having any initial rotation when shevqt ia5p 6p.-l f0n0k yd4cqm8 leaves the board?

The moment of inertia of a r1erlh2 j6yml- otating solid disk about an axis through its center of mass i2 y-j6ellm r1hs $\frac{1}{2}WR^2$ (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 ropdkrmt)1c0fbx;w r 59w g+k3 ztating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, willr1m09rd ww kxf c;kzp)g35b t+ your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical anddu7(7w+hzl q6 okcj e9 have the same mass. However, one is hollow and the other is solid. Descr(+k76 odc w79hj lzqueibe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In w8fxpx5 t1v,20av tbph hat direction is the linear v,pp2ab5 0v1 th 8txfvxelocity 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 freely rotating turntteu9;e.lt 8nu,x v: wyable. What happ xut,u;l een.9v 8:wtyens if you walk toward the center?

A shortstop may leap into the air to catch a b.: m5xn t igvem.81axnall 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 legsxg8.a.nv en:m5ti 1x m rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular m-qha:,j j:yhm4. y kcxdc/ )i fpkqh0,omentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to ikq j /qyh .m,kaxjy -0c,hfp)c4:h:dkeep the helicopter stable.

  Express the following angles in ra8v)mi1ysfa+v8k fm s4t me1 hq1 w6dr1dians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using the- dbnc/-;k. (5eq ud: tmemigr information inside the Front Cover, the angular diameters (in radians) e(u -g .rmicd-/qe:; b tnd5kmof 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 diverges ahz oifls2 hwo.u.u+7 1xmp-x) fv6)el) h. x+lz21xs fu6eofup.i) -m7ohv lwt an 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 is h5rkxha;v 45w xo, 7xuturned off during operation, the blades sl; auoxk h 7rw5v4h,xx5ow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another cm9o5lc,c qlm j8q+-fd hild. If the ball makes 15.0 revolutions, what is its diameter? ,8co- lq5qmflm9d c+j   m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutq wz g3ypv+)0pwajw dw4t p7dc8x*.q( ions do the wheels dpw)z vyj*+(w4 w wap .gd07ctpq3q8xmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2-cqdk 93jd9x(z u 6mti500 rpm. Calculate its angular vel9j3c 96zxtm-i q(du kdocity 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 revoluti(/vim8 ylga 88y wu2jl agf5)qon in 4.0 s (Fig. 8–38). (a) Whj)ug 5w8 yg i28vfq/(mlly a8aat is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its om:3,dum8ib1su k sdqi-n-;bi rbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sam(5 teefu:p(- wez*f peed 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*zbn-to)fyg8 rom the axis of rotation is to experience an accelo* f8yb)z-n gteration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uni(x l1nx3td:jcformly about its center from 130 rpm to 280 rpm in 4.0 s. Determid xx3: t1jlc(nne
(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 4(9 lm cmf2s/kxpwg; w$R_1$ 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 spacecraej28oyk mk9x s9 pzkybdez60z8p, snc, b9 77yft 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 intervps7xc ,z j 8,96y8s bop0d 72e9mzkebnyk9kzyal. 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 u4c)iwt9q 9y z-6drlgmniformly from rest to 15,000 rpm in 220 s. Through how m94q9i zyw -md tr)6glcany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 tr:p6rc6. wdqg7b werqv-(5js. 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 highspee*7 /q( j w9n0*v mxxnlbe6iectd jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutionsv0cxn/j6e*btex7 m l9 nqw i*( 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 diame qris w z9a8*pc-b6u/y)4hrl hter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. /9 6)4bq- rcauwhylz*h8p rsiHow far will a point 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 It t3 6 oq0vx(jgp(zemvl 2urns 1500 revolutions m p 2q6ev(xg 3z0(ovljbefore 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 revolutions as the car reduces its speed uniformly frbsse kg4z3 a;7gtuzh/, 9o4grom 95km/h to 45km/h The tires,sbg7e44 au/39ot gr ;hkzs gz 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 a msjmrdvdz,/51.u nn (s the car reduces its speed uniformly from 95km/h to 45km/h The tires hanm(m5/vsd1u. rd ,z njve 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 riding1k4 zl jstx13rtqg;,, um g.gf a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm r t1, kju.zmgs,g1q3g;lt 4xf.
(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 end8fcv7gj*t .acg337j6vsq yfyoo8x q5 of a door 74 cm wide. What is the magnitude of the torque if the force is e8oc 3ffqxvo j7g*s a5t8ycjy. qg63v7xerted
(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 rs hpuq-r* f r85ysz*:the wheel shown in Fig. 8–39. Assume that a friction torque of 0. r:urps*qh*-5r8z y sf4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mo 0 glb5phcv))-*,kiyv7vry zass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net ty v-ihoc5 ) ,gyrkb v7)0lp*vzorque on this system.

  The bolts on the cylinder head of an engine require tightening to a torqu+b;.4qxd4siu ol;qh c e of 38cdhb ;q;xq .4lusi4o+ $m \cdot N$ 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 oe tg8fn48k fosc5t(,,oam-lw br+;m nf inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through i f5f-bw84go8t n c;nsmm lteo,ar ,(k+ts center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wh8 g4nn75aa h4 n,cg8brvs2shreel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub hr72g8h, 8a5sb g44cvnsna n rcan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rob2vqn/z,; n4 pb ph6j ,kmgi.tf7vq5fd is rotated in a horizontal cir2/bz4v , ph,tq bfgqfi; mv.n7 jk5p6ncle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angua2id:b+ oofpi :p: k6nlar speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N 2: :anpf:boi +pko6ditotal.
(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 ;tu*xzuu3r d:objects shown in Fig. 8–43 * zrxu;d3:uutabout
(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 tl c19tm505c -/g+uav xun0mxwn)ppt 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 at the correct rat)vu+qa 5brbt-19 z hjb 0877t4y rpj;beufyeee, 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 min? j +ub-b5p8tv; 10e9 qtr 7ray4yfebezju)7 hb $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder d y+u7:+;kgrry*rz vi x6+lbqwith a radius of 8.50 cm and a mass of 0.yr+ v:6 x7rugiyd++lk*zb rq ;580 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 j aaw;rcq)(6 sbat, accelerating 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 tangentiallkm:n+vp)r/9leahf i7 vzz ,6 wy on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m : v)pkref i9m/av wh7+nz6z,land has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut c2h8nngrkv:dc:p8 4gk s t6 :zoff and is eventually brought un2cd:p n:k r nc8tks:h6g8vg4z iformly to rest 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. 8wj xcf b6l*k*xb6b ,p 8ixj(2r–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 ib,oc4zhvp6 j3 ehkcys ry(.yxt;gkb e3+k0:(s thrown solely by the action of the forearm, which rotates about the elbow joint under the action of thekvh+kcc6 y;rs j33 xpg ek:. 4yyt0bozh (,e(b 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. 8–4mry+hb a(6 2r3hrm+tx urw):d6mt)+hhrrr23m:by6x a ud +(wr.
(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 masses,kys zs4)f/ a5g6z 0w;cpk:rsm $m_1$ 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 g(kwggbn4ds8- dvq;-0phs :d within four full turns (revolutions) anddg -b0gkw4;g-p(: h8 snqvdsd 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 inertia of tx9 igng- w*4lruspq+0 vh2+ k$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a lj;,5-c) .p vjs3 jeprtaz/jo 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 radiuni 11k 2x4-uzhmwcbm -s/kp h,s 9.0 cm rolls without slipping down a lane4, m/k1h 1sh 2 wizn-cmxubpk- at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect toxwd4*r d8 piap97+g2ayu :ujyte .h: i the Sun as the sum of two termxrh2p4ay ea: g yipj+9.:7ti*8wududs,
(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 k-ven4l;q q*aof 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0ql;4 neqav-* k0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest 3t mebo u0-a0)pzzy ff8t6l l(and rolls without slipping dolaft) otle0f3 mz6p0by(-8uz wn 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 s/kix+kwu i zd8a8;e 1h o/+ fiqo.:7y-blmh kstarts to fall and its lower end does not slip. What will be the spemxewbokuihka;8/ q yih+is:dk+7o .8zf/ 1 -led 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 b5v7 mwr0z:6,yprmra thin string in a circle of radius 1.10 m at an angular r 7m5rmz0:abrv,6wp y speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical g25 akr5ly k7rq4mcctr6 / ikfj1e: /vorinding wheel of radikc/ /:lvk m7or q6ect 52a4r ryj51ifkus 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate+ecne r;y 6 b8x15tgme of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrease cgeeb 1 rmt8xey;6+5ns to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the o7 l84e9znki+t plru1o ne shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight poslr i4+e uz9lk7t81op nition 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 c( fb; te*v8gomt1 lrt (g75dpd7q j*urate from an initial rate of 1.0 p; jer1 t v5(7 * d*mdtlbcguq(g7fot8rev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis th,rr le oyp(e::rough its center at a frequency of 1.5rev/s The wheel can be considered a u (o:er:yerp ,lniform 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 momentum of a figure skater spinning at 3m3w, 0+lwohtd + va :7at4b*kvpitfw2.5 $rev/s$ 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 moment(bzaw f 5ooq cj0y;q,hxh(m z6f.+.z hum 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 cylindu. zb aayp0bn:uq/7-yrical disk of moment of inertia I is dropped onto an identicaa:qz.-yy7/b apn buu0l disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4sgi0s: o sv v.57 ;ypwgn)2jop $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-rou(ah e1 bs+r 3n7xnr.scnd platform of radius 3.0 m and momentn3r71s(xra.s eb+ h cn 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 an angular vely +pznh j:y39+c6vxewocity of 0.8 j9:v3y wxp+zyc+ ehn6$rad/s$ 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 halfa:: t5 vn ;rdkmea-u4e- ntw1e its mass in the process, and winding up with a radius 1.0% of its exis-ek:tar tm -:anwv1 deenu4;5ting radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds lo6 swaj +4*iuin 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 o/ogmq /s9/1u mu5g ff$ 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, initialt (f svvg9ih u3+l3f*oly at rest, that can rotate freely without friction. The moment of inertih + 3sv(tfug*f3lo 9via of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diame9(7k 0rcq 0wn+ f qxu;ctnlmo5ter merry-go-round turntable that is mounted on frictionuo5(+ l 79q 00kcxcmnrfw;nq tless 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 9(e bq02 ddjehd/jtq7 the ground with the end of the rope lying on the top edge of the s(d7he9db0 jq qte /d2jpool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Determ 0:+v ts0uhpq+p bj4oa*e hg7gine the ratio of the Moon’s spin angular momentum (a t0vgu7:j* 0p asgpb++qo eh4hbout 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 from3 a*5o hhmnwl-v w7gu, 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 uo)7y8bjhd-f ssu, zb6niform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelerb-o yh6dbussf8,zj7 ) ation. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg hyi yt u2iz e16(g/n4uxywx19baq0 v/ and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end o0e1yiq /uv9yi bh/u w(nzygx16a4 t2 xf 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 tp* d1bl gwp.-/ 0eexxwf0jm/phe 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 size of our Sqw2;7vg(wvh6 ee h/sdun, but with mass 8.0 times as great, were rotatsdq g/v72h eewh v(;w6ing at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the 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 storedu- .hyyz.z uo 9x:6(bl8pgibmr2nb- z in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywhub. 2( 8bybp-:r69hzzlzm.-g xiu nyoeel 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(56 thk3w *rmh0oer9r4kslgt gqpj*) s 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 horizontal surface at speed v=3.3 8/od rgl xn63z$m/s$ 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 yjamsa i-mzf1( tf8,: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 released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of thaim- fj mf,1zsa:8ty (e 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 verticallh *x*-yzhgn5 ny on the floor, and we want to exer5-n*gxn hyzh *t a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a fhz-) d79yzoejwdy /+*o;rf 3or;likunfw 8 1t lat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force +y*kdz-/our79 )o dhwwf ; yeot nf83irj;zl1$\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 le n(d/xfwa099bd.y8tr) hb8u4 ex umljngth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelehmn8ad e9(4 u0x)w/b9lutfbjy. r x8 drating 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 skate/a3 ya 7:)mb4ulzuoqdk+le+p r’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then ca4kdpa zlb:3lm+e q y 7)/+oauulculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platesf:wr1dydli5 kbo: *2c , of mbcr *:2:l5 dfo dkiwy1ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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)1 .i df1ugnoi 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 ofu.f i1oidn g1) the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume zrsd9fj );l( o$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducese)a8 /njg unsv6605yivp fa 5a its speed uniformly from 90km/h to 60km/h The tir5j5aia0s6 vn y v epn/g8af6)ues 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