A bicycle odometer (which measures distance traveled) is atta 74 4*ugsqlph0.v dupached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicypusl *4vqgp 7u4 hd.0acle with 24-inch wheels?

Suppose a disk rotates at constant k6w )/8hjbssb 1zctd .angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have/b 1twhjz.sc6sdb)8k 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 5mxs3ojst*2 opaw/c;single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grewlnuk 2/yy9kpy4cth f),by 6.ater 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 difficultj*j kv2;1 qpaul+z.va5yi p/g to do a sit-up with your hands behind your head than when your arms are stretcz;jqlja1kvp 5 ./p y+iva*2 ughed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threeahe5h(uuq n kk/g2:y) tw,wy( at the 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 ng 2(at h:,wyku/5w(qekh y)usprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender k6,aqd xm-0- u+d vhwdlower legs with flesh and muscle concentra-0+ 6-awhdqk,dd uxmvted 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 walkers (Fig. 8–35) cags(ps iks34 w8 b90jnmrry a long, narrow beam?

If the net force on a system is zero, is the net tor)4km( rb: ew uhjz5v7veeabj2k7o/: lque also zero? If the net torque on a system is zero, is the net fovjk(5u):z4rbwo vh e jae 2 mekl7b7:/rce zero?

Two inclines have the same81(y b vxzfl*x height but make different angles with the horizontal. The same steel ball is rolled down each incline. On whicfx 1y l8vzbx*(h incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres siejhge8g0: yh ;i:;tdnmultaneously start rolling (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 greater total kengyd; hg08j: i :e;htinetic energy at the bottom?

A sphere and a cylinder have the0 ).l; .yxuol8p gw pi)goei)z same radius and the same mass. They start from rest at the tw.oyllg i)ix0g ep pu.z)8;)oop of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentu15d(m;jmo w *tgss 6bkvfe,c2m are conserved. Yet most moving or rotating objects eventualw 2e5 *jso,(sbmg; 6km1dcf tvly slow down and stop. Explain.

If there were a great migration of people toward the Earth’s ewbmxdloih2ng+2 ; r/ 2quator, how would this affect the w; mh/gnxri dol22+b2length of the day?

Can the diver of Fig. 8–29 do a somersault without having anxigful s r9cl 2gsj 0g(t3.j9nt78xbzb6/*zu y initial rotation when she leaves g xgj/t slbr 99f7s63uj*tx 8l(.i bzu0zn2gc the board?

The moment of inertia of a rotating solid disk about an axis t bw13 x3 rfa (brkeo)pq3 *k9smd86qdohrough its center ofo3 s wb 3o9d d6qqk1r3)rk(xmef p8ba* mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass+td/r j2 :fugjw/ey 9h in each outstretched hand. If you suddenly drop the masses, will your angular vgjjfd rw/ut:9ye 2h/+elocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one ism0qr (39yo i+j9 3dob,utzu 3keemnz 8xklp1/ hollow and the other is (i3ojre mdkuob1qn zp+zk 3u9t9,m3l/0 8exysolid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle w9ww7xmy*ht(sm;z 3l rh547rseyov / h 5k -qxpoints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points eyz y-so l3hst4 mhm7rxw5w/h*ew r;x(95 qkv7ast, 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 turntable. Whatb mgz:(if/cbgh.z3u 3 happens if you walk to(zgc3 3bihm /:bu.zfg ward the center?

A shortstop may leap into the ai/t* njgqjjak:b7;c8 jdfc 0 b)r 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 tha 8n*jbtjg0k;c / c:qdj)bj a7ft his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum,(3sn2f9hr9p qr lcig* discuss why a helicopter must have more than one r9sc*hrfl qp9(2n 3i grotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following4h8 /qqsngo: h angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calcuo :2:aiddh/.o s knqz8late, using the information inside the Front Cover, the angular diameters (in radians) of the Susdi:hao qk.d:2 oz/ 8nn and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is dired qau 0 tzkxizf+3,r+4cted at the Moon, 380,000 km from Earth. The beam diverges at an angldt3 +zarxiu, zfq+ 40ke $\theta$ (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 turned mmsgsoa-; (-uoff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as thug-msms;(oa - e blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child.6 r ;: ;emeemgnz--cqr;s )da4jo.jhy If the ball makes h).;g6amemo r-r;cq-4:yz; e ens jd j15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diame0zs4r3:p z jn vte38t llja18lter travels 8.0 km. How many revolutions do the wheels make l3p z8zts8jr n:4ll0tv e3a1j?    $rev$

  (a) A grinding wheel 0.35 9d,+ gvuw3zn zm in diameter rotates at 2500 rpm. Calculate its angula +z,wgn 9dz3uvr velocity 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 complet ho6ynn,( e8ane revolution in 4.0 s (Fig. 8–38). (a) W n (o,ny8a6enhhat 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 ixr0ku x.oz8fp;/b n rn4g7su. ts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a(vrwb ck3+ d fgabs6s4/4tbw+ 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 from te +tr4v:,.kp0upkoc u he axis of rotatice+ku r4:u p0kp ,.otvon is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about /m )cmg2r-giy+q w2so its center from 130 rpm to 280 rpm in 4.0 s. Determing+o/)2-rgws2iyq mmce
(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 6,em*q fswo zfz*7 yk-v -os-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 spacecraft put themdcnqwnsi+ 0* 2bz (qf+selves 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 8.5 m. Determine2snf +zdn icqb(0w+* q
(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. Through hozw l6*z:s*draggo -7lw many revolutions llg s:* z-6z *og7darwdid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm ino. +gss(sz8 p)flbl)d 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-dalw((qds c 4s8 x4k ,dpuf4a in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its f-,(l aau( 4k8fdcd ds wpq44sxinal speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to) sr/q is27nun 360 rpm in 6.5 s. How far /qs ru7 n)in2swill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off whenk(mznu1bm3o8sh:c m- it is running at 850rev/min It turns 1500 revolutionsnub8z moms31 -mch(k : 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 revolutions as the car reduces its speed una*o ob j4n;au4iformly from 95km/h tunboo*4a4 ;ajo 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

  The tires of a car make 65 revolutions as the car reduces its speed uniformlwkz n0/ bi5,nay from 95km/h to 45km/h Tin05,bz w nka/he 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 her weij s-v.;j uqo-7 tcmn0rght on each pedal when climbing a hill. Theu0r-tm7sj.;j c-q von pedals rotate in 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 5ccgxi3bd:/b crtp691 5 N on the end of a door 74 cm wide. What is the magnitude of the torque if ttr1:cx6 c 9c/bpb igd3he 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 tn-oj yf3a9xf1lc, twl i d482dhe axle of the wheel shown in Fig. 8–39. Assume that a frictidc1yif 429l3otla-8n f djx, won torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attbl/*e, +w0w 4juntymk :ex)wtached to the ends of a massless rod which pivots as shown in Fig. :euy+xwjt*lenw, /tk w0bm) 4 8–40. Initially the 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 tightening to a tovt 3 u.xw5*x 5jfgn8strque of 38 .v5n3f jxx t5*utg8sw$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648xr;i zr*nbb 6lo,mqyk 44n 8p. m when the axis of rotation is throu,b .oi ;6pbnr m4yrnk qx4*lz8gh its center.    $kg \cdot m^2$

  Calculate the moment of elfs d3s4-ws 8h*ew9d x(/ pmrinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. Thewpselm dxw( rh83sf des- 49/* mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end otqm :e/s9geqop(tv4h 8* h f/wf a thin, light rod is rotated in a horizontal circle qetmtv/w4fehqo8p s/g:9h( * 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 pote55 n l ;bp9ctna+e4yhw, f0nxter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force betwh9elp,5x yw0t +nec5nf;4ab neen 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 arr7u* .m kwm 9:nmajnl*may of point objects shown in Fig. 8–43 mlmuma*:w j7n9n .mk* 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 consistso2fa1x7ms ccjdvimc4d5v 3pqox.mr :0 o 4/2c of two 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 the8xdn-ch7ugn axifs f+ 3:vc4ck6fp 5u lz503f 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 m5ck 4uuhfnvlgn5zd 63:f a xxp87 3ccf-+ifs 0, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8o lp(c75ud(yk.50 cm and a mass of 0.580 kcokp7u d(l(5yg. 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 frov 0g 8hjntsjp(f;(r7 nm 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 an ;xu g7f,:zbbad 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. Cal b,ax ;bfu:g7zculate 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 rota4hic 9 cvyvhtw 2sv6*5ting at 10,300 rpm is shut off and is eventually brought uniformlyhwh5vy iv2 69sv4 *tcc 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. 8–45 accelerates a 3.6-kg ball atg1kh3onush60* :nydz 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 solehfvid6+ ij3x35xr p)m1mx l0jly by the action of the forearm, which rotates about the elbow joint under the action of the idvxpj 3 +0) xf5r3l x6mijmh1triceps 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 show y lfms7,zy51qn in Fig. 8–467fzyl5ys 1 q,m.
(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 c6ng mpg. ) )vr;bkid(jonsists 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 he:8x0ot wg5 dq2hg: 37n(yqr udo hb8eammer from rest within four full turns (revoluqggo3ed :uhe5ontq2dx w8r7h 0y8 b:( tions) and 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 hyt.ewet6( wh8z;ed)s as a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 gmb;9sq 7*qjr,ib dzl ,i*c(x$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and rad 3i;yr*mhzy 4oius 9.0 cm rolls without slipping down a lane at 3. oh;r3m z4i*yy3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to thegx ,g4qdz-m .p Sun as the sum of two terms, zg 4,g-pm.qdx
(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 net2movz8ox k55 4kkp nyto *3.sw work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 3v4.om5sx5t kok k2y8 nzpwo*8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 c uil me;7ofgt60)t f ,ym2p,czm and mass 1.80 kg starts from rest and rolls without slipping ,0z t git 2m),6f7fc;ueplmoydown 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 vertud0sl4n v4-ht d9pc5xd v0(rcically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: r hv 4t0x -5sdp(v dncu9cdl04Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg baquc. 8p 5ud.a4uu7esrll rotating on the end of a thin strip.e8r 4suqu u. dua5c7ng in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gri31 prysy))z, t v9t, n2edqluanding wheel o) 9 ,3,1azyut) evyqsdn2tlprf radius 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 platformcc;ive)hvhcd .8dy 4u +b4c 8a that is rotating at a rate of 1.3r civ4cb8h +h 4d );eyvdca.u8cev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inkf- /g :qg)nmwertia by a fa)gmwkn-q f:g /ctor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the 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.v8hx8nn *igb.+52u y ydtdz 0n0 rev every .d0+*g t y2ndxvyun h85bi 8nz2.0 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 through its centsh/ z.wtsu /2aer at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 s.2w z// uthaskg 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 rfr3e8 uww)v3 figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of t/pwn d - f5y25oz )al:psl ggm9vdjo+1he 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 cylindrieqy9t e6u 7wt1cal disk of moment of inertia I is dropped onto an identical disk rotqwe9uy1tt e 76ating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4hnxbi4ly w+mrv43:n433x . g;bkyu vy $rev/s$ 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-round platfork+8;da )5,oducgdpzt d 3 uz,yk -lsw3m of radius 3.0 m and momeda3+u ,yz;)p8-d 5gdk,3 kwcdot szu lnt 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 angul 5dkg8 b,:aelgsmvi( ,ar velocity of 0 ,dva(: ki5e8slg ,bmg.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 aboukz -i*: udg4nwi,2ceut half its mass in the process, and winding up with a radius 1.0% of its existing radc-dkniu*,w:e i u42zgius. 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 3z 5xk maha2cq8)rp*xin 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 gdi+;5; uoup x$ 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 platj87fbs :or3wzt 4bp-qhy 4p7 lform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the plaq- ts4pw8bpfbh 7:j r37 y4lzotform 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 6.5bx co1n*x/sg*-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertiagcnx1*os/x b* 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 ropm u ys4gcg*w*,e rolls on the ground with the end of the rope lying on the top edge of the spool. *s 4ymgc,w *guA 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. m5hzow 79gy0d Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbitigo9ywmh 70z5d ng the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rnoc:7vj;umzm .7e 2p yate 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 -46d3 ;hbh)dvdh- s h/moni clkeh.b4)kg :aishape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rkndboihd6ihb 44/.vh:c)g dlh);a-ke h 3 ms- est 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 tl7f8+rrhmhak + u9p2lw)u2 h kwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.0lur7lwfpah2 +)kh2uk 8hm9r +75 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 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 an0:5 kf,qeu cgt.+ vpf il2j5rtgular 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 Sun, but with mass 8.0 times as great, lhq-o: gs 9-gui9vwfla x3o)124dju u were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular moment )1s9o9-g uuifg4:h3-oljlxd uq2avw um.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energ4gj3502tymy rtai db0 y stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, bj dt5mrg i430t2y0ayuses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates ankg/(sm95 cye/ioo)i vqu/o8 (u xx5yh $H_2O$ 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 horizontalp4xcvw ac) +a :-vrj xjqg0u7; surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., fp)rbjkytf w8ig66 z7th m;4/ 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 acce6p;6rmthf yzjb g/7 4tw8 )kfileration 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 stan/ (n9m 2k pess1bhk/guding 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. 8–5k(eg/ ns92 su1hp/k mb5). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a t xa:myf.i r+w6urn with a radius w6 y:a .mir+xfThe 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 m and begins whirlq;gi *zdtr/0fempu,2 uo4wvwnp (4y ;ing the rock in a nearly horizontal circle above his he*uof/y(;drzwu2nvq ;,g p wime440p t ad, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skateqbrhu a1b3k/)r’s 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 outstretched arms,/b u 1)kaqhrb3 and with arms held tightly against her body.   

  You are designing a clutch assei hup5d9 1ee-dmbly which consists of two cylindrical plates, of maseihd1e9dp- 5u s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rqzn4 niv.p02 l rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that thezv i.lnp 20n4q 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 not t h2,j/*cfsc:4 cjcwx assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly f +ww m:ezc7hv*rom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eac*7+zvecmw:wh h 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