A bicycle odometer (whi pd is3j)mzhz*sw;*p u r83dy2ch measures distance 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-inchyzmp j8 d;*ds*phz3 3usrw)i2 wheels?

Suppose a disk rotates at constant angulp1-b)b23ndpqtw(xskjwo ;6 ear velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration wwbnp ; 26k-o(b xqje)ts p3d1change?

Could a nonrigid body be desc3)j qf :ike;yas3j 4jhribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greatery.w w8iib cy2) 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 habqu5cjj qa2p py6 e+h3g1 l0(eu4o.d rnds behind your head than when your arms are stretb36qq4 g5 uju(1pdee0+p. cajorylh 2ched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear whel-(kc cl4gd.n94j behel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockc(ndc.ke4hb-l4 lj9 g et? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowl9 .rz -sgq.cac*:zrn i *n-jt/jrv ,ler legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rota:qrr zgs*tnjc..v-rl nzjil9 c, -a */tional dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fif22m xbb nn;1h1iha7v g. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque alnu c 94ia;qs2zs5 rz7fso zero? If the net torque on a system is zer ar;9nuis7q24sfz5z co, is the net force zero?

Two inclines have the same height but ma a/7 z:zhc 8wlm1mn5tmke different angles with the horizontal. The same steel ball is rolled down each incline. On whicnmmwzl 7mz t:ah81/5c h incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously 9 4ki6g nomav17wr-t.p w5vq fstart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Whi9wq4n w 1afm7 prvkti5g-v6.och 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 start from 813+g shn qcmarest at the top of an incline. Which reaches the bottom first? Which has 31a8cm nqgh+s 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 anonocm)r) ya77 d angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain )mr7ycn7)ooa .

If there were a great mreqi6+jg c2v: sr6j1 vigration of people toward the Earth’s equator, how would this affect the length of the dv16q:v+2esgjcij 6r r ay?

Can the diver of Fig. 8–29 do a somersault without having anyz36kh31(pv x9npww7 xw s,yvu initial rotation when she leaves the bw91 k3zvw(xp3u n,7x 6w svpyhoard?

The moment of inertia of a rotating solid dis w x pxi-h8mayc)6:d9qk about an axis through its center of mass isam cx- p6d: 9w)x8iqyh $\frac{1}{2}WR^2$ (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 in each oz44s4z7rxvqzi(z 5guutstretched hand. If you suddenly drop the masses, will y4z 5(x4qizu z4vsrgz7 our angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is holloxf 8haq(9az0 it ,c1vzw and the oth(ci t1zf8a vz,qx 9a0her is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horvo- ) 5)nl -co,kfgdy0mga; viizontal axle points west. In what direction is the 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 increasingv;)),gi om ykocfng5 l0a- -vd or decreasing?

Suppose you are standing on the edge of a large freely rotating turnt yqi/w o8df9 tfgv-/kkr:xd//able. What happens if yf-8 /v/f rkwo:tgqid d/y 9/xkou walk toward the center?

A shortstop may leap into the air to catch a ba6/cxem 4ffl-, gf sb1ynr88o vl1 rpl-ll and throw it quickly. As he throws the ball, the uplg-8mf -8pl,x 1yfvb1cs 6lof4/n rreper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a htlwewpq 51s1dm(pb9 -ivz. /velicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stablv l/w1m1teq.pvs5b (w-dz pi 9e.

  Express the following angles in ra pu58y (1nh*znxhrj/ udians: (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 ofcp 4 ,o3x hivh+qdh7m7 an amazing coincidence. Calculate, using the information inside thed h3p, 7qhhvo +mcx4i7 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 from9vk30nm zxomo(;f ux(s,we oyb2bg */ Earth. The beam diverges at an am2m3ke (o,s yx;*zb v9og w(/funxob0 ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blende(rhrphpm/rd 6+ a, 5ter rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bh6,hm +drtp/( 5prearlades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. I)t 41ufbhto i23tkz3 uf the ball makes 15.0 revolu3k43itz1)fuh b2ot tutions, what is its diameter?    m

  A bicycle with tires 68 cm in d 3 vxl ;wvxg:v2 (6vma2fl8sloiameter travels 8.0 km. How many revolutions do the wheels :v 3 s mf ;2ol2v6xw(8gvvlaxlmake?    $rev$

  (a) A grinding wheel 0.35 m in diame(a;2z /hqgc6 cjwcbnn(eia/i/41 pr ater rotates at 2500 rpm. Calculate its angular velocity inw 4n a2qeni//bc rph(ajc1;czg6(ai / $rad/s$ $\omega$ =    $rad/sec$
(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 4c olo livfk.3n65hn/complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cente c vol3i.6o h5nf/l4knr?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular 0npm1 /zu yv2zvelocity 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 poi glib1om6-8,jg rhg7sk ;4sbi;m w)fant
(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 rotatep-p8,sr r.fl pqiw: my*(3tpw if a particle 7.0 cm from the axis ofr rt:3wpm*p8-q,. (ys ilfwp p rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center k3-:k sq ujlo1(pj 0h35xrt r m/h8vljfrom 130 rpm to 280 rpm in 4.0 s.j 5r oxmhjhkl:8p(ul1j03tvq3rsk/- 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 il r:e0 ktlf54(kj bh.3wj m)g$R_1$ 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 2sm4jp 2, +qbimg+o*q :z cqv ulq3)daMoon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolutio,34 mj qaub:s+2 qio qpq+ldg2*mvz)c n every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,d 0qxkgnllk skk4fx2+*5 +4 uo000 rpm in 220 s. Through how many revolutions did it turn in 0dkon 4q s*fx 4u+gl2l xk+k5kthis time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calgp d qf9+1-lojvd9dz 7culate
(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 strej 49mjd ;kpgw)sses of flying highspeed jets in a whirling “human centrifuge,” which takes9jdpmj g w)4k; 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 3 ,lxtp-zn jn;nqp48 sbr0qo,060 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in qnnonl,r jq4px0,8 -0;zt bsp this time?    m

  A cooling fan is turned off when it2*,9skw me0n.zig rsgwvmsi *n/ 9t,d is running at 850rev/min It turns 1500 revol, g gm t9/*snin,k rd s90.w2*ziswmveutions 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 itzgjw*p0c0x ne 9w4h3ts speed uniformly from 95km/h to 45km/h The tires have a diameter onp9 wj3xt*zg00h c4ew f 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 carg -jaa- wegc,7 reduces its speed uniformly from 95km/h to 45km/h 7g-agjawc-,e 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 her weight on iqdydmq r *beg8 gzvh6x-x387t v(2+ x;,phjdeach pedal when climbing a hill. The pedals rot7h(d68 r2hvxz-dvpbgxm8+3,xqqi;*jd etgy ate 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 55 N on the end of a door 74 cm wide.jy ea*mi3 3m-rld*yyrveg68; What is the magnitude oi y;m*dg rj6-a *er 83yymle3vf the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the 2 i,6 * t,w1 jdfmgdvm(v*ocgvaxle of the wheel shown in Fig. 8–39. Assume that a m1ji(dv*w, g *cmv,dfg t2o6vfriction 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 massle wk: t:px*ord e0m/*nyss rod which pivots as shown in m*kwd/: oytn0: p *exrFig. 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 :occdz+/.o7u :vl pdmto a torque of 38 d:v:.oc/c7 z d ol+pum$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the abq fl6 mlq7ysn;xl(vwe* -v6+xis of rotation is(6 nv;7w-sll*fv 6m +bly qexq through its center.    $kg \cdot m^2$

  Calculate the moment of ineqxsf,a k.jw i-8 7.wiirtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. T7 if,asq8-wiij.x w. khe mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the ehc*2cmy bs:7j a(ss;ond of a thin, light rod is rotated in a horizontal cyb:(*maoccsh7 js; s2ircle 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 angkqnms l;p89/;wqf9tz 8dzd2vular speed (Fig. 8–42). The friction force between her has9dt29v;kzd8w8l;/p qq n mzfnds 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 obi+cgl qsye, sk 6xed;qd+6 k/*jects shown in Fig. 8–43d,sid ;kykgee/q6+xs q6l+c * 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 two oxygen atoms whose total mass is tzw7)z+ x*u gr$5.3 \times10^{ -26}$ 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 spinni+(0+z.ambg k/pvtt )lpd 8ruing at the correct rate, engineers fire four tangential rop(8zt/ ml+a0 v+t)dkg. ipubrckets 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? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a ro5( f8ils)b viadius of 8.50 cm and a mass of 0.580 kg. Calculatbi8v5fo() slie
(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, accelerhay9a-5i2-au;,fw i;dlp os iating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small ha6j* us bmt;k5 1msky)gt/ +bllnd-driven merry-go-round and is able to acceler+ljyum)/stk5mstlbg1 k6 *;b ate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, 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 and is::wmb; h , vyo94yrmww eventually brought uniformly to rest by a frictional 4mrw vb o,h9my:;:ywwtorque 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. 87kvhi ;z7rpik r+-. mi–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 of2/cw1yg rkp+b,t nn;v the forearm, which rotates about the elbow joint under the action of the triceps muscle, Ft w 2n;+, rncpy/vbkg1ig. 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–badc7-*:vb cx1,rdis46.d7scv:ir*x- , cabbd1
(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 mas9a 0zp 8zolc si)i9w(odc(n0dses, $m_1$ 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 withe ,hu*f , kt0k71opnqtin four full turns (revokk*uep,hf 0qo, 7ttn1lutions) 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 has a moment of ink*byy5 k 8s go/pf:7ceertia 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 torpp ei 123/wc4 5lkkwh(s 9fsqrque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls wi15hj:b xf ify(thout slipping down a lafb5hji( fx1 :yne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eneylm xo*su7:,t tbso0)rgy of the Earth with respect to the Sun as the sum of two terms,x,t )0b*t msy:7losuo
(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 ma0j5e.x, .+tz aqwqqr uss of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotationuet+.qq,5xjzw0a r .q rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and ma8vtu ;e 0 j7(zne/cluuss 1.80 kg starts from rest and rolls without slipping tuvun;u708e (zeljc/ 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 fall uho;n4b7ls e )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: Use conservation of enls )bhnu 7oe4;ergy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the , mlmw4 y,i v/elbzvt5d)1yb7end of a thin string inw/y45d, )7li lbev,m1mbtzy v 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 or:mj* ur7vt8x v0;isf f a 2.8-kg uniform cylindrical grinding wheel of radius 18 cmr7 s; v*v:jx0rmutif 8 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 rota+h w9ve2x z4 3gaihs4gting at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases v9eh 3gwhi4a4z +gsx2to 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. 8–2y9 rrhr-x i)nvc)9vwp4 vjv d/0)p-sd9) can reduce her moment of inertia by a factor of about 3.5 when changing from the srx))-hvys9 n0vc-d/rr v) 4d 9pi pvwjtraight 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 spi6v)m/ gbq:uq zrg,xh 9n rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3,vq rb6 umg/xz)qgh9: $rev/s$ 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)ts fw/ zs*4 o(tqlzp6xkr:5ivg 5(ui vertical axis through 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 frequencyg5xtus qwifok ) 5z(:*v t6(i4 lrpz/s of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater ns/f i 0gft.,gspinning 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 the Earthic5if. d ub 4/2hll-sh
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropihki zk :d;; w9otf93hped onto an identical disw: dk;okt9 hz3f; hii9k 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 20(-,ok 0v3cixd tu n vlmm7a4n.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg st+wt9 (gs-p gusands at the center of a rotating merry-go-round platform of radius 3.0 m and moment owg tgs p+(9us-f 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-rout bparru n8j).8mj)u-nd is rotating freely with an angular velocity of 0rm -)8)njp r.abtju 8u.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,lj et;k/* roz into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest inteozj *;k /lrt,eger)$\approx$    $rad/s$ (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 phqi69c ,tw .h4eac jt6/zzd4winds 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 a p5,urphg -(nvx7.uu$ 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, that can rotate freekcyr-- q ukdj(3,zd+lly without friction. The moment of inertia of the person plus the platform is qk(y-,3k-d+d z rlcju$I_P$ 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 diameter merry-go-ro 1bp (4b:gnv kyjd-t8vund turvkbg 8y1tj b(v:p4dn-ntable that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with th5)+ fex/ cgv,tz0hl xqfg.*8exk0 y yje 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 ./*x)f0j,kxle0t8+x gzg5y f yqh vceit, 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 zgtu8:(k* . 9xg/va i ne6bwapEarth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angue8 (.*akvb/:wz pg9itgu x an6lar 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 (v10 mg2xtuskxfg+n) from 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 thevk)x tcvm+*6bm e/neu4s/rj) shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque de cmkvv6sbe*)+4 )tju ex m/nr/livered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soli/.oyx pl ebdf0m,c 0l)d cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if )p x cl,ebl/.y0fomd 0it 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 ikmr,5gs. * vxthe 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, 1p hp)*vsol 5kbut 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 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 sphep5 hl*k)osp 1vre 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 f *4o iccxc v4svyn,q9)or it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinupc4 s,yn9ov4c qciv* x).”
(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 acrr4furz 5*( $H_2O$ 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 hb. 6ay. 4x0y zyt :-k/naroiebrbod;,orizontal 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 pivotlgb;m .8c. 7d9 nrgijc 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 9c 8;7jmidgbglc. rn. 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 rv ;9l0opow/tR. 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). The step has height / vr;lop90twoh, where h

  A bicyclist traveling with speed v=4.2m/n ywa. lbnbn)hfom;j+ phn9+-tv6ya b j:x38:s on a flat road is making a turn with a radius Th ob 3lybnj6a thbn;n+:j hn8- p:.mwx)va+9fye 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.v9 89u7 q s(wmrthda6p50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelera6d9swt7v8( upm9 hraqting it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and k20+t2 c :tm-ecxe/aulbfk v,her arms as thin rods, making reasonable estimates for a m+ e,kc20kl/f-:xbt cv2uetthe dimensions. Then calculate 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 whi a;yfg 2iw*2bjp1 lba*ch consists of two cylindrical plates, of m j gl1f2a* bbpa*w2iy;ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 nt6qz/zhm38 jqq) (7 t8x yxjdalong 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 hxm6) h /7jntzyz8d3qj8 xqt q(ighest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dm20/ b cnkugul axqksgx8j;*u0 :-ah5o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions 5rty8 *pj-govas the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the pj58 o-*tvg ryangular 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