A bicycle odometer (which measures distance traveled) i92-dyhefh wg) mk5 zu4s attached near the wheeldzgy 294 )hfwku5meh - hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant9pcl.2qmudxpu5j ,13wt ak 4l 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 radial and/or tangeuax t u1cw9.kjl35ld,4mpp 2qntial 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 anguwfp9-z3t4 rwk2n z2tg lar velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exple +z7p1cks8kkain.

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 7b)eim ynxrv+kx -tb)4uh1l, with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thh-t)v)x mb kxbyi4n+1r,7l euis.

A 21-speed bicycle has seven sprockets at tu8q ,iit ,pwn6n 9enp(he rear wheel and three at the pedal cranks. I pq(une,t npwn698ii,n 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 large front sprocket? Why?

Mammals that depend on being able to run fast have slq6 mc58qy5uzc ender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why yc qc65mzq u58this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow b7x if y5;wtfe20v1c2i9 nwwh peam?

If the net force on a system is zero, is the net torque also zero? If the nhf(mgq*j,e q.g. o1;g v/hw*boc 6xndet torque on a system is zero, is thh*nvo,fxq6 h/ .mw e.j1 *(c;gdob qgge net force zero?

Two inclines have the same height but make differwde)x5 : +yiyqix;)gd ent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom bexd;x+)eg )5:iwy yiq d greater? Explain.

Two solid spheres simultaneously start rolling (from rest) 15qmijoqjju;dh g q7 .t 6;ep: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 grq;g;eij56q:u.pt7qjj 1 hom deater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radd+ kba/riv2fn8n 92t6w juuk 3ius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? uj nn9/ w3t 8ua bfd2k26+vkriWhich has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. una-g6mth mdi8o1:f4 Yet most moving or rotaam:m6g-tfon1du8hi4 ting objects eventually slow down and stop. Explain.

If there were a great migration of people toward the 9k:bpakq m* t+mt-h3pEarth’s equator, how would this affect the lengthkpb-mmth*k qp39 :+at of the day?

Can the diver of Fig. 8–2 m g,gaol2jzbxn5yj2tg5 9n:9 9 do a somersault without having any initial rotation when she leavz5 m5a nx2yg9gt o j,2bljg:n9es the board?

The moment of inertia of a rotating solid disk about an axis through its ce+ aw0zaq1a3wj be: n(dnter of mjab ed+ azq:3a(w0 1nwass 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 ze*lzu9ln es8 5:pzq+a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or su 8szn9q5 :e*lzlz+petay the same? Explain.

Two spheres look identical and have the same mass. However, one ituz0 z- sadc03s hollow and the other is solid. Describe an ex-t zds3z u00acperiment to determine which is which.

The angular velocity of a wheel rotatingka-m pay,2bm0 on a horizontal axle points west. In what directip,0aabmkym - 2on 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 increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating b/b15)js ibj. .my frrturntable. What happens if you walk toward th/..b1bf5ijr m j rb)yse center?

A shortstop may leap into the air to catch ae4 e6 ,bdn0crr ball and throw it quickly. As he throws the ball, the upper part 6nber0rcd,e4 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 laz e4( ai imd-jo(ohb7,w of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways theaid (h7zm ooe j(-4bi, second propeller can operate to keep the helicopter stable.

  Express the following angles3c xhjww1gj*:54unba 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 amais8s r5f lf 8/jyha9-azing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in h8j9l8r/-fysa fs5 airadians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directedz1h7do(:sn97p apej1b2b gpu at the Moon, 380,000 km from Earth. The beam diverges at an a1p 1bpaz9onp 7ud (seh7:2gb jngle $\theta$ (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 ratpn1gsd:6, -wb9 le xq.i+il qbe of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is6gw. ii+lp :dxnq9lse 1b,-qb 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 child. If h n,te 6vv3ig.qxby 5*the ball makes 15.0 revolutions, what is its diametevynq3 6vx,bei.* th5gr?    m

  A bicycle with tires 68 cm in diame nnr wi u-8clrj( 8j.bg;be;d9cpekny6p83 w3ter travels 8.0 km. How many revolutions do the wheels maknli;836eurccb. wd8j egn- w (rjbp;kn y839pe?    $rev$

  (a) A grinding wheel 0.35 m in diamc70vp he o(eh iuc1r (k1oez0ox)b5-n eter rotates at 2500 rpm. Calculate its angular v(ou cv1ncieh0opbh (57k)ero 0z1e - xelocity 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 rev21zw5gvg:u yz:laid +olution in 4.0 s (Fig. 8–38). (a) What is tdwzv yu :ig5+z:ga l21he 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 orbit around the Shk sa- 4fjoj7kg*+5 hsun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poz5*6q s ubr;j2b rm9bfint
(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 4oka- g /7zuacrotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration 4a7z kuog/c -aof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abo2nan s m;7bhlw1e;-r out its center from 130 rpm to 280 rpm in 4.0 s. Dete1 2el;sn- ba7;hnrmo wrmine
(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 radiusfq5ix 8 q89j xkau*-napy7 yg/ $R_1$ 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 Moo-ug4iu, fp 5u 47qwuzgn, 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 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter oqpiufu7u -4g u,z g54wf 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 / d 2u,n*o/wixoyk,zhfrom rest to 15,000 rpm in 220 s. Through how xoyoh ,nuziw*2kd/,/many revolutions did it turn in this time?    $rev$

  An automobile enginelv89yj*yad;q bu4aj, o/f hn) slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “h -d-r .5;vtuyjyy 1kuhuman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.u; vu-t hdry-k .15yjy
(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 uni6ff9y6 ckm j1 m/uv.hmformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled fm/mmuv f6jh y19c.6kin this time?    m

  A cooling fan is turned off when iaz -okaj,b4oa 1s. 4ymt is running at 850rev/min It turns 1500 revolutions before it comes to a sa. azba k4 myoojs-41,top.
(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 undi m/v6m+-bq3;ttr vg iformly from 95km /gmq +3-6rvit bvtdm;/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 cz rn nqsq(6)1pc, ,pvrevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter,r pcn q),6qv p1(czsn 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 al15vz j s)yw2: cqzoqxoo u) 2(f:ny6wpl her weight on each pedal when climbing a hill. The pedals rotate ic26 n: ) z2wufow1qysoz5opjvq:( xy) n 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 cu;jy2iome5fs;afz* b (c+k5the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerte 5( kf+ua;25iycb mojz;*csfed
(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 th ,gj p30kdyd(2c6njnfe wheel shown in Fig. 8–39. Assume that a friction t(y pj n gk36cj,d2d0fnorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached t6gysbakua-/ )s4h3 iffao f84u a+t.zo the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in 4 ios/ a4 ktfby hau)6sff8zaug.+3-a 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 engin5 6d ;nwd3g jheal,j4pe require tightening to a torque of 38 d6aw5pjeldg nh ,j34; $m \cdot N$ 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 5j;6m2prskmu the axis of rotation is through its ce5uj mk6; p2mrsnter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wbz3p78t5 7spaiivla4+if 3ipheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignore5 v3 i7tlpbpisp 8 ii+7aaf43zd (why?).    $kg \cdot m^2$

  A small 650-gram ball on the enbmcr:) ku iwa4mlnr/-i:y( q+rsd:k: d of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calc: synmmriu/:k ibl+ ar4: cw)qd-(k:rulate
(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 conseul86m(wzmnc:1r a 8 ctant angular speed (Fig. 8–42).m8e1u lac(w zc:mn68r The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point o: ud +/7eudqzrbjects shown in Fig. 8–43 d+urq/ 7zd:e uabout
(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 oxygelscd zh 3:vs+)n 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, uniformg*,3vtseh6 xy)sk0k 0zi*csj cylindrical satellite spinning at the correct rate, engin)* s06kz g v, jtse*iysk3x0hceers 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? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0ee ou6rt+ 9*up.pue *e 9t6rou+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 bat,oo-sqd9exu *axg8 ;sgjw2 +5sia*w4 gwrfa9 , 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 tangentially on a small hand-driven merry-go-round s)np s e;7:wirnm ; 4a)6gollaand is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional :ei ;oa )lnn w)raml46p;7 ssgtorque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and i,l9ng / 94cdrw e/)hya :rvcpms eventually brought uniformly to rest by a frictional toc) /m en9r,vl9/ar 4 gdcphwy:rque 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 mkmy7nw:o5kxt)5 ai7 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 solelyz i.1 /zpyh)l-cmsgk8 by the action of the forearm, which rotates about the elbow joint under the action ofp 1gzkl )s-ihc./ 8zym the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade 6oy lahha)t 08can be considered a long thin rod, as shown in Fig. 8–46tha )8y60l aho.
(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 b5;1gm kw,h rml dm1p5or8a-3t 9nskz masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (ree,r.r z0 +cnmc.;kyufvolutions) and releases er+r;nckyc0u,f. .mz 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 -ns5r,yg 0g-furf wxz 1i32ina 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 de.(sc +bcx4(vwl 91ujt5 q ydghvelops a 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 radius 9.0 cm rolls without slipping f63weg k.5vys yz0+cadown a lane at z e5svy fyk+30.ag 6wc3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Su4e9r 8dc r;eocuk yh),n as the sum of two tedhr ;eucekc9o8 y ,4)rrms,
(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 agd; mz0s:q69 fsg0n/ 5kj hqh2pu3axo radius of 7.50 m. How much net work is required to accelerate it from rest t /s63o29jxk0qgh0d:n qsp5ugafmh;z o a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from restsa.j3i qs)cn9 and rolls without slipping down a 30n9iq )s.j3sac .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 verticallwwn5u5g:.)ke6- v ttk b*l,zicx dnk5 y 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 betix-gk)kzwbw vek 6n5n*d 5 : 5c,lut.fore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-k).ud ha:fgcdz8a(y2 mg ball rotating on the end of a thin string in a cd( u8:zmgc) 2af.h dayircle 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 cyl/lc6r . 3j7ufw; kxpnj7c1pw lindrical grinding wheel of radiur 63x.7 1lnc;wk clpupjf /7jws 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 platfr fvh)iq-x45i8 ujs l,orm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrjh)sux ,l 45q8-vfi rieases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the o +pbh1ip,id/wne shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck positip+wi hpb/1 d,ion. 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: iybfpa4f.lp0g-n)x rotation rate from an initial rate of 1.0 rev every 2. pp:g4lbn.y fx-i)0af 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 rotat2sm,-nilots-d z bo1 )ing around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered 2tbn d-s o l)m-soz,i1a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figue *to j7ypqf waz:d; 7c50cf.qre 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 the Earthjn a/w/gc 42 .omhw:ix0 x/wdy
(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 mn4(c zfyt9tgg.t- ;wdropped onto an identical disk rotating at ann9-tf;wcmgt(y.4t z ggular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 8ufix(; heur3at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pl)-q.t3axiqzc6hk w; v atform of radius 3.0 m and moment of inertia 920 ckaq )z;.ixw v6-tqh3$kg \cdot m^2$ 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-rounj5l iaeefl :*2d is rotating freely with an angular velocity of 0.8 aeij*e: 2ll5f $rad/s$ 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 evenbc uar8y3a6.s3c5e vbmok2/k tually collapses 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 abcarv8as.bk3 6y u /cm32 e5okway 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 in excess ofsu h8z27 +mc/qyeg2( rexf a,m 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 0/:kygkh5 g dg$ 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 2 f vfi8tz.s*1 9ssrzj3d1mlh 89wtfu rotate freely without friction. The moment of inertlzj f9 svd8usfzr91w*82t f3mi. t hs1ia 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-:s2 cbqshn.r 4-k ve6ym diameter merry-go-round turntable that is mounted on frictionle6.-keh bqcvry s4s n2:ss 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 thelban,2)4ug93l ndts1a u /pb p ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the sl)l2 buu1 dg 9ba 43p,tnn/apspool’s center of mass move?

  The Moon orbits the Earth such that 0 -3ield,x a, eh7eirothe same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the l,hxord- eliiae7 e3 0,atter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a22danh0 k za.x 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 uniform cylin vcthn4*2x4l3yq 6fm,)aabg hg/abc 0der of radius 0.20 m acquires a ,mqbg2 6ctna x3bcy4ah0*fagl/v 4) hrotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050z f7i1se0h5qq 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 s50sh q7f1zi qepeed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rearo *xehec17pq 5 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 p917/z h whj)cyh0golour Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If h9p)c y1/ hglhoz 70wjit 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 energ2b2fdw,pp: u 2znba.p/*do jty stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50p2p:db2d/ oztwp.2*buajf, n 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 am0j3 kwkshakgwhd 55h/*z(0 un $H_2O$ 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 surfacyylxtn9z+:298i:brfj fx w- ce 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 ces)36 ks,tsidv/y8q 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 the tip of the rod. Ass 3i d8/v,q)ksyscst6 eume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on th.xn odw (2 tt9ewyr.q z;er:i.e floor, and we want to exertxi .9zre :yrtn.ote.w qd2(;w 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 flat road is making a turn widn31;5 dn xyjmz/u6mwth a radius Tnx63j51 nz/yd;mudwm he 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 whie/ce3x ;,q)cyahmd / qrling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the tma3;q,x/)y ehc e/c qdorque 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 * h/i)mfexdh + vhb)ktc n+r:5and her arms as thin rods, making reasonable estimates for the dimed*m)h bk+r+/ei hxnvf t5h)c: nsions. 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 assemblyqp 5s09u4 2vued6a phe which consists of two cylindrical plates, of massa4eev96 ud phs5p20u q $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of 7 5eqphgw) 5wiFig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach tw5hq) ewg7pi 5he highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bb+1ayllv9 10a8e rpc kut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fyn4+t-+sgqyfqwr ): u:wh 6z grom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire?4w+:g: qwf +ytry)usq- hzng6 $\approx$    $rad/s^2$(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