A bicycle odometer (which measures distance traveled) is attached near the w0 jmhy(slj0)f) v5, dn+obongheel hub and is designed for 27-inch wheels. Whatj j )0l0n 5noyb,o(m shvdfg)+ happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constan(+kof cu14uo c*4pylp9x7 dbst 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 tangentic 7(s1uxuy +o*dob lpkp4c49 fal 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 angulllfb obom 6v mk .:est(l4-q*yb9a09oar velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explsnpvulyc:z 2ome gt/ w 3((w2/ain.

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 ( z;+ajpnv4swhands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer+p4nz; w js(av this.

A 21-speed bicycle has seven sprocket h)v25ytwix5y b3qagd yr9/ t-s at the rear wheel and three 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 hardx5/hy 3ytq ) wgbtadr2y5i-9ver to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have s xu:7gv. 24 +o4lcphvf-amerblender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of masvb4frmh2.4 +cog- xev 7pa:lus is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bej5 h 5msgl/u;xam?

If the net force on a sys1qt5toj8 p:wcjzyf(.8lury+ r4wa w 7tem is zero, is the net torque also zero? If the net torque on a syste(8u w5r1.+8 py j7jz:fttlac 4wy qowrm is zero, is the net force zero?

Two inclines have the sami vna9z9xqw3 ,x2 lso,c(q3cne height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of(aql9cxw,nxc qz3ni 2, 9sv3o the ball at the bottom be greater? Explain.

Two solid spheres simultanq7-mdo la6+c xcc5s7 neously start rolling (from rest) down an incline. One sphere has twice the radn cq s7-ca5 mc7xdo+6lius 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 kinetic energy at the bottom?

A sphere and a cylinder have the same radiua7*v qb /ap3 o2.5e 9fap9wuy)krnq rps 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? Which has the greater total kinetic energy at the bottom? Which has t/w2)nrp q oubvp*rf3aq 9aa7yp.5k9 ehe greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or ro-qwsfi1 6e 3nftating objecwe3q 6i1fnf- sts eventually slow down and stop. Explain.

If there were a great migration of people toward t6:r z f,3swqyll )9v-ta6livzhe Earth’s equator, how would this affect the length of the da9 ay:3sv,tl)-rz6l6l vf izqw y?

Can the diver of Fig. 8–29 do a somerf-ug (/hv/x,/lcoyidsault without having any initial rotation when she l-lu/f cyx/ iog,vh /d(eaves the board?

The moment of inertia of a rotating solid disk about an axis throughav/;03jhucsyhsp 9w ) its center of massyph/ 9svwcjh0u3 ;a) s 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 rotatiwo20erzpk2.r ng stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocr.e2r2zp 0 kwoity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hol;.qcv+p2rrcjmj3 p1b low and the other is solid. .rj;3rbm2 cvp jq1+cp Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointsa ra rc 0s/pm4fp8p:d3 west. In what direction is the linear velocity of a poi : p8a4/3a0 rcfpdpsmrnt 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 turntab due.4.t42 ono+acsz ple. What happens if eun4 . sat4pooz2.d+cyou walk toward the center?

A shortstop may leap into thmvcod lv+ laa4:xe )4i;1c a+g;koz y9e air to catch a ball and throw it quickly. As he throws the ball, the uppaa;; vlm la4zcev)oic9k++o: y41 dgxer 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 momen t vfr6u*v*v3btum, discuss why a helicopter must have more than one rov*v6f*u 3tbv rtor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following ak8 ig(cv ..llp+w3ywlngles 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 coincidbnw12fbze o )n3y,7xd ence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.3,7oz2ynnbf ) d1b wex
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, i;zwam 5p+ :maks)j 5s380,000 km from Earth. The beam diverges at ampzm si):j ;+a5ks5w an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender h /,;ztb jnyp82i7z lhw7heb8 rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow h7e tbi8l7w 2 b,/zzhnj p;yh8to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a leve8w 51oj iyum*fiql;b -m4:uvzu-,evzl floor 3.5 m to another child. If the ball makes 15.0 revolutions, what iseu:y5--mfj z loz 8m4i u*iu;bwqv,1v its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolution:(w n4y -9uym,i 7q lf(vefy ixy+ymi8s do the wheels ma,qi 8fxy9i 7(y em:lfy(vuw4yi- mny +ke?    $rev$

  (a) A grinding wheel 0.jt0;ph8l cm a135 m in diameter rotates at 2500 rpm. Calculate its angular velocit;jh0 1ltc8p amy 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 revolution in 4.0 s (Fig. 8–38). w7xcer3nra i+ osu )u 51sq;x4(a) What is the linear speed of ao +ei71r ru3x;scnx auq54s)w 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 vz7(l p;;+2x 8.*jaoadyjz/)w6a j ftmojwzpgelocity 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 spy2a .ay9* +stpicouf 5eed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge royeeed15rj8zo 0 .sul6 tate if a particle 7.0 cm from the axis of rotation is to expedu r l08yeoe61 zj5.serience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centeg: )vt8rtdm )u06 rdyfr from 130 rpm to 28udmgt0yr8 f):6)tdvr0 rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius vtb8r;mh /j 4si/b 2iq$R_1$ 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 Ap r:wqo8kze*g7ollo 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 s wqe:8*k 7ogzrpacecraft 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 fd8zaz g+:0ic *x ihkrjzz06f,rom rest to 15,000 rpm in 220 s. Through how many revolutions didfg8x0 h+ :j dz6ii,rkzc*az z0 it turn in this time?    $rev$

  An automobile engine slows down from vxw:jkrn3 u /+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 *6sdfn0.4or4 uonmc s a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.n du*04 scofomsn64r.
(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 ac;won-p jxb: jww.)xv,celerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point o)bonw wpj. x:x w,jv-;n the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running eg, eq o+u8zu)at 850rev/min It turns 1500 revolutions befg8ze +),ueuq oore 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 revolutionc7ca1, fy, crvd1hrv/fh *5 ddeoz8k*s as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 md5a*fck vrdo*/1hyrcfzdc,8 71h e, v.
(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 makem4 mxxih-+c0q/.nc mb 65 revolutions as the car reduces its speed uniformly from 95km/h to .mmhx+ xbi /q4mcc0-n45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing at;7bm/6mq scguj +9dv hill. /7 ;bmd 6j uv+gmcqs9tThe 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 55 N on the end of a door 74 cm wide. What is t :erzaqy:):nv m/,bw-xbz m7qhe magnitude of the torq-)nwz,7xqa bmb: y ::eq/rmzv ue if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the whk)1++rrzn-loiq3 k kc8u-vj ceel shown in Fig. 8–39. Assume that a friction torque ofrq1k c-v + zlkrn-+3j )c8ikuo 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacheddq7s m vm- s)avos7p ot*b9;2g to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculq-v)2mbva sms g7*9od7spto;ate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine req8 yz 0 g2xwfbfp5*xblchck;/ 6uire tightening to a torque of 38w*hx2 zkp0l x6 c;8 b5fb/cfyg $m \cdot N$ 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 radida13b4 ry kx)/1cd tjzus 0.648 m when the axis of rotation kt/dzy rj4d1c ba1x3)is through its center.    $kg \cdot m^2$

  Calculate the moment of inertgys*v ); nyx;7zil,btia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass) l,yyv; i7tb gxszn;* of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is j g,ffn ,o;nx2rotated in a horizontal circle of radius 1.2 m. Calculat,nxo; ,jf g2nfe
(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 aw:jbn2*-hp;fwi, lqz bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clab :;nhp * -wfzwiq,l2jy is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8)*ye5p2b zi8zey try e) bj/-j–43 yb8r)z zy/)jt eyebi2 e5*j-p 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 g4s:: gho:vg1ng(c fctotal mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, e5jpp. c9bw3;g ob0dnc ngineers fire four tangential rockets as shown in cp cn pg3b905d ;b.wjoFig. 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 cylinxmy: x9u:)li4wq6jj6juq n(tder with a radius of 8.50 cm and a mass of 0.580 kg.4qjm )tlu wnjyi( uxj :69:x6q 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, ag w b /:l/sa9biwz;i4iccelerating 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 aheu/xv5p/.7 ahz :6mfucbv0a nd is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, fepav7m:.6 /vxuhu0h 5 baz/cand 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 rotatjvm i(ppz .7g2zg(e,iing at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictionaljg, (p(vzmigzi7p.e 2 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 accelerate krz0i xsf4s1(s 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 gyhz0p+ w+w8igc f 5)0qhr7spby the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball iczg qhf8p0i+r 7w ypgw+0h )5ss 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 bliam+s8p t gh9,hy zd5m.*0ytq6nddb4ade can be considered a long thin rod, as shown in Fig. 8–4g*qt5d h iz b+ s.ypmd9,myat4 dh860n6.
(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 +vs+; :t;+ uxdb psq4afx)qjbconsists 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 thezz:q1una pg licm u +u oj(nw0-5m5j+) hammer from rest within four full turns (revolutions)0 +1ailu 5 nnmjmcqg:)+ow zjupu-5(z 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 mome6uii j8u bg;a,nt 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*jk-q7ovh48fynh afk,l-jt: of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 742- h6djbgdc ld ksh:6.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.ch46 ds2k6lg ddjb:h -3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to tpbx3qps1c ;r 7t-zxl4he Sun as the sum of twsqxrzcpx- pl;1 3bt74 o terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg9kzz,e8y ,20a mx2bouiu, kh a and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutionx92 ,akz io2 0eaumzh,bu k,y8 per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 ko 3i6.o9c ah+.ot7 mfnwrbtr 3g starts from rest and rolls without slipping 97+moor.cfarnio3 t3bh.t w 6 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 bala3 . zvr/u*gski9 lzxfpq8n +:knced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upg zkzi 9xsu* /8prf3+k:q.lnv per end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a chxmgyvu*s2b4r647r- 9zl (w*tjtnuthin string in a circle -rbnx * 7cty9l tzw2umjs4r u6gh4( v*of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular6uyp *obftc0r,ag5)lflzu (1 momentum of a 2.8-kg uniform cylindrical grinding wheel of radius ,5 )rg cutff(0zul6bl*yp oa118 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a r;h j7 f6umbchzdx 1;w7ate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decx u h;fz17c bdw6m7j;hreases 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( qt) ovojf:3vx-5 dpv–29) can reduce her moment of inertia by a factor of about 3.5 when changing fr :dvp fxv j5oqt)(-3voom 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 rotatio6 xhc yr 9,ix+noo2ez-n rate from an initial rate of 1.0 rev every 2.0 s to a final rate oyrx-o9x ei2oc+6zhn, f 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 vertical7+oe.vc hzba 9i+em2 s 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 f2+bac 7oveh sz.ime+9requency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater sp/wyvh)/qb8c zfif 11 pinning 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 Earthh/ e0c4wfe9c j
(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 dropped6pk 8 -flit0im onto an identical disk rotating at angula kml6f0i-tip8r speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.3;;w:mga skbs4 $rev/s$ 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 platf(oi3h niydb ak a).5-5*cdtbborm of radius 3.0 m and m -dab c5i bi5(byndh ta)*k3.ooment 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 arb: j6c d c*-caa42hjfreely with an angular velocity of 0.8 *c2r jh46c:jab adca -$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half i xjm,l2 o.qfcb(sc8x3o f8d3c ts mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost coxx clfm b3oj.fdsc8 82q,3(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 in excess of. yxa.0jpzu)t 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 6gze9qlaez c8(h3 k;qj cq1,g$ 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 rotateoqhvw- x+ 5r6y freely without friction. The moment orqw v6-xh y+o5f inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round l de;bf n;wvg5mbt ;bv 1;:u9w fw+na4turntable that is mounted on frictionless bearings bfvm +vw 4nw;a;dwe;g;u9 5lnbbf1t: 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 the end *i(6ynt.leo yf syi4 c/2vc b*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 spooly/f62bsevtlcy c*yii.n( *o4 ’s center of mass move?

  The Moon orbits the Earth sucd j*.vc8p 1p rxfdl)ob2.ceatxelua. /c 3.g0h that the 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 latter case, treat the Moon as a particle orbiting the Eart xpcpbo/.1laed j2 ec)a3x uf tlv8d0.rg .c.*h.)    $\times10^{ -6}$

  A cyclist accelerates from rest ataeaxq3(- fm lj2:f s2qelmz537 j ne2k a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.2(:q(vp )x nt(csrmn+ o0 m acquires a rotational rate of from rest over a 6.0-s n+q:m(s)vx(c(to r npinterval 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 0.050 kg a mv1jganhj0tk(oh q1xz/)t 30nd 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 1aj gkzo01j) (3tvt hxmh0n/qto calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the re iia5m sy5 * emq5hcbr3c049nuar 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, were rotatutt+mnq 34xzk 7n r0e(ing 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, wq 4untt mzx7ke3n+0(rhat 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 automkr15ls2n a9em obile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has1 r5enl k2a9ms 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 “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 illustraax *vphj7-6lotes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at s:hz5oyjv 3-rn9; dkys peed 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 (fs9w8iw: d -h0 ngixoM and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the inh-os(8gf x90:w diwforce 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 stwd jm3 0;m*nxqanding 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 m*q jnx0;wdm3height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with09fr0 7xxnje x a radius The xxer0 f 9nx7j0forces 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 anb 3 .i oj*xjfsxeitd1mzx +c+d,y6j1;d begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this f 6z3tm,id1xji;+x+x c. f1 ojdbsje*yeat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder an6f+l 3ac9qimid 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, and with arms held tigcfi+a m6 9l3iqhtly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates,k. )x+th mhz9i of x mh)t9 z+hk.imass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loo jiq8j i/mmxf9i8s4 f(mjlj9)xx; (hoped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest poijq;i( j9xj4ijo() mm8x8flhm/f9is x nt of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume* duaiz29a 5hn $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the 6incepu-q* e6,glj7oj .nk92ots mresk n(9. car reduces its speed uniformly from 90km/h to 60km/h Thq e g6ot9.l,krjk2p9c *n(6 sn.u7jnee-som ie tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s