Angular displacement is usut:c py rrw (k8sz8-m-5gzaa8ually express in units of

  Angular velocity is expressed in un7p2n nky-icn+n tpjg*-8-gw uits of

  Angular acceleration is eyoh na467a3gj xpressed in units of

  A boy and a girl are riding on ba0o4f9pgxq,le p:y: a merry-go-round which is turning at a constant rate. The b4ep ::pagy0x b9,lfqooy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridb. 4x1znyao7,xr uyn9i m:xzg(8tc lg:id+ 0ping on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular spee:x iz 1yyptr(c0nmzgo 9d8 ,4in7.ugb al:+xxd?

  A boy and a girl are riding on a merry-go-round which is turninkxage0:c9- mq g at a constant rate. The boy is near the outer edge, and the gir:ka0q ce g-m9xl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whcoa 9q,l.qw4gich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who hcaqgqo 49w ,.las the greater centripetal acceleration?

  A boy and a girl are ri(x/ gpp m (;)uwoguqy:ding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer too:u(p qu;p/m gw() gyx the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the f:4i3b a1qmuw;ck (yah vv-d5s g-g2 uvollowing is an accurate stuv34-:b2uq(5gv;gsdamvi wy1 k hc-aatement?

  Rolling without slippincn/us17yb9 rt 3ujgo0 g depends on

  Two equal forces are applig6zd)bbhj;fjp*h0k vscltw7/ / x1.med to a door. The first force is applied at the midpoint of the door; the second force is applied at the do6khjbf/)1/0vcgw l;hs7*pz j. xbt md orknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. Thp7 a7 fvlzr i3b)rg4v,e first force is applied perpendicular to the door; the second force is applied at 30e to the plan)77, a3r4plvg zrivfbe of the door. Which force exerts the greater torque?

  Two forces are applied to a doorkno252(/meulwu ej g5osvb, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of mugjol5 /52w evs( ue2the second is

  What is the quantity used to measure an object's 3l3)7z sgzkewresistance to changes in rotatie 3zw)sl3k7gz on?

  Consider two uniform solid spheres where both have the same diameter, but onehj/s gx1775dzodt8 l h has twice the mass of the ghl 178 /7dhdoz xs5jtother. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same5p ntdcsyt)6 fj6wy39 mass, but one has twice the radius of the other6f3jt)dcp 56ty syw9 n. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solidrxszg7gd(ji*)-p iz ; spheres where one has twice the mass and twice the diameter of t- i(*s7rdi )pxzgjz;ghe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are inpa0 -og9-3gg*)ot mry6tb lzfcreased to 2M and 3R, what happens to the sphere's --*6glmba 93ztpoyog ) f0trgmoment of inertia about a central axis?

  If a constant net torque is applied to an object, t1ib,q qds wf/1hat object will

  The moment of inertia of a solid cylinder about its axif2 qjx2mf:g o2y;w*nk7-nep js is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatio*f2y7j:qenjmk ;2gxop 2-nf wnal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel ool; j,o9msw mg5y98 tx+ xy;oxf which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kiwx slgt x; 99+ ;,yx5o8mojoymnetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radiusbzye ) jh+.l05pozm7u :m hi-e R rolls without slipping down an inc+m.oi h hlbyz75eepz-m0) u:jlined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withou0e:fc od5g 8m y)ugla10cepm:t slipping down an inclined plane stac10 dme8f05c : gp: a)elgmuyorting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net 8fx 0lt regb, 35yefj.(6sjxz external force acts on the system." This statemez6es 3b 0.(l fjej 58,fxtyxgrnt is

  In what circumstances can the angular velocit16yp(fo2e x c:d: jbvcf9yt p*y of system of particles change without any change in the system's angular momety(jc:: f vfdp9 b2pec1x*yo6ntum?

  The Earth orbits the Sun in an ellipticai6 1se8u qbsla24 ;jsrl orbit. Ignore any friction which may be pb1 28 sijaql; us4ers6resent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As thvm9ozi2*3ke .u qwtww 5sxf.6e Earth moves close to the Sun, then which of the following best de 9k3i.2 6u5ztse*xmovw q.fw wscribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by 0 y-zlxx l0(rqpulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotatil0l-x0qx yrz(on?

  An ice skater performs a pirouette (a fast spim,y9 t292 tlexo 5tmpan) by pulling in his outstretched arms close to his body. What happens to his rotationt2e,op9yxl tm5amt 92al kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched )/wp-xk3c+xbdfz1c yacq u 5+ arms close to his box + w3y)ubc-fa5k1+q/c z cdxpdy. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentul+jd rk+ra;vil 5,xt -s*oaj0m.

  What arc length does the Earth travel in a three t3pq r /4xst5uss5hgp c6d;e(month period in its nearly circular orbit about the Sun withxs5hrp;c3gses (d q 5pt4u/t6 a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0. y(zrb2waqg /130 m. What distance does the tip of the second hand sweebgzq w/y(1r a2p through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutecbuouf496d /j equivalent to?

  A bicycle wheel rotates ue 2um6 tj;t piix+2y:wniformly through 2.0 revolutions in 4.0 s. What is the frexut2: i;wt6my2 pij e+quency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsebw 1 150pwo2safmac 6xs at a frequency of 0.40 kHz. The period of its rotation ismw11 50bcpaawf6ox2 s

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.:- 4 wuqng8hfz20 sqguh -w:n84z f?

  A wheel of diameter 26 cm turns at 1500q .y0ncww) +lv rpm. How far will a point on the outer riynq 0 .wvwlc+)m move in 2.1 s?

  A bicycle wheel rotates uni:rq wys -ru.q;formly through 2.0 revolutions in 4.0 s. What is the average a ws rq;:qu-.yrngular speed of the wheel?

  A bicycle wheel rotates uniformly throughk1w3.s 7d r+rsf t3ehi 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from thes1h t7 dk rrei3fw3.s+ center of the wheel?

  A cable car at a ski resort carries skiers a distance ofe-py x0wq26 b+ katfp(y qiw55 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the twkxpiw(+byeq0 52-6yaqf tp 5rip in 12 minutes?

  A wheel of radius 1.0 m is rotating witp .p f.mt* i4mg9mpx6mh a constant angular speed of 2.0 rad/s. What is the linear si46m xtm.p p.*m mfgp9peed of a point on the wheel's rim?

  The cutting cord on a l3 1(l vu 9zcrkm4vq5ygas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the appro(kcuql3 5 ylrm1 vv4z9ximate linear speed of the end of the cord?

  A wheel of radius 1.0 m-ljcaqo6s:b* +cz 34c oa8oxm is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's6ojz c+ mc3l8o-cxasq *ab:4o rim?

  What is the centripetal acceleration of a point on the perimeter xk zob/:gy,7jo3qus4(i rqj* 9o ;os sof a bicycle wheel of diameter 70.0 cm when the b/bu zj;g i(os:o y4oqqj3rsx7 ko,9*s ike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cilplc d8ou2 9g/zxj +c1rcular, rotating space station (r = 1000 m) c2u 1lczp d+/9 jg8lxorotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat c:y;(po rchf( h9 ps5dtircular curve of radius 50 m with a speed of 20 m/s. The maximum cent hp5:tcy(s;fd p(9hro ripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a speed y6m4- xl v1kbw-i3 m)sho+clq of 20 m/s. The maximum centripetal force (provided by static fwh4q-lx y +oi13sc mmk-l)6 bvriction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is s-j2op;k2ynu u1 ,pb9qu :kmdfg/ .hbwhirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, tb jpuf po s.gkq9-1um2;hd:y2nbk, u/hen what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10bwodka.m4a fbk.gk ;st(*xwyzb8lt ,bw;70: m down a lan(a,k:yt. t b8wo f gk4wdms*a 0;bbzkw.;xl7 be at 4.3 m/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a constant;gb0+ s:u kwcpso3r/t angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constant angu8- /kqqy-3 wnwb tm/ltlar acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m radiup(rze:5uarb g- l b30us automobile tire rotate after starting from rest and accelerating at a co uzup e 0b3:(-brlrag5nstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has tgu4jh9/f79 yypvq;cd8( xj)yeec :k an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constange; qxzh 4 iyrrm:3++enek99vt angular acceleraey g r3q9n+9xm:h vk4z;r+eietion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while tur8lwsf q 1x2rt-x;ob8x 2ip y7wning through 2.0 revolutions. Wo-wlx1i;x82yqxw b 8tf 72srphat is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over a6a18rxcyb zi8) q3;rgpx)nsdfo 3ds) distance of 115 m. What is the total numbeid; o6fz)r s xgaqx1rs3ycnb3)8 )dp8r of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 lt92ci94pdjys g o5.u m/s to rest over a distance of 115 m. What is the angular acceleratio9dtj9ypgs4c i ou52.l n?

  A wheel of diameter of 68.fk n 8nj0uh;l5wdv*v+0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115*5h uwdvn8l;f+jv k0n m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at 4sk9wwa3f klbv90u:yjfl 3x *a rotational speed of 3600 rev/min. When switched off, it rotates 53 kjly u0x a9wsf 9f3w:*bk4lv0.0 times at a constant angular acceleration before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require tightening to pl:(ao b(2 o gbsupxo)., -tvla torque of 90 Nm. If a 30 cm long wrench is used, wu2g -vl()aooto,blpb x:(p . shat is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighteni,9gveya99;ep1 kor(; oos bk:l x9l ojng to a torque of 90 Nm. If a 30 cm long wrench is u;9(vol ej:g,;ebplyoxk9aroo9 k1 s9sed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertzo0x.p9jiwzf7.ysjlgf3 p7: zg*i7 via $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m isrpdwgop04 h 74 at the origin, mass 2m is at x = a, andr4p4 p7d0oh gw, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoubxyz) svg7c ,.ght the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second vgx,)c .bzsy7rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about aj;4:gxf 3t v cp *b-p rv.;2qakvho 0x08khxht frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, ex0gpfh:4aqhktph2j c3;bxov ;r 8. x vkx-t *v0erts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The m:ii f k8f:+(.1ol.q3c1jhp o6cb cma-ywflw rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular accelef.-oq8wf.:oakil+wc: phfc icym1bm(lj63 1ration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 (r7 0nr vx:rsvq8ez1xspgn u:o2b 6b/kg. Neglect thsq:v2rzr bxeg 8b07 x/ov1pr: nu(6sne mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictix -.o0cfb4s.sb0un yei8o ( wqonless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of w4xifs8- .cyq0seb obon(0u . the pulley?

  A 1.53-kg mass hangsk8fk vpmg2 sg179(jfwynm2 8s on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cmm9jv(82kpw n2fg f1sy7gk8sm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy-:yo3r+kho(e mni7 0grpxb4y u 5bg7p . If it is required to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of inertia of u1 .zhm(4+5+ddpyuxyan1o qi$5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and radius 0.010 m starts from rest andt2-/ ov k7gs acy2hwj0 rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphey7wg22 cj-k vao0 t/shre when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed fagwlx dt+l4,6x r)k8 of 10 m/s. How high up an inclined plane can it climb before coming to reslx+ rdg,al4k)6w8 txft?

  A hoop of radius 0.50 m and a mass of 0.20: zs/ rki,fb+gvd90xg kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 kr z90gxs/b+,fg i:dv m?

A solid sphere of mass 1.5 kg and radius 15 cm( jz;0dh*jw ue rolls without slipping down a 35e incli;* (ez0djuwhj ne that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum c p 9a ,(sonwbz 83cbkqrs:oj79hanges by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a mof1 0;j yy.rjlzment of inertia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s p+,rs d.nmz/ khf n5nvz ),+inwith arms extended has a moment of inertian+ sm ridk,h,.vpfn/+)5 zzn n of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?