Angular displacement is usuar1vcw u z v3n+vi4n-,slly express in units of

  Angular velocity is expressed inl/:*dbcc xzd/ units of

  Angular acceleration is expressed in units opyo//nx 4 g,)v) xganff

  A boy and a girl are riding on a merry-go-round which isxwp zqd ;-y0t7 turning at a constant rate. The boy is near the outer edge, and the girl is closer to thewqx yp -z;7td0 center. Who has the greater angular displacement?

  A boy and a girl are riding on a mera clb5iq1lg18h/cn7 z ry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the1nlqgb /8l517cz i hac center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning tlf43a6 ymyk0+n js x3at a constant rate. The boy is ntn+3l30fmy xyakj4s6 ear the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a,xubinco hej0v g35b p0z+ c150zfy7c constant rate. The boy is near the outer edge, while the girl is cuh5+zec bvn1ic30zj y7pgf0x50ob ,closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-ro3 xw(h3mhc6y wfy*3 s( ibm oi2v/su,pund which is turning at a constant rate. The boy is ns3 m(*hiw(h/mupbo3x3yy,vfcis 6 2wear the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is antq oubvj*w w ,0rfi,61 accurate statemeo,i jw1 ubqtv6,*fw0r nt?

  Rolling without slipping dep n/odvgk,-b4fx,hr9psgu c: : ends on

  Two equal forces are applied to a door. The first force is applied at the midpjh:n hzihd bcp( jn3*(j m24u8oint of the door; the second force is applied at the doorknob. Both forces are applie 43(ib:h u2nj8jh dzpj (m*hncd perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the door71z yvkl5 d:z(o4tvxvep n;) rknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts they vp;edlzv 4:rz(n51o)vktx7 greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firs2kxpo;pvw4z0spl1+( /ybgw qz l(*cy t force is twice as large ; /zqx* ppko(pl1c 0v(w2z yblg+4wysas the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's 5qsk z3l ./jprl*(mod *qz:vkresistance to changes in rotati k.* qks5lq/jvmd3(p :lrz* ozon?

  Consider two uniform solid spheres where both have hhat;v g ,d3v4kotxmfk*6r;;the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of*ft4h6kt r;dg ;3ak; hvmvo,x the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but zg3q*aig bo3i+4yu w+ one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that ofi y3u+bw*gizagqo+34 the smaller sphere is

  Consider two uniform solid spheres me/s 6igth c,uaz+w4m u2),:znp qo4m where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inesmn g hum ,4iao46z :qz/um,+)cpw2etrtia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If9d zor -eljl:: these are increased to 2M and 3R, what happens to the sphere's moment of inertia abo:j lez9rodl-:ut a central axis?

  If a constant net torque is applied to an object, that7o+tml7we3r.pzj l d9 object will

  The moment of inertia of a esp/ :kux 2+,b ajkme:2daf5e solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without sliaek+ /b m5dx:epkfsj2 e:u2a ,pping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whigvz :6-dc1t7c7g ( lo wh qsd3dblxu*(ch 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 kinetic energy of the bike? Assume the wheels are -v(x ltz6h3:lscbwd( g 7g1dc d uoq7*uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without s1ssj-do km 5k7lipping down an inclined plane st5skj 7k1ms o-darting 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+z fn hz/o sn5jnuc;cu -t1r36 rolls without slipping down an inclined plane starting from rest. The angular velocity of the 5 orf/;u cujncsz613nt-nhz+ sphere at the bottom of the incline depends on

  "The total angular momentum of a:yqt*ihmn t ;y1lt7r8 system of particles changes when a net external force acts on the system." This stateme7til; :mr1t *8hytqnynt is

  In what circumstances can the angular velocity of system of particles chanj0bjyhs 9rx p+g*o 6c6ge without any change in the system's angula*g6 hby6o9 c0jsrjx+p r momentum?

  The Earth orbits the Sun in an elliptln qp,zjzdz8hasgb53 we wf*+ :*e6 5oical orbit. Ignore any friction which may be present.enj,we+ 6fos wzb853dzg* a *phql: 5z What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit.)qzp8i:.os4 6xv pb5jyurv.k As the Earth moves close to the Sun, then 8ky ppq)u.zxj6i4. orv sv: b5which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullingvdtbnf8:oo7.u0 *d t g in his outstretched arms close to his body. What happens to his angular momentum about the axisdt do7ugof:8n.*bt0v of rotation?

  An ice skater performs a pirouette (a fanqzc l vyv*m)82 r,f(0z0c wkwst spin) by pulling in his outstretched arms close to his body. What*yrf0lw v,k nc(w2m zq 8)cv0z happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling )kud.)d9 vouq8- pwo0;tr e3eoe)mtzin his outstretched arms close to his body. What happens to his moment wvuo))m 0-3rz oe9keoe;dq)tp t8 ud. of inertia about the axis of rotation?

State the law of conservatio,)3q ev:c ub,5s4tuxw zr,uh an of angular momentum.

  What arc length does the Earth travel in a muw6v+cz v 9l.three month period in its nearly circular orbit about the Sun with+zv6ml .wuvc9 a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does p4h 9:1:y4sjuj9cif .seawtn the tip of the second hand sweep through in 3 minutes and 45 seconds y:c4 j1st 94feip9wjn.h:sau?

  How many rad/s is 25 revolutions per minute equivalent toi je c.gle6hraay3jg-zcsa2 + z( :)r(?

  A bicycle wheel rotates uniformly through 2+ zz:pb uj1/ohe9l/nq.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatiouoez/9 :j bzn+plq/ h1n?

  A pulsar (a rotating neutron star) emits pulkc ./z.oxh8 88xljg :qcuqkc7a q 3d8sses at a frequency of 0.40 kHz. The perxc.z7qhadc. :3sok88 qgkqj/8ux8 l ciod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tur oa8u3)i:px7nn gl e(on in 0.20 no7 a(:o3leui pg8n)xs?

  A wheel of diameter 26 cm turns at 1501f.nv67nyvyp 0 rpm. How far will a point on the outer rim move in 2yyf6n 1.nvv7 p.1 s?

  A bicycle wheel rotates uniformly through 2.0 revo8z.*ykq mjlsf98mdu7y;skf*lutions in 4.0 s. What is the average angular f9*ms*lud;sy8z q7k myfjk8. speed of the wheel?

  A bicycle wheel rotates uniforc qlyyez65/9h mly through 2.0 revolutions in 4.0 s. What is the lin9 6lzqc5h/yyeear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance ofaf3, ex3hamxj 0(6 ep3+nxyco 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fas a xp33xy m6xc(0fo aeen3jh,+t must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.59 6xz k/t) ziho.l p7erqhb5k0 m is rotating with a constant angular speed of 2.0 rad/s. What is the liniolbqz7h.zrp5 xk)khe9 t/ 65ear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. pbp0m*0a8te 8 xfhfn1If the motor rotates at the rate of 20 rev/s, what is the approximate linear sp t mp xfh108*fpe80anbeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speedwl3 2oa0c3rxg*xx xu/ of 2.0 rad/s. What is the centripet a 3*wlxgcr0xx /x3o2ual acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimetpch*6ksyy2i; fo )a /tdg6 ay4er of a bicycle wheel of diameter 70.0 cm when ot/ 4 af2asd hg ;py)k*yyi66cthe bike is moving 8.00 m/s?

  How many revolutions per minute (wn6iot)ndex9q-y4 / 3 -twqu5uhi nl2rpm) must a circular, rotating space station (r = 1000 m) rotate hq-e w456ny/i nwxi to -utn3luq9d2)to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cir)nbf6ks/; qu)e cy ,qwcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction)su;)/ wf yek q)c6n,bq is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circularwe 5g 2;rkak,k curve of radius 50 m with a speed of 20 m/s. The maximum centripet, wkrkgake5;2 al force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the e otnswed9l45 a6b:z -fnd of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass haf 5 t:o-d zwensb4la69ve if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without y0j 9d 9dslm;geafg1 b5e:q( tslipping 10 m down a l gd:5aegt(1dejfb90l 9y ms;qane 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 anfyrsc gue8m10 6:(q.rp .a:3 uzvzz ,x6cnzq fgular 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 ::fa7q, fq:mdn a f;faangular 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 doesq9pss ( 2csfh(rlfq, )(:i fks a 0.300-m radius automobile tire rotate after starting from rest and accefs)p sf(2:rsq(9ihq f( k l,sclerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelhdf2cf1 mc-9n eration 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 constant angular accelexj gp0k mdu(:+x*8d5mpcm; mwratik;wg( 8dj +x5:mudm0mmcppx *on 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/03gtp2za d.css while turning throud3c pa.2z0tgs gh 2.0 revolutions. What 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 674sbb ky7 + aqvugyc5tm+b72av5udl rest over a distance of 115 m. What is the total number of revolutions the wh27 b6 qlym4tvvg as57+ay kbdu+cbu75eel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r*e wtxor:j ee-z82:a piha t:+est over a dista *ja2+h8x:ae e:tezrp:i-t w once of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 9b+agfk 8ugf1r 1x di:g zu*l,8.40 m/s to rest over a distance of 115 m. How long does it ta ax1 b89u+*iu1 zfgl:,gdgkfrke for the wheel to come to the stop?

  A centrifuge in a medical laboi pcj po-) ea)6f0fsu) .vcr.yratory rotates at a rotational speed of 3600 rev/min. When switched ofi .fsup c-)fy6 j ov)e)cp.a0rf, it rotates 50.0 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 tighteniq0ktu(p sw(q jg2;,n zkpyd9d j-(b,0ywz np (ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force,(wsk9n w(d(z2uzg dp kn 0pp;-(t,j 0yqbq jy is perpendicular to the wrench?

  The bolts on a car wheel a+exp2y*7dbp 7 dk8pa sr )lj3require tightening to a torque of 90 Nm. If a 30 cm long wrench is used+)pljy27br 87a3p sdpxek*a d, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine mz-x d/ lyf:y 2hgpz3pe.6-tjrtia $3.00 \; kgm^{2}$ 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 is at the origin, mass 2m ise), 4ma*ql1ubhj;, b jyoa:ji at x = a, and, mass 3m is ayql ;abj:ou,* i 1, bhm)ej4jat x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mas+-q*81voc y dne3pnlu(t( vc os 10 kg is pivoted about a frictionless axis thought 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 rope wrapped around another sectdq-l( p+cv8ne3yco*uvotn ( 1ion 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 t , 05* e0mgb q3-arseqwjtct0mass 10 kg is pivoted about a frictionless axis thought 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 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 530tqg0 metqrjc,-sbw0 *t5ae .0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at oni36 1c cqs2cijwls1 )be end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a rq 2lj3scic1i c16 )wsbod about one end is ML2/3.)

  Consider a bicycle wheel to be a rim+k e/wpazm34 4)gcy lng of radius 30 cm and mass 1.5 kg. Neglect the 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 doe3pk 44+y ewmca)/ lgzms the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pud)uky1cgli*s7(8 p :b7ibjef lley of mass 7.07 kg and radius 66.0 cm. What is the ad e u7 gcbyis8kfb:l7j*p1i()ngular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskkwc3qi lfzh-.)+ ,1swoj3qfh pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration oh3z)k, i wl-jc.ff1wsq+h 3 qof the mass?

  A rotating flywheel can be used to st)w :tb0oh trtm06cee-ore energy. 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 b bbc*iuu 7sn-:t8)ek of $5.00 \; kgm^{2}$ 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 0.01bd /fvj5x2o2lz f g(-r,r cj0k0 m starts from rest and rolls without slipping down a 1.0-m high incl02z f,jrc/j xrv-5 ofbgk(l2dined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg an.ow 6qq 6bk/l55zfu pbd radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before cob/ lwuqqz.5ko6 6f bp5ming to rest?

  A hoop of radius 0.50 mn6 am o6ezy bllg4c8,0 and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast ilb,o e60g cl zym8a46ns it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 r0gn 94co m7nqkg and radius 15 cm rolls without slipping down a 35e incline that is 7.0cgnm on q79r04 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 momentus spi2e6w1yp8m changes 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 moi fdeb0 *5z(tomu ;s)dwxjru:u ,c6; mment 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 with arm/ingt5kbf v4pc **2styv b/5os extended has a moment of inertia v5vby/2bfs4p/* t ogcti*5nkof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?