Angular displacement is usually express ny1a:s38 sjcvy c, dl*)w.dxt in units of

  Angular velocity is expressedqxuoex3y0 s5oz0 8+c ,zu c.bt in units of

  Angular acceleration is k )eenzp( :ao2expressed in units of

  A boy and a girl are riding on a merry-go-roundn)cv+0xya:7x 7yksvc which is turning at a constant rate. The boy is near the outer edge, and the gx)k nyyx: v7+c v7cas0irl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round wf+ :fqvf5n+vxbc;r;a hich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has t:;q v5bvf+a+ xfcf;rnhe greater angular speed?

  A boy and a girl are riding on a merry-go-round4l j2wlw/z7 wc which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who l2w wjcl /wz47has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant 1qd3h0ybc(gg p2 d/npzc31hd s x58is rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleratios8h211 c ip 5gxb3 hg n0qsz3c(ddp/dyn?

  A boy and a girl are riding a merry-go-round which is turning at adp .a.szixi4pe - o76a constant rate.s ia.dpo46-i7axpz. e The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rg*hj( ps;/1mhpm;bin otating. Which of the following is an accurate statementj*mg/pm;sn(b1i ;hhp ?

  Rolling without slipping depends ozaggledll f5ok 02p61:c 1n72 yk sl,sn

  Two equal forces are applied to a door. The first force is applied at the miygrgaw0. (my0* ha)wmdpoint of the door; the second force is applied at the doorywh.gg)*y0waar mm(0 knob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied * tu(7 c/wtqu6cd8u*gj-v qff to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the ptf*/g w(*8 v dfq-u ucu7jqc6tlane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firstak1;l 2q gy-yvw(by9v force is twiclv yyaby(9; q2kw 1g-ve as large as 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 resistance to changes jju:hd 0fypd-g2,c 04+ nq0n2cu0p m)yv ejlf in rotation 0fpj jf2+vgyn400 ujhcpcd ,q-n: dy)0ume2l?

  Consider two uniform solid spheres where bothkcb vm-g+5/ y lo6-lph have the same diameter, but one has t c+h y lkbg/lp5-mvo6-wice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the raw al 1fdlxee .;7+ozs;dius of the other. The ratd1 e e+; zslf7wal.ox;io of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice zml)4 7,zc5la/d*pw6ywh8vja9g stqthe diameter of the other. The ratio of the larger moment of int/9sy c5h8zlpaz)6l qva4wg, wmdj*7 ertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incr - ;i4mkl8kxarf,l6l jeased to 2M and 3R, what happens to mrakllf4 - x;li6kj,8the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to anj,,2 io9nq etk object, that object will

  The moment of inertia of a solid cylinder about cn- cj4hz7g*fb(gcb 7ni0 g3c its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic eng-3(7z7chcc04fijnn b*cg g b ergy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 tgs:d,+ kgjoqoz /9)mkg and a radius of 30 cm. What is the ratio of the rotationa, mos)9ogd:gtk+z j/ql kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ;kybvx, 19vhsof mass M and radius R rolls without slipping down an inclined plane starting from rest. The lines vv,hy1bx;k9 ar velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoup+zo) f1rpbn+t slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclfnb) r+p+z1poine depends on

  "The total angular momentum of a system of particles changes when a utnil 3u-.m s0net external force acts on the system." This stl .n3ut i0-umsatement is

  In what circumstances can the angular velgx*gh o8*qd,focity of system of particles change without a*df,go 8 qh*xgny change in the system's angular momentum?

  The Earth orbits the Sun in an elliptict 0q,ve3aqk 8crioe3 6 mggps)0mk:*lal orbit. Ignore any friction which may be present. What happens over c0ge 36pk) ot3 k,qeir0gms*qml av:8time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clos 3jk)*j3ukd:vee2 k tkg(o: t lh89cgse to the Sun, then which of the following best describes the o sg 3 ojl*):u:k(kgthe8dck 2 t39evkjrbiting speed of the Earth about the Sun?

  An ice skater performs -1;0kfqizt jv 7 em3ida pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular mome-i0e t7 k m;ziv31dqjfntum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in *i4j m)cgot5*hd iz2n his outstretched arms close to his body. What happens to his rotational kinetic energy about the axisg *5idc*njzhotm 4)2i of rotation?

  An ice skater performs ydg+ o lyqai0if12m97a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of7dqlmay9io1g 0 fyi+2 inertia about the axis of rotation?

State the law of conservation of angular momentuwdety 1; u*4nn:b+t mjm.

  What arc length does the Earth travel in a thl1q,ynpn6lv p8 br* 5 jf;q jw2f:u9kmree month period in its nearly circular oj qpn8,nf5l2r ;j61 vu qfy *:b9plmwkrbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length4-75ac)nwei bgge*qa of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 secwngcq4g5 aeeb*) i-7 aonds?

  How many rad/s is 25 revolutions per minute equiy oat1:4v, lufp a(yz9c.lbp 0valent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is +-/10qsf,rkrzdc)cee / sbkb-r can2the frequency of the wheel's ro rre /c2bknzfck-/ s c)1e-b0+,da rsqtation?

  A pulsar (a rotating nxcyzjlw3o 8ve7vm *)dm3mh eie*xdy +(7 94cmeutron star) emits pulses at a frequency of 0.40 kHz. The e7 cd*ymexm w8v+ 73h9mly iomdv(xejc )z*43 period of its rotation is

  A phonograph record rotates at 45 p1ocpinie 7;*u6r( zci:ms5 n rpm. Through what angle does it turn in 0.20 nrie i1 cpi7*5c:;mo6nu s pz(s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far/ zb0i uc f 0/ucso+mz(j70kus will a point on the outer rim movecuo0 sjz7i(s+/c 0bf z/um0ku in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. k rg,v 1ntpqdx8r*) dmvx5p0bcg,..d What is thev v ,x gn5.rg0pmcdt.*k,qxd1b) rd8p average angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ishi/fhp;jz,p7guwf6 7 the linear speed of a popg zjfwpf ;7/,76u hihint 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skierswu-3s0gn:dl gsq j7l) chv i5. a distance of 6.8 km. The cable which 7lgs.)uch-j:5 0n 3sgiv qdl wmoves 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 trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angularjku 6 2,xvwd /u7jwlexx64f7 qy -q4bb8a a8kg speed of 2.0 rad/s. What is 68uvbjdux,x7w-7 x6 b2k4yak4 q8gq /wjfe althe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.1)-ph/mk2,f6tlm co(4 j t vnfg6 m in length. If the motor rotates at thf ( v2fo6kgm)-ptt,4n/hcj lme rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is roapq ;p onx;hm 388kfi:5-nr cuv*afw7 tating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a porfn 8au5q;h8f 7cpm i;-oxn wva:kp*3int on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeteraox*v8prp-6 zuz p;)m of a bicycle wheel of diamev6ox muz;* arp8pp-z )ter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minutt ko v kqsr(35w.0e(qqe (rpm) must a circular, rotating space station (r = 1000 m) rotate to produco5e.(r kvt 0kw3sq(qqe an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular g;9np2rl p1m scurve of radius 50 m with a speed of 20 m/s. The maximum centripetalm9s2plprgn1; force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiatingj:atg 3i e:/r2becmd* a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provt*gcead:e/ i23 br:j mided 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 end of a 0.750-m string, is w,svt 5pxtyd. *hirled around in a smooth level table. If the mvt,tx*.5 dspy aximum tension that the string can withstand is 250 N, then 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 with)2p o6q0tg0 m evmwk57zrx 0ktuk (i-tout slipping 10 m down a u(iek)7tk vzr 2tg 0ox56mt- w0qkm0plane 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 a+( v(ioho((m xe4hldcngular 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 angucoe6lf1) f:vht1q 0 yhlar 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 radius automobile tire rotate after starih/4o frlldsfig:1 3t dg)c57ting from rest and accelel h/g :fi)tdd4rlscf 713g5 oirating 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 angul 36fk9it 8.ymadigw )5cwqg q.itxl:2ar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating aqy+ 4ehe c7,8; uuicns2svnz;t 20 rad/s decelerates with a constant angular acceleration of,e7 uhc y ue28c;zisvs n4q;+n $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an anguhw 1l s/r)dycxl123( wvc1or rlar speed of 6.0 rad/s while turning through 2.w11 yl)cdvrxw hr2/3( co srl10 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cmx.p vau ja 2c-qzuk* ;h73ifi3 slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotakuxv*aip 7a;23uz-hcf.ji3 q tes in coming to rest?

  A wheel of diameter of 68.0 cm -nmze)i.t+ udslows down uniformly from 8.40 m/s to rest over a distance of 115 m.u znm-+)e dit. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t3;p;i jnjs b 6ag1 7b4shzlsv bk4l(7oo rest over a distance of 115 m. How long d 4;4 1l j7k lbn;pibhvszaj7gss 3(o6boes it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatibcc :.t.jsg k/l:sm k3onal speed of 3600 rev/min. When switched off, it rotates 50.0 times at a cgk..mlc :k:3c tj s/bsonstant 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 a torque of y s,u/bml9o5 x90 Nm. If a 30 cm long wrench is used, what is the magn5ux,9slbo my/itude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tmons4b -3 ceb9ightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo n seocb-9bm43rce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertl+5mt5c-c osl, oq) saia $3.00 \; kgm^{2}$ 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 theo1n*zr* igo(e origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the egn*1(*ioor zmoment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a *b. dq;iq(fzw frictionless axis thought the centf (qd.w;bqiz*er 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of pk fuxz,wj2*um(/ t7s mass 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 downwar7sxkztfp*2 j wm /(,uud. 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 rod is initrl)kqum8dk:+ 6i q*8d)yf xxuially 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 rod about one enddr8q)): * ukkd qf x+luixm8y6 is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Negbcv3 fj02 jd2c95o vntlect 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 does th3bnj tv2205 cfodvcj9e wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionleqy/ pkwjn2p1t/r8 q(css disk pulley of mass 7.07 k18y (ctq pj/pwqn2r/kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapper34pive ew3-b, 7lrm xd around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the 7rw3, el mv-3rbx4ei pacceleration of the mass?

  A rotating flywheel can be used to store efe 6y1dajb.iv 7kxd4px vvy u-8f;9f *nergy. 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 omvm) qylz9,p+f $5.00 \; kgm^{2}$ 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 massnrbyj3.12z,j/o ynjz,cgg5b 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined pl y jzg23ygjc1 5,rn/.,obnbz jane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls wicnpffo,28x3-f +pmq9n6 hesp th a speed of 10 m/s. How high nce p sf2nfq,pxfh6po9 8+m-3up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed5vw2 quuxt3lhu+h)m1 ,hby3g to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0uhb+3q 5wxt 32 hmugvlhu y,1) m?

A solid sphere of mass 1.5 kg and radius ejl:;n vbfk9415 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it st nekvj ;9f:4lbarted 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 change h (gckd; h9kqv9ne4 (hkkgf*:s 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 moment of in gp,tw7p1a4qk h*yc0eertia 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 arms extended has a moment of inertdn+x d9zh o/d+ia z +d/d nh+d9xoof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?