Angular displacement is usually express in units tj; xx8r h)*eb6s4evfof

  Angular velocity is expressed in unb) oh6v*b4zd fd9nan4its of

  Angular acceleration is expressed in unitsvoasyo . rg3qefw- 1;oc7y41m of

  A boy and a girl are riding on a merry-go-round which is turning a0y;hu zrd/69l7 8 .uscw5dobr ni7vuut a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular di ol06wc7.du8r 5su u7zubvi/ n9;yr dhsplacement?

  A boy and a girl are riding on a merry-go-round which is turning at a q 2stj qzm( m*z*afo4g(ck3u. constant rate. .ga2u(*jqz omkt4sqf 3(zc m *The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on 9om cjg7wx8r lr6u *62rgy1vt o .lb;ra merry-go-round which is turning at a constant rate. The boy is ru rjm7y;v6rotl gcb6x .w9gr*2 l8o1near 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-nnzy2;h 8p. eground which is turning at a constant rate. The boy is near the outer edge, while the girl is c;pe.n8zhg 2 ynloser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whic,vp*kwzm+0 xd:nd 3 zkh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who hankzdd* xzk0wvm3 p :,+s the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accuratbpwq/qgpuk1 0 *g-f, ge sukpg1 pfbwq gq*-, 0g/tatement?

  Rolling without slipping depeluv) xpk2p(y(z0 m.bfq .mch .nds on

  Two equal forces are applied to a door. The first force is applied at the aomteq. 2b50)poq d wn;yo7u: midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpdey.t;0 qpwo)2 qou:5bom 7anendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The xuu z3x*ohfs-u9jxdix:,( h( first force is applied perpendicular to the door;s: z,uxo3uxduh -x9 ( jhfx*i( the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiqpc ra( uwt+aj2.b0,zcular to the door. The first force is twice as large as the second force. The ratio of the torque 2ac+( q.,j0ut rzb wpaof the first to the torque of the second is

  What is the quantity used to measure an object'3z(:jg:/cqj w c nsaf jgssw9/1-61jg/epi lps resistance to changes in rotatioa s:g /1q /ligpjs( j6/jznep1 w3w-g9c:jfcsn?

  Consider two uniform solialez:lgr5s+. yiu5 5ftxrr. hp u/*a0d spheres where both have the same diameter, but one has twice th5 z t.i/r 5auhf 0+l5asepr.rg:yx*u le 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 ra fz .vmxt4t-9sdius of the other. The ratio of the larger sphere's moment of inertia to mtt.4-f9s zxv that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and tp06lr9p.z o+ lyq:don9bd 7gawice the diameter 7n+q.albrlp9 9z6 dpgyo0od :of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphev+g7 zdnn-w0jre has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphernz+0 gvd7w- nje's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wi72 +jope ov8 pg fp-gbt)n4x:jll

  The moment of inertia of a solid cylinder about its ax.x9*tw)5cx2fe pyep dis is given by 0.5 MR2. Ift epwe9p.y25fxd)x *c this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle1nf zgfiagl7 v)s pa1s (3va91 of mass 150 kg, one wheel of 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 translationf3n1gpiag 19)zas a7(1vvflsal kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and r0z fd9foq0:xoadius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottz:oo qf900 xdfom of the incline depends on

  Suppose a solid sphere of mass M andkf(:5fr-r lla d0bw3 m radius R rolls without slipping down an inclined plane starting from rest. The ang3b fr(w :dmrla0-f kl5ular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles change/;f54b8bmx7awi w2a2cn :x w; hbclrhs when a net external force acts on the syste :/wbi5cf8 bxl;47 ;arax wbhn2m c2whm." This statement is

  In what circumstances can the angular velocity of system of par4i ueh;mjnf:;:rypa+ticles change without any change in the system's anguh4ui n:pmj;ae+ ;yr:flar momentum?

  The Earth orbits the Sun in an elliptical orbi(e4q 8.(6nlcrwc fjxp t. Ignore any friction which may be present. What happens over time to the Earth'p6e x (jlnrcf .(c8qw4s angular momentum about the Sun?

  The Earth moves about the Sun in an elliptica; rmmbujjmiqb j xv.c/n2n1j+,:o,6pl orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the ;ub/jiv nx,m +j:.p1jmoq,2c b mrnj 6Sun?

  An ice skater performs soc1.xul7ik *a pirouette (a fast spin) by pulling in his outstretched arms close to his body. W ul*7k1cxos .ihat happens to his angular momentum about the axis of rotation?

  An ice skater performs a m(ir8z+: q ibepirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy aboutz8mqri+ei: ( b the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b+)we21 fjed0zyvrpn(j, k*v yy pulling in his outstretched arms close to hisnyrj0 epvzf *(vy1k dwj,+)2e body. What happens to his moment of inertia about the axis of rotation?

State the law of conservat aw:w0ah8n o8bj;xi b6ion of angular momentum.

  What arc length does the Earth travel in a threexu0h8 )eax vg5 month period in its nearly circular orbit about the Sun with ua50)e8 hgxv xa radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 xg js;(/wmj:ddu ;l1am. What distance does the tip of the second hand sweep through in 3 minutes and ga1 :(;ju/sdwxj;mdl45 seconds?

  How many rad/s is 25 revolutions per minutmil5c6s5u0j 6tk*dqzjt 1z ;ne equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t qvj;qeg., mmeg jh.f+l:x-(ehe frequency jgegmj .vqf,e(.- xq:;+mlhe of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a freqoau3*sxy2ulq /z9) rcuency of 0.40 kHz. The perio rz9uco/ xq*2y3) ualsd of its rotation is

  A phonograph record rotates at q ,)9nmve(mc -tf,fs z 4ax2dq45 rpm. Through what angle does it turn in 0.20 s cfm4m9 ,(nsx,fq ve)dzta-q2?

  A wheel of diameter 26 cm turns atoxka+ j*:b 1so 1500 rpm. How far will a point on the outer rim move in x:*sa ko1j+bo 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions iajdrchvz,2o266b+un n 4.0 s. What is the average angular speed ov6d, n2 h2 6arcbzoj+uf the wheel?

  A bicycle wheel rotates uniformly through 2.0 ret, qhb,sp4f8kt (p d0fvolutions in 4.0 s. What is the linear speed 8 fk,bt4fs t,(pphd0q of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable hxc.w/ ;4g belwhich 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 xwlch; be/g.4to make the trip in 12 minutes?

  A wheel of radius 1.0 xb(vm ;soe(t4 f9y+kreyy .8y m is rotating with a constant angular speed of 2.0 rad/s. What is the lin;y. +f ksy otevyxe(ym( br849ear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter ilqt- 1da7mip +s 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is theiqm+d1a 7t-l p approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angularylfdca9 (5-p d speed of 2.0 rad/s. Whafyd(5ad 9pcl -t is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bic*4oe2+jgxf5 z9 otebcycle wheel of diamet 4 fcbj9e5tox*o zg2e+er 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circ4*)jroflrx c2 3k 2bqo4cyo *jular, rotating space station (r = 1000 m) rotao c **4qr3okcjox b24f2yl)j rte to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat ( kae7sz,3w wncircular curve of radius 50 m with a speed of 20 m/s. The mk(a3sz wn, ew7aximum centripetal 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 rp f0t0h/ hqm,h 1ug hk9m6,fmribz;0o adius 50 m with a speed of 20 m/s. The maximum centrikt/mp ib6h,of q0m hg 01h0,m9; fuhrzpetal 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 end of a 0.750-m string, is whirled around in qakh- asi05+be 1u dmffj zd(e(k,y;mh/da)/ a smooth level table. If the maximum tension that the string can withstand is m e1(, fa5fbk jh dd) s/kza/(amhdi+- ;eyq0u250 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 ij4ji,b.sryu x62ax7 t 6le:i.0 cm rolls without slipping 10 m down altiy.x,6 2s xjr:6ui 47bija e lane 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 constant7f) e3itsf. bxcrt66 q 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 w+-x ougay aze95njlj gr/v62 (ith a constant angular 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 tilmab /m5sk 9-zre rotate after starting from rest and accelerating at a bmz-5l9/ askm constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an apecc 9qc/ g:a(( zpczb028jo3 vr-ffongular 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 co 3nok2bmmerw,pk2f g**xb9a52hj c ,bnstant angular acceleration9fk22mbc b 3hawe*gox25,n *k jrmpb, of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches afpx/q378 in hkn angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of th/nq8xk7h f 3pie wheel?

  A wheel of diameter of 68.0 cm slows down uql9k bgd2m f69niformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions tb fgqk92 dl69mhe wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformlsz-3-rqrikt 3l/-x gwy from 8.40 m/s to rest over a distance of 115 m.l3-s3rrqzwi x/-kg t - What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s ts 2tru yc -pyoom/l8 .nao(sgg) y0k72o rest over a distance olo78-t 02g/yosyrn y()k apu2o.mgs cf 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/dlv pzcwak3h d5w;6c1 qd:3wz )*)cqcmin. When switched off, it rotates 50.0 times at a constantzc:l 6 kcaqwpz33d 1*w;dcvh))cwq5d 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 tightkq ,v+q+azu w8ening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitud q+v ak+zw8qu,e of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a *nkgxq5 2 ly/ng :,gnt30 cm long w kqgln2 g*n:ytg n5x/,rench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in0ab pi 9ngk0lr(ur *ftg 3;x-lertia $3.00 \; kgm^{2}$ 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, massdcbbj baa5o5e cm a7(ns(6cj;dz59: r 2m is at x = a, and, mass 3m is at d6cj5 ce;:5r aa7(cbod9jb an(z5bm s x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg i;1z+ bygjye:d s 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 e;g yj:e1zydb +xerts 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 picgp m qa: ;b4r.id05yqvoted 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 : iapdm0qrb.g 54cy;q the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initiqikxzt aq ;.:4j1w*iwally 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 on4t;qw*kz. xqa:iwji1 e end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5)opt:5l gmzd7v* g eb0 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 dobzptg:o d7 0*e5lm v)ges the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on acx+m wh*1+8r ;t ve nx/bg7bvzni72js rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. /v7m1 v ji;cz h*bgt +n8 xs+nrbw7e2xWhat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fric/i(vz8j+ gpb8 n 3duw*c.tg ngtionless disk pulley of mass 7.07 kg and radius*ti dv.pggn8g(j/3zu nc 8+b w 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to storcclkho-s g*;. 7u5k mee $1.00 \times 10^{6} \; J$ 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 infhb)0wa+ .dx53 uq hmgertia 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 rad;5j . xbv1i ly htvz59cf1fh)eius 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 cfhl;b1z)h e1 9v5tyx 5fj.vireaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed o re5gcreiv4j *(pjm7; f 10 m/s. How high up an inclined plane can it 7ee(*4prcijjrgm 5v ;climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is reld9url7z-ldx srp2(v 8eased from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance ls-d 892 l(d7rpzx vurof 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without 5h b79f7qpylcz4ey.: lo7 oe tslipping down a 35e incline that is 7.0 m long. Assume it started from rest.yocy7fhqo7p9 z :t l5lbe7 4e. 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 changes bybn 3nps7 :3;3ag5;zglqvqw cm $20 \; kgm^{2}/s$ 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 momen.(sx.rqu/o n4ht 3 ws 7tngvy8t 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 wine6q-*ulqppg8-ywj,hh 8a* 3kt0pi dth arms extended has a moment of inertia u3 q-gihh*yt pe-kd*l0w n p6q 8j,ap8of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?