Angular displacement is usx5 5/tmn(jy:ps8in xbually express in units of

  Angular velocity is expr9yfo6dk fnx2)essed in units of

  Angular accelerationjzxy 1w1vonxo 27 m hg,js61jymq*1s 5 is expressed in units of

  A boy and a girl are riding on a merrypz.zx p9i/5ilxmd g(l:dh3- m-go-round which is turning at a constant rate. The boy is near the outer edge, 5x /zpd(zdl.x 3gml im h-i9p:and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-roci1 +ydh8q jg0und which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whodgq+8hi 0 cjy1 has the greater angular speed?

  A boy and a girl arej +xrw4w7u/amp 9doo 7 riding on a merry-go-round which is turning at a constant rate. The boy is near th9wmoj/4 xrop+ a7du w7e outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridi paqsg.-h 9wwhf1x94ang a merry-go-round which is turning at a constant rate. The boy is nhg .aqs4x w1-waf9 hp9ear the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding0go7lezym8z3w q-j)zf.u + u r a merry-go-round which is turning at a constant rate. The boy +3ojlgzw 8r0uum.zze-f )7y qis near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Wh*1eovd 9b r272cy etztich of the following is an accurate svy tz *1cbeeo92r7dt 2tatement?

  Rolling without slipping aa;b,l5 .xeivdepends on

  Two equal forces are applied to a door. They +xp50vhlr0c first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpe h 0ypxrlc+50vndicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force iupr2z-y0 (,bvz si-tqs applied perpendicular to the door; the second -r02z(it,-sub ypzqvforce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Tb lj8fv+g 8a9phe first force is twice as large as the second force. +bf9 8pgljv8aThe ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistanzy 9rv d::s;nrce to changes in rotatio vr;d9: szynr:n?

  Consider two uniformfa ;t4gd p5yt( solid spheres where both have the same diameter, but one has twice the mass of the other.4d;gt ay(pft5 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 jl2z 8.c-k+vd49 fypjhvx/lc c2/ kzstwice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smalfl ky4zv .j9jz /c spcdh 2v-k+c2/8xller sphere is

  Consider two uniform solid spheres where one has twice the mifl 8,d xtj;p9ass and twice the diameter of the other. The ratio of the larger moment of inertia to tha9tdfi8xljp , ;t of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2Mglfx(g5t6p3u +t pdp * and 3R, what happens to the sphere's moment of inertia aboutupg 6+3 dfp l5t*gtp(x a central axis?

  If a constant net torque is an/s6ilojy6)aug 9, s/vh hh5fpplied to an object, that object will

  The moment of inertia of apq8c,4 fbgz:f2 a1ycb solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kin28fcpf: zg4bq c yab,1etic energy to its translational kinetic energy is

  Consider a motorcycle of m1d8u5llk 8dzf )qt7 jhass 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 energydflqj)k1zl t87d5u h8 of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippx.z ( vvjfqs/i,:*vjy . zn1yn/yzj0ting down an incli ,*xf1z.yj/j:i szy.j0nvyq vntv/(zned 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 dqy5qnev;1v 2d t 3 0ylib,ne/and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the t3 nq/qe0ndd,iv y;51ylv e b2incline depends on

  "The total angular momentum of a system of8zqge yi5 -v0h particles changes when a net external force acts on the system. e5i-qgyvh08z" This statement is

  In what circumstances can - ar6zcf1.u)wgr e0 bgthe angular velocity of system of particles change without any change in the sc aew6fgu.)1 b- gr0rzystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction t 6k. jzd;y et t,lmd:,f :(vuns6aur;which may be present. What happens over time to the Earth's angular momentum about the Stskl;6fj,6a .e nrmvtdy;,:zuut :d (un?

  The Earth moves about the Sun in an ellipticax:)6dqqz8 b gtik(nx r/jxj ,+l orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Ea :zqd,b8 gjrt+jk6) xn/xxi( qrth about the Sun?

  An ice skater performs a pirouette (a) ugfpym/1(o)zmx d* w fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotatio*f )w) ymz1xumg (d/pon?

  An ice skater performs a pirouette (a fast spin) g7ew4f/f.ha(q nc ; klby pulling in his outstretched arms close to his body. Whaql74 w/f cf.hnka;ge(t happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs cog5f up 6. hr)ro9.vtg7xfu )a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of ro)huctrx5og g6r.97)uv ffp o .tation?

State the law of conserv4or*.mk1 :slna s,s miation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cizwfa6fe)), h,j*h: * s8zui2udtmhz nrcular or2zhjatf,z6wehmdi:szn* u),* uh) f 8bit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30fk:9i2kx/iagniy r) w sv o3* e4l:tq4 m. What distance does the tip of e 4ikrl gnyfkiat/v*)934 ::iqo2wx sthe second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutol pm/j,xsi3 k bx9ku1.) z7ycions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. +.; xbx fzwobj40s4fx)dawi5What is the frequency ofabfz5x ibs4 4wxfwj;do) +.0x the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.,: dkd:yive :owuf/;b+ q fa *ctw(m2n40 kHz. The period of its rotation iad+ :: 2/d*v:(ftonwqewbc,u ykm f i;s

  A phonograph record rotates at 45 a w4u k8si: qlz+ uad0)gp(,xprpm. Through what angle does it turn in 0.20 s x, apuik:+p0sz4 l(quwa8g)d?

  A wheel of diameter 26 cm turns at 1500 rpm. How far tq ftdnhd .wirabbab w0 (t99t7d62x/; :rn3kwill a point on the outer ri/barn bnt .xd2 (btd9 t67a;k rwt:3ifw9qhd0m move in 2.1 s?

  A bicycle wheel rotates uniformly throug4;drpg*c0r*iug 5 plqh 2.0 revolutions in 4.0 s. What is the average angular sp0;g lupi*c* 4 g5rpdqreed of the wheel?

  A bicycle wheel rotates uniformly noe*0r16*i0ln j9wo5uwlslu through 2.0 revolutions in 4.0 s. What is the lineaoel0uilu 9w5s*o6 wl n0j1*rn r speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers whbt*u6 :*btl-j.vs i kx 3+jfa distance of 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 forkv -lju:bhx .b3swf* +jt6t*i the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constad/ +uozvon ::znt angular speed of 2.0 rad/s. What is the linear speed uon:+/z :dvzoof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in le xh-zg5;e5rl v5e ycy1) k by0jpj5ir(ngth. If the motor rotates at the rate of 20 rev/( 155j;ckgb ryz-)x5lj5reh0pvy y eis, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 y21,av)s7rr7laai9mo; u g o trad/s. What is the centripetal acu; g)ilvsma27t ao97r ,oa 1yrceleration of a point on the wheel's rim?

  What is the centripetal acceleration of ,zc0aeg b8a oe8 da9d9a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bi cd g8ee8,a9ad a0oz9bke is moving 8.00 m/s?

  How many revolutions per minute wck5.+vc3gb u(rpm) must a circular, rotating space station (r = 1000 m 5cwc3.+ukvg b) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiu*h lwqiw3f xsoes;/-d 9te0 8us 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fx30te if e8s/wh*ul-w9 so d;qriction) 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 slm-hxg 2b s.d-peed of 20 m/s. The maximum centripetal force (provided by static fdsl- mg.x 2-bhriction) 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 /q +mpt, j6pdlzsnk(3k,g s7pwhirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linelpp7 knkj6 gqs/ ,,+td3mpz s(ar speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 c 61bvjp 1dteohv+ .c9)h ).nigx sz/fum rolls without slipping 10 m down a lane at1 /)o9 cs)p.6bhv+1 vgnz.fujhdtxei 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 ana8 ysku ;*n)/mvl5al p*dsoq6 n*a4tfgular 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 con (gdeyw, sfrgp5 t7;l/stant 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 tire rotate aig nc,;x,3 kfufter starting from r; niuf,3kxgc ,est and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, -:sjh0sbjj w +wj w j4lcfk4+-and has 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 cons4/c*v ctnpp/v tant angular acceleration nt*cp/c4v/v pof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest an; k(9*g kkhje k/evsy2d reaches an angular speed of 6.0 rad/s while turning through2khej/k vyk*s gk9(e ; 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down tpsg *wi;9,jnk7vmo .* uod.j uniformly from 8.40 m/s to rest over a distance of 115 m. What jd7 *;oits.w,k.j mn *9gu povis the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rested s ,c40xtox,9pp-lf over a distance of 115 m. What is the angular op0sl,f4d9pt c,-xexacceleration?

  A wheel of diameter of 6h(vg)8)yr8erhye) r c:svz .w.l n3ti8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long do8s 8gyezrt v().yhr.c i3ew :nl ))hrves it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotu-7hq : zrn6t utn+5hjational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration beforeu6nhtzj rq5: -h+t nu7 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 67u 3 qqm9qzoewz++ wltorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force re6lmz+ uoq7q 3qez ww+9quired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque 19b98jbf +wmbs mdnd+ of 90 Nm. If a 30 cm long wrench is used, what is the mb8fw b9 d9 n1+dmjbms+agnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner4ub(.fh l 4+ez g/ks4qrdkoz 1tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mvfb xv2iw8jw:(-.p k rodeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is wbpvkjxvi:r8(2. -w f at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pi jufs3tgshv+;/e (mrqi(t:7n x2b c0mvoted 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 radiujs0m 3h v+mencqb7tg/2ui( ;x :tr (sfs 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 2/kjd.l-ib pccpg8m 1 v,m;d jis pivoted about a frictionless axis thought the centerj k;,.-ljbdm12 i8v/ ppgmcd c 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 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initiallydl7k z0)lo p zt/fpb 86;v,tml1aob6z held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as itz)aktb70omz/l l; vp6oz68 ,fltd b1p 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 zci 3)15nlub- -0-tchorf bfn4j sf* b1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentiazj53*bsl0- nfbfb-1ornct-h4 ) fui clly 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 arjez2 gmg)m;, round a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What isj 2),mmrzgeg ; the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlesn2nd hwu 5)lrco f51-vs disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of 5hr-)nl n 2c1wvd5uof the mass?

  A rotating flywheel can beaf * j1u c : :hgous+5m 7-khiubtqbo9k/;ft)p used to store 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 of v,t1+wn;g: 5wp/.oh-lzshs h uy /gu 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 massx +w54g werc-kx1mx 1d 1.0 kg and radius 0.010 m starts from rest and rolls without slipping dw 1-1e4x wgxm+5crkdxown a 1.0-m high inclined 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 and raoy-30r ) qlre(3s gl cskh gw4paq;x2+dius 0.010 m rolls with a speed of 10 m/s. How high ggc-0 p3k 2 +qrs ehlaxslrqo(y;w)43up 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 dxj.yrd7o /h c vh;j8cg6 3tsw7o4/afand allowed to roll down an inclined plane. How fast is it moving after dropping a ;cscrf7j 8o43gh/6y vj7dt.hdo/wx a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radmam2aqf(e w,)5p3 m.dud jvr4oje-t*ius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it jfd 4emwae(mm.5q3d*)-rot ujp ,2va 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 changes by7oz 8zldgmmga(c ji 6j- (g,(b $20 \; kgm^{2}/s$ 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 b)*17mal tz 8bho9+7ive mly*j 5vs rwmoment 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 arms extended ha(wc cvrx,qfi 4 4:s9pus a moment of inertia iu(9w q r4:cfx svc,p4of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?