Angular displacement is usu7 -ggr8rz tzs-ally express in units of

  Angular velocity is expressr025;:62xpr; ok5ac wutu2ujnhm gghed in units of

  Angular acceleration is expressed in unit p:a p 6*y0;lswgftlb0s of

  A boy and a girl are riding on a merry-go-round:kgl* anvq g// which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cen nvq/gg:/lka *ter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round 89i9lt9q t wtu+reg3q which is turning at a constant rateqw9rliet9 qut9 + 8g3t. 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 a merry-go-round w*0ct ua1nskrh(, d,ca 7n9 bq-8yisb jhich is turning at a constant rate. The boy is nc( qyjn,ua 0khdb7s 1 *rba9si8-t,cnear the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding *g8xx(a4 )5p99utav1m j rhzh uwnvf+a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. u+w9gaxj5 nvv94hz f * pt1rh(m)u8ax Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at hmus0 -w eu6dwz 1dr0-a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangdr-se1u w- mh0zwud06ential acceleration?

  Consider a rigid body*s2v*/a9( o/ej vw ixhojs kt9 that is rotating. Which of the following is an accurate s2 whtiv(oj9sje vx oks a*//*9tatement?

  Rolling without slipping depends9o o4)0cwno yph9kda; on

  Two equal forces are applied to a door. The first force is applied at the mid(ockq2s-wlcs- wy9u a6 0ef- kpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Wha s6(09ek cquyo--f -s lk2wwcich force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first )s)1 1 1 m5yya.tmt bydzk6xsnm 8pj2sux+l/aforce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the great y1dxz+ a)tualms.t18xyy)mjss 6215n/ kbmper torque?

  Two forces are applied ph 37npbb)dw 7wydr hf22*gd/to a doorknob, perpendicular to the door. The first force is twice as p3hdh7 f)7/ydbn pwr 22d*wgb 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 chanbz/ 98 wlc1o 6ju+it5vi4ha2klwt 9ggges in rotatiojtz /lu av64blhgc95+wwikigo t2189 n?

  Consider two uniform02l1h ,v 4 5aaxhak4ivs5hv l0 nse8mf solid spheres where both have the same diameter, but one has twice the v,i4hma hs f5lv 51 2v8 nhxaak0l04esmass 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 c.i)o- ldia34afub a. one has twice the radius of the o. i)oiad3b.c- ual4a fther. The ratio 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 mas7k)21 mjtk kpvs and twice the diameter)k p 7kv21mktj of the 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 incr+9zw l 5ftm s3-jthk k(asu;s+eased to 2M and 3R, what happens to the sphere'f+at-+lu(;zskt53j h wskms9 s moment of inertia about a central axis?

  If a constant net torque ijy)vgc-slkk k*h) 0,uev34 p os applied to an object, that object will

  The moment of inertia of asf; g,3/+ncnek0 u lnx3mh-ua solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its trkn 0xh/, useg mfla;c +nu-n33anslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which habhyd5 ,i*yjr m,v2f.fi j27ens 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 te2bj *vmdi.yijh5 ,yn 2fr7,fotal translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipvv0+5m ; g -fa87skfzmkj*kbtping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline 7j8*5kv+;k kam0f-ftvmgzb s depends on

  Suppose a solid sphere of m acq5uy5zc*m)w;;j2 .ihi vgm ass M and radius R rolls without slipping down an inclined pligm u i zmav2y.);55jcwch;*qane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systemk+ on bf3+o4x)6ulsp v of particles changes when a net external4n+o klv+)6pf x3o bus force acts on the system." This statement is

  In what circumstances can the angular velocity of system of:uc6*b -2chn pzi-az e particles change without any c: z-chceiz un6 2bp*a-hange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may)i fz1k)9/ s/kj2rc z cp sy+ysy7(vsk be present. y+vy/ ck9r)/z)1(kpc fsiz2sjy7 sks What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical4v94tx q+wskn 6c.r1 iox)w i/+ cxzya orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth ancxxxz9wkaw s6 c4 i+y4.)tr+i1v/ qobout the Sun?

  An ice skater performs a pirouette (a fwx( z/i8j/sv+2d,p,ipnyqh vl2xc9fast spin) by pulling in his outstretched arms close to his body. What hf/zx v,p, s2/l i92 +dyv8 xiqwj(cnphappens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullinc wiaol( c( 42eca,7lng in his outstretched arms close to his body. What happens to his rotationalawc ccn(a,o(4 li27le kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pum3mo uxsp7z :n))(rtlo)o 3 pplling in his outstretched arms close to his body. What happens to his moment of inertia about the axi73u3p( m) motno)zlxprs:o p)s of rotation?

State the law of conservation of angular mo27jxfm x ,d.;tw8htcq mentum.

  What arc length does the Earth travel z-i(m p.bh xe1in a three month period in its nearly circular i(-1ezbmpxh .orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance doe2: qab(f46cok :ornl bs the tip of the second hand sweep through in 3 minutecrf6 2q(4:lbknoa o :bs and 45 seconds?

  How many rad/s is 25 revolutions per minute equivs;g9 39vc27n hylo yzyalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatrwq7efj6 0k; d is the frequend k 7;efrjwq06cy of the wheel's rotation?

  A pulsar (a rotating neutron star) eqb f k30:fl7t6lscph7hff: i.t8nb( tmits pulses at a frequency of 0.40 kHz. The period of its rotati078 3 67tffb lfhf.qtilb:hnts(pk: con is

  A phonograph record rotates at 45 rpm. Throk lq+-,uo -io gpksak9jgz.1 vlzm 6/:ugh what angle does it turn in 0.20 o6i/kg-o-9,z kaj+ g 1zl.kqpm vl u:ss?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point ohbya jw, * 8skurn)/v-n the outer rim move in 2.)8rbnkh,u/ a-yvsw*j 1 s?

  A bicycle wheel rotates uniformly through 2.0 revo;sh67hftp:7g u l,gtflutions in 4.0 s. What is the l ;7gttsuf f:hg67p h,average angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutiob- w/yng;n5s gns in 4.0 s. What is the linear speed of a point 0.10 yw /bnn;s5g g-m from the center of the wheel?

  A cable car at a ski resort carries skiersef.z:.ny 3ijn a distance of 6.8 km. The cable which mov:nif3y je.z.n es 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 c0py+b spa6ya.i2 od uqqd6in9q,.6a d onstant angular speed of 2.0 rad/s. What is the linear spee+ io6yup9s20 yiqqan6.d6 dq paa.bd,d of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lb zp sd/ey0-p-ength. If the motor rotates at the rate of 20 rev/s/syz p-e0 b-pd, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m da:25; hyhsaje-3m aoo:s2uor w df9-is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration ofwu2s52oa9o do :rh-ajh e af;ms-d3:y a point on the wheel's rim?

  What is the centripetal acceleration of a point on vn5op6826ke tlupd 5h the perimeter of a bicycle wh2 h5e68dlp5ntup6o kveel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per xdjq 2h3y c3 taoq8+hq6;2pfnminute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artifh y tdj +q62;3pxf 8ncqa2oq3hicial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with -kgw zf/ef-t)a ru) l1a+maj ,a speed of 20 m/s. The maximum centripetal force (provided by statifm-)a gatf1/wlzk, a ue-)rj+c friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a -xg-st5+ a5tfd mmpv1 flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pr5 +- gmsap5-tmd1vfxt ovided 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 inhg)*a1ok25io8ot+ay ; jrwrx a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maoiakh yorrx+;*j 852wot1 ga)ximum 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 l /,yme/oa 7hq vzb7n6without slipping 10 m down a h 67lze 7/n/vqaby mo,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 constant ango0u+zdgbq+ 8z9pn/d8y-2 x9it wh riw ular 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 angular p1ffjtu y-763s f8y abacceleration 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 rotou-ec6xsy3owq twml x38-( (pate after starting from ows-w um3o lq 3 8(x6xpe-t(cyrest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has anc8myj ihdecm.w(fh3y;1:ud /w 0g v 1b angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad,nl4 ;; + x2pzys 0xtuutmu8yb/s decelerates with a constant angular acceleratio, pymx2;;+y4 s u0tbx tzn8uuln of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachv (f;cn/l:sw2eyh3q ges an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration o/ey:lf n3v;(h wcsq 2gf the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rez 39z;rk cg8lkt7a1 uest over a distance of 115 m. What is the total number of revolutr lgczakzk897;13e u tions the wheel rotates in coming to rest?

  A wheel of diameter of 68y5z:9 y,t45i-ijz fqpov v.p *+ vrsnk.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accel jy-5f v4.zpq5svyi:+on9 * tvi ,zrkperation?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest7kizq3)uvj ;mcfdc5a er n2,4 over a distance of 115 m. How long does it take for th53e u rcazj)mikn4 d,vc7q2f; e wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a ry dq08 e7;sw4j;bt ewdotational speed of 3600 rev/min. When ewy 4w ;0e;dsd7b jtq8switched off, 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 tightening to a torque of 0o)t;ohp od 02lgas7c90 Nm. If a 30 cm long wrench is used, wha a0oo c;tdl7sgo02)pht is the magnitude 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 30mo 063p8e8ptklsy x c. cm long wrench is used, what is the magnitude of the force required06pl8 .c83xet yomps k when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ooby( zii, ia++f inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled e z9n:1nzs -xhjk e6(las follows: mass m is at the origin, mass 2m is at x = a, 1nnz(zs9klx:e ej- 6hand, 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 thoug/bveu (b)m* g 1f3geeuyy)g2f5xcf o0 ht 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 radim) ) /yfubf2cggyeue(gexb051vfo 3* us 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 10any 8rds9-g +v 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 = +v-sgrd9n ay86.0 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 issvolx:cer.2 -hfc;*3 pghb i9 hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is aei pr*lfx-:92 ccb ;svh3go.hllowed to fall. What is the angular acceleration 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 tvmmt m5* vqv(/. qm8rand 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 does the wheel achieve, assuming it rolls withou /8vm5 mvt v(qqmt.rm*t slipping?

  A 1.53-kg mass hangsjdim- faz w,76 on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration ofz j7i-m awd6,f the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley p og: e*i 9mu*)vxbd*zof mass 7.07 kg and radius 66.0 cm. What is the acceleration b v*eiu*dg*x)p m9o:zof the mass?

  A rotating flywheel can be used to store ener-l )nptb5 ryw l.y +bwvs:c4l/cog1r8gy. 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 ineu3 pevjwu ( g+j8e(9 -6hnh0j*njibyzrtia 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 0.8 wc rwb(a2i*l010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of theal8cbr *i2ww( sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1ada 6a okcd-:1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comingcka6 a ad1od-: to rest?

  A hoop of radius 0.50 m and a mass of 0.20 7iadn,l j5 t+ 92b*y792x:bxgot hgxjqnnr3bkg is released from rest and allowed to roll down an inclined pl xod j b r7 lnb+5nhiq 329gx2n:7xtb,t9ay*jgane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mas:isf1ps8hzz7 m72em as 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment ofh m1mz siz7sa8p:fe27 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 changeiroq25 9rz-1q 1st jfas 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 inertia of jlou l 3y7ee *df1+rc9m2ob)q$5.0 \; kgm^{2}$ 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 armsqx;l */w qy n5fs*htumyem.:. extended has a moment of inertia o *n ;t.yeu:/fqswm .*xhl5 yqmf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?