Angular displacement is usually expyy d632w 1k/vg5ln jvmress in units of

  Angular velocity is expresl xw::. qx qst.n1.d tmbs7h(vsed in units of

  Angular acceleration is expressed in units dd,y; s yd(.ygs,t6 ffof

  A boy and a girl are riding on a merry-go-round which is turning at a consv jh0xgrn+,m0* bcm4q tant rate. The boy is near the outer edge, and the girl is closer tbjnh+*0,c mqmvr 0xg 4o the center. Who has the greater angular displacement?

  A boy and a girl are 6. qm7.e ls 8cmtgp7i(pgo:teeps;irt9+8 sq riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and tp:q 7s ig(seg triptp8emqet6oc.; 9slm+8.7he girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ruts-*hu)3p4f t 9k tvxiding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to3t hx-v4s9ut)k* f put the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round w )vnds8y 6o4zylvd)e*.ofig, hich is turning at a constant rate. The boy is near the outer edge, while the girl is cfdviv ,)y )s*o8eo6 zldyg.4n loser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridinc mrfz. saog0w+5ooi8):t(-)fgcb ii9jqv z4 g 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. Who has bo4 0tgqsj:z.i foccr ifz) 9 -mv8)5 wa+oi(gthe greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following isy* exxqfe31 st 6jutb;zbs141 an accurate sta16f ;s*ebty13qu 1es4 bjtx xztement?

  Rolling without slipping :j +24 4 qalljxuy0gam bs)yq;depends on

  Two equal forces are applied to a door. The first force is applied atfk3mn 0r;xfh qn+e 3+kw-qq/l the midpoint of the door; the seconk3+r/; nqef3nqflqwh+0 -mx kd force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at thhm vr1rfb702ikspiv* ;2bc4ne doorknob. 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 the greah smc107f*v2rvnikbp4ri2 b; ter torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firstnt5j* cwep )6qo,svr,vnc +;z force is twice as large as the second force. The ratio of the torque of the first to the tor* enrc 5,jqp;,6cw+snz)tovvque of the second is

  What is the quantity used to measu0 k*zvomsg 9,zre an object's resistance to changes in rotati,kg *sm0zov 9zon?

  Consider two uniform soaak4.ego :zf +lid spheres where both have the same diameter, but one has twice the ma: gk4 eaa+f.ozss 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 twiq)fu;fv:k8dv 8(tzva ce the radius of the other. v)d;zv8afut k: q(f8 v The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one hwynpm,-sr1uv my: 1 m5dj8gt (as twice the mass and twice the diameter or (p81ym: m utdwgs5,ym-nj 1vf 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 increasemrngt6b6( wv4v1;yu7; 5l v( tm mygttd to 2M and 3R, whayt6 g5uvn v7w1;rt(ymmg bm; t(v4t6lt happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an obc .v8ri(9aonf7lp-oyq k.i/ yject, that object will

  The moment of inertia of a solid cylinder about its axih3ekkgom- sxj, z )bo; (oyl8a5s4g anx0 9mj4s is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatx mgkjo,93hsa4o m(lyg;0xe-so n)4 a k58j zbional kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a masm0,flza lzr 5 h)h9ai6s of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the t6 z05,ih f)hlaaml9rzotal translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and r:d8 pk1b9pr 9 3x,0nx*gafpd1fy o yxcadius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom ob 09:ppdx3k px1 gfa1nrxfy8 od y*9,cf the incline depends on

  Suppose a solid sphere of mass M and radius R rolls w sfn 1p71pi3:,i ofko7hego/eithout slipping down an inclined plane starhooee f :p17, 73gkn/i 1foipsting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net ex(.lij co5pr6a5o l6o yternal force acts on the system." 5 oi65ooy l.(cpar6jlThis statement is

  In what circumstances can the angular velocity of system of particle/e.p p fdnyu2.s change without anyu y/n.fp2ped . change in the system's angular momentum?

  The Earth orbits the Suqrx8 )fryy qt egr/(8;n in an elliptical orbit. Ignore any friction which may be present. What happens over tim xq(/r8f;tyq )e8rrgy e to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As thel8x p fb gi8kdg0-+h,y n6,tpv Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the S kid6l gn8 ,b0vgf8y+p-p ht,xun?

  An ice skater performs a p2ur qjca:(zg im,/f ;dn-,cmyv, r i5oirouette (a fast spin) by pulling in his outstretched arms close to his body. What hz (j q;m , d c:gn2,racm5fryuoi,v/-iappens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (js*0u*4o8 wbxbxd rz6a fast spin) by pulling in his outstretched arms close to his body. What happbw*xuo4zx 6s*b8d0 j rens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs 0 wz,mhe83hq fp j);ejz(o)nga pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis o0g;,fozhw )h j ze)n (qjm3ep8f rotation?

State the law of conservaqmm21utz6 u v6xe3 r9ytion of angular momentum.

  What arc length does the Earth travel in a three month period i91.oiiqlycun:h8+,ag b*p uz n its nearly circular orbit about the Sun with a radius g:qy buuni .,z*hl 1ai9+pco8of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance qcurt)1 q 1ouxy.8h +cdoes the tip o r)xo1c8 c+u.1yqqu htf the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivaler:rh aobh5 7c /a1xnep:-on;dbyz ;/t/zq- o pnt to?

  A bicycle wheel rotates uniformly :/ y3*y aamr/u da;mjpthrough 2.0 revolutions in 4.0 s. What is the frequency of the wheel'sm amupd/ a; yja:*/r3y rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHpytatz9up,94kjt,iidvjkn/e+o117 k:.c r az. The period of its r+n ju1k/ iz9tp.:ve7a4j9ay kc,o,t i rt1dkpotation is

  A phonograph record rotates at 45 rpm. Through what angle does rp *mb 86+vdwyit turn in 0.20 6yp +*bw mrd8vs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outert zwny/;x br+ags/12u rim move in 2.1 s/uztx +w2b1/g n; arys?

  A bicycle wheel rotates uniformly through 2.0 revolutionpez cm:1,o)qys in 4.0 s. What is the average angular speed of t:m p z,)1qoecyhe wheel?

  A bicycle wheel rotates uniformly through 2.0 ref4ic*;l4kl)l.j,a u ola cil/volutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ofll co *a4fl k/ul.j)4ial;i,c the wheel?

  A cable car at a ski resort carries skiers a dista-p:,8ow yu* .uc/jo27 eapqnjtlh(f jnce 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 -uo. ,7* u opw/fntyjj2j 8(c:l peqahrotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0kje v9 g/k;6, di1fpw;ss5ukk rad/s. What is the linear speed of a point on the wheel's f/ws 1 jd p9kkkk,gi;u6 ;sve5rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motorpeu n(4m, ehm7q oa 8z*:ym*nb rotates at the rate of 20 rev/s, what is the approximate linear spee(7u*nbye4m p,a:8m o*nq h zmed of the end of the cord?

  A wheel of radius 1.0 m is rom 5 c q 0/s/tkh 38y3 lskuh-ky-v)fl2xopx-yntating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on thek-ptlu - 5 m308hcxksy/)yl ovqx3y/sfn2-kh wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a yd u1- ynw:t-4kun:xzbicycle wheel of di:n-nxku4uy z yd1 :wt-ameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rsn;)y wxqy o eq:9/:adpm) must a circular, rotating space station (r = 1000 m) rotate to produce :s/ ya;xynq9): ewqd oan artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/svk g z(j:.s9jcv0tj7h. The maximum cevgjtz 0sjh : 97(k.jvcntripetal 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 hv0w3qu2cpb d1crs)4 w2 ;ujyflat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by st; vq)ju3bhsp122r uw4c ywcd0 atic 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 ssun7 yn u,1)cuwvq,y;tring, is whirled around in a smo)7ucn su,yw ; n1y,quvoth level table. If the maximum 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 kgs2mo4 2ku9+txen zt-c and radius 9.0 cm rolls without slipping 10 m down a lane at 4.34 tktsex 9m+cozu-2n2 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 cons5:ho ilb +j(w++b0jm fc,r ehitant 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 with a constant angular acvmu.qjs6l/0q g; dz j5celeration 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 nr868ebmu l58 2eiyy1kvbico/t w: 5ctire rotate after starting from rest and accelerating at a constant angular ar6y8: 8 u owb et8ebvc2i51 nyk/cm5licceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at reg2y h96 ra-c+snkg rc,st, 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 wi1 g c0;zi6doqjth a constant angular acceleratqzi6c 1d;0ogjion 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/s whiqekj c.bt l u;c4+;,uple turning through 2.0 revolutions. What is the average angul 4cuue+,jkt;lbc; .pqar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oww:yky5( li hhf5*)+j y 84p.jiice hcver a distance of 115 m. What is the totalii plwij4+8.:y y) e h f5k(h5y*cwchj number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformlyfg51pqm0)tf1ys(u i2 we0 q mu from 8.40 m/s to rest over a distance of 110g)mwqufy50 tp12 uqsi f1 m(e5 m. What is the angular acceleration?

  A wheel of diameter of 6o, .aw vx bfk*/m)b5pm+m2qq y*qyt:p8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for they+poy p ,)xkm2 m.mf bwaq*v/ bq5*:qt wheel to come to the stop?

  A centrifuge in a medical laboratory r8;by7i7o3v d8vt gelhotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constantviy7 v7btdeg8 oh;3l 8 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 top1 /tkdl lae 82(8cwcz a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the p81wzcc8l 2d(/ ake ltwrench?

  The bolts on a car wheel require tightening tndtr0 .bao13gwk 6 f1bm /zp+ao a torque of 90 Nm. If a 30 cm long wrench is used, what is the m1b+fzk /b1 6aw g mt3d.n0ropaagnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iuo706wpmp5 oprzc8 *om;q*cgnertia $3.00 \; kgm^{2}$ 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 orlg0ek*s k2 l0q9peb0u igin, mass 2m is at x = a, and, msulqe*g 0b 0k lp92ek0ass 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 frictio3hxmrdqzs 072fae+ : snless 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. (See Fig. 8-1.) What i0az :d2+ sefs rq3m7xhs the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a friction1s4tu9gmuzf c )btt2 (less axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a fcb1 tt t4(fsg )um2zu9orce 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 initially held0v; is,nxxy*)za(e hx in the horizo a; ix*hexzsy() ,v0xnntal 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 end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1ovrb,.a5 fl*o.5 kg. Neglect the mass of the axle and sprocket. If a forrf5.* ,aoolvbce 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 without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frict;qd6up8+v haiionless disk pulley of mass 7.07 kg and raq ph;iuva8 6+ddius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mas24t0ope3, /b- hsrsh ikzx yg9s 7.07 kg and radius 66. 3s o zr,e9tsbxh2-k4p0ighy /0 cm. What is the acceleration of the mass?

  A rotating flywheel can be ka)i(9 g6zh ikused 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 inerti:bpw;v0; v92sqd t lkia 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 0.010 m starts y/w*pxh.4 dm0z k9sf gfrom rest and rolls without slipping downyzwdxsg*/ p0.k49 m fh 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 radius 0.010 m rolls with a speed o1 s4lon2rtz4g f 10 m/s. How high up an4rt24zno 1lgs inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg ic-k-(3piqu xrr 9t6e8d1p+ vvs5e wbes released from rest and allowed to roll down an inclined ple9rsweqcrvi ex b3v +85u(1 - -dtppk6ane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls witho+ jqm:4ej0+,relady out slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of r:old+j qjy0+,me4ea 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 z n-r:py4 db2coglcm/ -b/8ytrsb3y: o wr,z: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 moment of inera xtkr.)jr ,+xtia 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 exfbulmr+tdnozva -2(es7 y 3 55tended has a moment of inertia rdoam2u n5tey5( 7fs z3+bl-v of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?