Angular displacement ix i e(p.pr9u(2-u*vth;r+rldh:ar,qt kglh.s usually express in units of

  Angular velocity is expressed in unit fzu)6j6j wdm 9u9+8- ltljtin yrl9, cvw01bss of

  Angular acceleration is btf4w /k4g sg)t5g5e:5fd+ qy oc n8rgexpressed in units of

  A boy and a girl are riding on a merry-go-round 98e7xwaht twik;s,z2 which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to th2tewhzi a8t 7x;,s kw9e center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turnin/ nl5 n.x43 axnzkf6rhg at a constant rate. T3xnlhn xzk/4 f6 r.an5he 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 which is turning atdj6p g8 d)v0lk a constant rate. The boy is near the outer edge, and the girl is closer to the centerd6gj8plk dv)0. Who has the greater linear speed?

  A boy and a girl are ridinghxzre;i.0q1i6l: kul 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 haszilq.1uixe0h6:k r l; the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round w a6bage: li.i15 h)ufphich is turning at a constant rate. The boy is near the outer edge, while ta1l b:huaifp 5ge6.i)he girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatinz0.y( equ(yi 40f yl+x a(xhzhg. Which of the following is an accurate statz uy 0( fhxzli+yye0a .q((xh4ement?

  Rolling without slipping depenu-9ny jiuzz5 uo 0s0jj3p:f;qds on

  Two equal forces are applied to a door. The first force is applied -jwj)xz w3dm 0at the midpoint of the door; the second force is applied at the 0mjzw x dj-w3)doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forceuen1cz 1 t-ou4 is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Whitu1 4ecoz-nu1 ch force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first sf7u*js3p t ,z 5 pf/tscc::ipforce is twice as large as the second force. The ratio of the torq,f5pc ic futs:*p:s 3/tp7z jsue of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotab4b +x nkev3)7tam3 cbg5h. pvtiamp.t cbv b4)5x+ bgkn hv373eon?

  Consider two uniform solid spheresp( cneg,2yy l8 where both have the same diameter, but one has twice the mass of the other. The ratio of the largeryl ,gn2ey(cp8 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 rada2jwquz zmgag2-:p 0+ius of the other. The ratio of the larger sphere's moment of inertia to thatj z u-p0gq2a2m: ag+zw of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass andy+8uhi, g h7gp twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertih+yg gup8h,7i a is

  A uniform solid sphere has mass M and radius R. If these are6r /d eg7dt8xp) do(gi increased to 2M and 3R, what happens to th7 p)(x6/rdg 8ite ddgoe sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an oncx i2o g)z5i,qk+p)hhh ;d*tbject, that object will

  The moment of inertia of a solid cylinder about its axis is giv49x7rrx ht+oc gym b5(en by 0.5 MR2. If this cylinder rolls without slit 5rom r4hb( xcx+g7y9pping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcyclo.ypehmi-wx0a7l:(w *y 0fp me 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 translatax0w-mf7ew.h yp:0(*y plio m ional kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R r(; 9p uqk4+kfp6fjg vsolls without slipping down an inclined plane starting from rest. The linear velocityf(; pqgs kfv+kp4u6 j9 of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radiusdu1kap ld6. +e R rolls without slipping down an inclined plane starting from rest. The angular velocity of the spul pkaed6.d+1here at the bottom of the incline depends on

  "The total angular momentum of a1r*3bew3yms1, f0lmq ga;ked86 mp ma system of particles changes when a net external force acts on the system." This statement,q* kyd38mlmprbfw3gaam ems61;0 e1 is

  In what circumstances can the angular velocity of system of particles changmo*jm/ e7xlu-e +xco 5e without any change in them+me5e /xl7cx oo -*ju system's angular momentum?

  The Earth orbits the Sun in an ellipticalv-h6h aq j9h)eobm;5c orbit. Ignore any friction which may be present. What happens over time to the Earthh)h h;q6a mvjc-e5o9b's angular momentum about the Sun?

  The Earth moves about the Suc1otpx 66umr3(wub)qjfwp.wd30 . sa n in an elliptical orbit. As the Earth moves close to the Sunw0qt)dm. wur ajcu(6p3x bf 3 6pso.1w, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchel d3:hezkww;g:v3a u8d arms close to his body. What happens to his angular momentum about the axis of rotatiol3ve 3zah8 wd ;wkug::n?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre(i opoklao+5y;3 kr f6tched arms clo lkpr;3 kfo6ooai5+y (se to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou)ley,( j0bvbhtstretched arms clove l0 ,jybhb)(se to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular c9tb .nd 0 xwe8holi1 era/-w7momentum.

  What arc length does the Earth travel in a three zbbq5n7;2 wa:j:7ddsgh- obe2 a+ t txmonth period in its nearly circular orbit about the S5- bhdq7to d2b:g bena:+2z ws;a7xjtun 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 does the +- qaclr)7mjyofm:bmk3 a:f8;fal9 btip of the second hand sweep through in 3 minutes and 45 saf8fa l bmj: 7q-fa om 9:);kycrlb+m3econds?

  How many rad/s is 25 revolutions per minunxd fwc4uz 2/9te equivalent to?

  A bicycle wheel rotates u /mr219ls gek8-ju.talpb 1gw niformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotat21gb g9jp.1/asltm l uk-w8erion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Tmc p n(yui)6yb;ioa*mz *7bp)he perio*b mo) 6a iupiy*(7bpmzc); nyd of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doesuryrm4 o1jb8 oc-+bk. it turn in 0.20 s?bok.bu-mco 1ry+r j 84

  A wheel of diameter 26 cm turns at 1500 r8e1i/ p/;*bjbz8i /vg z4ym7ghjru ocpm. How far will a point on the outer rim move/r4* 8bi7g/h /8m;vijz g ebpoyjucz 1 in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions inbd4md +ql7eagc/+k7f 4.0 s. What is the average angular speed of the whe g d4c+q7kdbal/ e+mf7el?

  A bicycle wheel rotates uniformlym 1-d;d-sa(b hn3bpxdl*abd 3 through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ; hl3b-bpd*(dn d1dxmb -a3as of the wheel?

  A cable car at a ski resort carries sh8* i1v gv4gbp5do 1l p9av*rkkiers a 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 for the cable ca lk 5pv*hv9dv4o1bi8ggr*p 1ar to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant l5: p, k:v2qj:avzo.p yguocn71 eqvt 3vg,x1 angular speed of 2.0 rad/s. What is the linear speed of a point on5c ugjanoz,v 3t qpp q2vlye7:1ov:gx: v1,k. the wheel's rim?

  The cutting cord on a gas-powered weed cud)ij q-241crbq)1fx hzli1ye(a k9rstter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the1rzq 2blf(d xec9 ksi a14jq)iy-r1 )h approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatinc7jq0 (aw25m4gjs:xnm hd/s squ2v o(g with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a pointag/ s 2: qoj2mm(hsw0 (7cvsd5uxqnj4 on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter o3gosam fv;* 5lf a bicycle wheel of diameter 70.0 cm when the bike is moving fov5ga;3*lsm8.00 m/s?

  How many revolutions per2,ppx,)m:7 zo t / ebmrf9dm5fv o7wwp minute (rpm) must a circular, rotating space station (r = 1000 m) ropdp, ,m5:fe 9)vb2omt 77f/zp rmwo xwtate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a5k w/we6i6s5p-c4h 0 wahnyzx speed of 20 m/s. The yk5p-sice / n6w5h4 6z w0xahwmaximum 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 fl;jx7z 9 +uhavf c; z9xm2ucvj.k8dsc2*9 jmcoat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal fm v7z +jccxv28j;cmu xz ;92sf*u. c jka99hdoorce (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 the7byv 2q7s)zfb end of a 0.750-m string, is whirled around in a smooth 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 s7bqz2svfby) 7tring is not to break?

  A bowling ball of mass 7.5 kg and radius 9vq 9l, mxg(u(l.0 cm rolls without slipping 10 m down a l (9m xqg(ll,vuane 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/ qlv ahga3gfw ) aw8hr+8ts60 constant 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 angulu v ar(gk2u-mk/htu03 ar 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-vr6- vviqr -uodl..a.300-m radius automobile tire rotate after starting from reidu v-. r -qa6r-vv.lost 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 an angular acceleratibm5vf fd,90wyon of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelera(us8y ;y/a.wyue1g eyoc0n0 ltes with a constant angular acceleration ue/e w1an.yc yy yos l0u8(;g0of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from r*vksl95*z;fvtcl wv vr9oh1 l4y +8klest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of tvl;y15* lkvlkrf+so 4 h 9w9v8zlc*vthe wheel?

  A wheel of diameter of 68.0 cm slows down uniformly frq ex z/p)gytp z8p+,3zom 8.40 m/s to rest over a distaet+p , y8p3zg/z xqz)pnce of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 6 v pl e*lz2n1s7i7pg0s8.0 cm slows down uniformly from 8.40 m/s to rest over a distz2p7 le0 spgiv *s17nlance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.402d kupbr nm)gfjby5zi k7z-k3yt55.2 m/s to rest over a distance of 115 m. How long does it take for the wheel to com 3p rzd2f5gb755 ki k z.ty-uk2nb)jyme to the stop?

  A centrifuge in a medical*4j 5 pbilpv8r laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to84v* pl5jprb i 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 90 Nq r yj6tu1 ,mn ;pe1rk,3pyg)hm. If a 30 cm lonq,3yhyupj,te mgr )k11nr p6;g wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel ruc2qw 6 rv+d6uequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requd +2vwq6ruc6uired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in dd5p+a7w h0qhertia $3.00 \; kgm^{2}$ 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 a2pqboz4yji14 qw) h9ot the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the ori zqjwhb9 p4q 4)o1oyi2gin?

  A solid cylinder of mass 10 kg is pivoted about a fricti.zdc i)r1ama( onless 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 r i (1aacmd.r)zight. 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 masnl5wo7)crkd av-s k,6s eph5.s 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 Nho6p.ln)d55-sw, k kas7evc r 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 hinge dcor -mwni2n( n:e-kao 5;7cfd at one end. The rod is initially held in the horizontal position, and then released as to7km c w-rondcan2-n 5i:(f e;he 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 1.5 kg. Neg+jct+y+ l*qee5 (aj o e,(gbvulect the mass of the axle and sprocket. If a force of 20 N is applied tau,+5glb o+ cv e(e+ejt(qjy *angentially 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 fricsyilv 2 -,45 kvohls1yjpv(m4 tionless disk pulley of massl2pk -h(v s54ymv1y, slovi4j 7.07 kg and radius 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 6f7+ mt7 v tcg53mjg.co.yoytof mass 7.07 kg and radius 66.0 cm. What is the acceler c6jm fttyoo.7g537ct.gvmy +ation of the mass?

  A rotating flywheel can be used to store energy. If it is required to stops0s j9a,fej-a-k s u:re $1.00 \times 10^{6} \; J$ 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 oy z 7n sr48h.bq6m/lainertia 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 0.010ufup+ r, voa 0s.v t(gw-h8jm(zp- 1b6 nrf9lh m starts from rest and rolls without slipping down a 1.0-m high inclin0 -r p w 1o+,uf(pnuv9gz .8j(strvhlfma-h6bed 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 radi-h)x))j,sh r- plhp(twypxnvaik8+cg. +f g4 us 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming a- jh+g (k-x. h48cppsfgwv)ri h)+xly)tp,nto rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fr0 s hurg7,m6 o6j:vu:b0newvwom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of:g 6 :rv, 0um7bow0jwvneuhs6 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippi;(qno4n tu3 n d73gnimng down a 35e incline that is t 4n 73(mqg;uon3idnn 7.0 m long. Assume it 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 ppk0zw 5l0 z-i2 *kg3bt(jlvzmomentum 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 iner)-i)uvh 1 )mtnsidk/zy ii-:ptia 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 wiruh d 3 isjmv..m/5p1ith arms extended has a moment of inertia mmiur5. . p3s/ 1jvdhiof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?