Angular displacement is a 68+r .klwg2dygcnp8p 7lep*usually express in units of

  Angular velocity is expressed in units o od 07rsbpb(a*f

  Angular acceleration is exm wog5xc8h(ei.4qo b 0pressed in units of

  A boy and a girl are riding on a merry-go-l+j7t+(f5 nx,a tdk))+ yxznx/nbmv3 hp*yg dround which is turning at a constant rate. The boy is near the outer edgej, zmn+/+nv y5)d)3ng 7t+xh(*d xfpkybxla t, 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-round which is turnin, lftipwzu,+: g at a constant rate. The boy is near thlwzi:+f u,p,te outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding b cs5:tpcmbt 8:v+up*on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer t5bv8p:t:c t* cu+mpsb o the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which /q4/ l riw6vb) gh8 :yaaxky+o7vv wo9is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centri):wgk/vb 6rwa y8 h7yqxl4ao/9o+vv ipetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at w8(pu /d *qimda constant rate. The boy is near the outer edge, d du/( 8*pmiwqwhile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an acdx3 * u,zyw el3*rf+wkcurate statemenk w*urxe,l33+d y*wzft?

  Rolling without slippins:6l9(+ej mgdiq zun* g depends on

  Two equal forces are applied to a door. The first p.q u yvb :*dp(kuiz;/ n74qmaforce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torq(ku.bpaq7/iun:4d *v q;m pzyue?

  Two equal forces are applied to a door at the drptj * dboah kq48),ez90 s:ixoorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of tha9kp: j 4bo8td h ,zqrxe)*s0ie door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicula rs3f,/3p orvkr to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torqu,rskv pro3/3fe of the second is

  What is the quantity used fsd*b,g ebe3,w1 idl4g 2eyx5to measure an object's resistance to changes in rotatio l , 4b5e1 y,d2sxebdwei*fg3gn?

  Consider two uniform solid spheres where * )82sgnvkcmwboth have the same diameter, but one has twice thecwsg82k *nv) m 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 same4pjmvv 1 gh m;;q-npe9 mass, but one has twice the radius of the other. The ratio 941vmp j qng;pem; hv-of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres whqwi- 3xs z2-vz/hnz5zere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momenhzs5qw3z/- -xz2n z ivt of inertia is

  A uniform solid sphere has mass M and radius R. If these are increa;vzy jo0pecv+kl213ci 6vy) ased to 2M and0;3+2y 6 zyova1pej)cl cvvki 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is appt ;zw9z.,chwvi y9*gl lied to an object, that object will

  The moment of inertia of aq: mb 0:aczr6o 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 translational kinetic c ::m0z aob6rqenergy is

  Consider a motorcycle of mass 150 kg, o0c /tmorpa p8an*4e8c ne wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotati4p8tae0o * 8/mparcc nonal kinetic energy 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 n.vb3ur +nfe mkyu, ./slipping down an inclined plane starting from rest. The linear velocity of thf/n,rv +y.n ubm. keu3e sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without syz5+ypkndsj;o- :af+ lipping down an inclined plane starting from:y5k dp;-sz+fa+n jo y rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system o*7 hou(sup.vv3w)z /2n 15rarcau rrbf particles changes when a net external force acts on the system." This statement inwrra z/.subv)7a2vpu(15 rh rcou3*s

  In what circumstances can ther4whl:d +1 mvc angular velocity of system of particles change without any change in the system's angular 41: mchwvdr +lmomentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fr) 3q5swrvt37 pcmz8bjj zjy(-iction which may be present. What )5jsq-3yzc jr 3ptm8v7 zj(bw happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movesi h+6ync8+v qt14bd68kt02 f uihufch close to the Sun, then which of the following best describes the orbiting speed of the Et b+hq2 dnvt fuy0u+i6 ck4681c h8ihfarth about the Sun?

  An ice skater performs a pirouett ;dnvl4,0) *zd/bm(jcttn yzte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momencd)tt, z/4nb ljznt y dm;0v(*tum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstr)u i0nsfv(* jgetched arms cifjv (ngu*s0) lose 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 ok/-yp4 y +9jygen(q elutstretched arms close to his body. What happens to his moment+yqp4jky9g/n e yl-(e of inertia about the axis of rotation?

State the law of conservat+bf tgcg.357u i su4zdh,4mwuion of angular momentum.

  What arc length does the Earth travel in a three month period in its nxkgmx; +h1in7cgt58 .bw8a r6 ,ole vyearly circular orbit about the Sun with a radius of e6bg .t,o x+lmnyr8ic87 vxha1;w g5k $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. .t1im e8ou.vhWhat distance does the tip of the seconmo81e vi.hu. td hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent thj/t )q-xeq g;itr *t7o?

  A bicycle wheel rotates uniformly wysac0.(-:s:o std br4ym lw 4through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotati :s a(ybs0td - rl.4c:oyms4wwon?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T;w3-; lh2*pprxls5 mpn-lq/ucv q-rbxp) c 6the period 6pl )hl ncr; m c-35qwl;/t-2p*qb r-x uxpsvpof its rotation is

  A phonograph record rotatehagjs+ c8-xl;.ux1x .d;dwi os at 45 rpm. Through what angle does it turn in 0.20 s?d+j 8gxxoudw.;hlix.a-c1 ; s

  A wheel of diameter 26 cm turns at 1500 rpm. vkd ):bul( fncsbe/ic+w (+gewk11u) How far will a point on the outer rim movef1 ()ve)uw1nk+l+ ( ub /cbcdiw:kesg in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whas5 w6al +9morvt is the average angulaw +a l9o6s5rvmr speed of the wheel?

  A bicycle wheel rotates uniformlyew /c kt*t7/lk through 2.0 revolutions in 4.0 s. What is the lik e/ct*7ktl/wnear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski r8.viuky u9 lxgh20e; cl+a 5rresort carries skiers a distance of 6.8 km. The cable which moves the car is driven by rl0ag8y ; 5+.uk ulr9xh2evci 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 constaxuas5bo ha 1r3u99 q9ewj,;6cn * vhzqnt angular speed of 2.0 rad/s. w65ah,u hbqz qaue s1 j39x99n*ovrc; What is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0 *)wvgcw*6;l zqn /.v ych.bna.16 m in length. If the motor rotates at the rate of 20 rev/s, what is bq z.cyw.h ; nclnvag*v6w *)/the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m l2 e 12:i8xtm .xcxvjuis rotating with a constant angular speed of 2.0 rad/s. What is the centripeta.:x2el i1 x2jmucxt8vl acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on ml s-9*w;h b-gfgtgv*ozj5y6the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mo*wg9fg h5-to-gjm *v6zyl;bs ving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating sp0slepedapm.-bl cm jt2, y)18e*3r-m fl e s6wace station (r = 1000 m) rm swyf63pl,l m ebeacet*d2- )8jp-e.r01mlsotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with 0*jht:s6 );kguxlbek a speed of 20 m/s. The maximum centripetal force (provided by stkhtb e6)lk0:xgs u *j;atic 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 radi(60io.sqa uaa s f05vaus 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictaosq.asf600i (5uvaaion) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attmcbuh0558rcn8;gtw kached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the strig b;rwntc5u5c m 08k8hng 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 kg and radius 9.0 cm rolls without slipping 10 m )tq gksuot2q:.k:l8 m8d fyf* down a lane a)t :8qsk mud*ol8qk:.fyg f2tt 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 av:fz p*g3 c9kuz)igg7ngular 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 acceleratiotr ocp-g ((duv1e5,um izy(-on 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 doeu4 ixy4(3t/g+ rld+dc,bo-7xp5v4fqkh q pzg s a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular accelerat+fpgrlh-xx kup/4i 4tdygc,4ov+ (b 73qqz d5ion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accel2abmb6,vbbp .4) zkq aeration 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 5vhfd80pfi , g9j4gkl a constant angular acceleratiogf 8pvh0f4 5gk,9dli jn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an ang;xu0 c vc z41o;k 1qza4zzgc l3xop6b(ular speed of 6.0 rad/s while turning through 2.0 revolutions. What is vx;b 0 cap3z1 oc4zgx1(4olkzq;6z ucthe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oe 0)jr7dml/ jover a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?rj/ml e 07)djo

  A wheel of diameter of 68.0 cm slows down unijt/uks9.-ph huz ehb*9; 9 atgformly from 8.40 m/s to rest over a distance of 115 m/g.tab99 -kp *he;t sh9u zjhu. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fro4mf6oimj). hxc x4ky, m 8.40 m/s to rest over a distance.h x)f 6jyiom44 kx,cm of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical78*f 0mrqvp bq laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratiovm7* fprq0 8bqn 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 90 Nm. If a 30 ce ox, +1ut x .y:jbexyx,a59zfm long wren efo,ax95yxjx.ux y : +b1e,tzch is used, what 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. I3xnyy0v 5h *ed-qs(cd u*u k.wf a 30 cm lon*h y.w3ynseddv*-q0u (x5ukcg wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofd9*q(( h jk88 gci v.wxm.trklh0ei*h 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 i9*ji:n a9kxwv/b3 05tcjkl mrs modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the*j9at klb9 r:jw3nmvki 5 /cx0 origin?

  A solid cylinder of mass 10 kg ismaxo b,5qdggch 7br)g x*,z3r y2 4nb3 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 = 6.0 N downward. (See Fig. 8-1.) What is the angul* 33,xbrgnm bx )cbz5 hro,yg2a7q4gd ar acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a ((ll::az *s r/sxiwml +o0ec gfrictionless axis thought the center O. g l0l+*ml::o(wcs/e(isx raz 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 rodapsc:/ww e4 mrl2 +k/w is initially held in the horizontal position, and then released as the free end: spcwmwr+4al2/ wk/e 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 wheel5wdn3 ba 1(btr to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a forcbb n3a5r(t1dwe 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 wrapped81c( bb mlqcp. around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is cqlpcb.1 8b( mthe angular acceleration of the pulley?

  A 1.53-kg mass hangss,kkx20 ,q hz(/ggc sg on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the ma,/k 0zxghg g, qck(ss2ss?

  A rotating flywheel can be used to storaslysf,bh/6io0 1m4q efw*hbo 4s9 -ne 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 ofa)v.6vt(xpspn .y1th $5.00 \; kgm^{2}$ 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 fr6b9+d1o6* gi 8m ctppqkj)oypusc c0/om rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphjcy)ip+1q*p kdgcm c8oo6 utbs/06p9ere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rollseh cf/l9/o3qd with a speed of 10 m/s. Hq//loec dhf39ow high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.s(hoy u4ef4a8va(. idh18ds q20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distan8a8v(4q1ayeh. 4(d sfd suohi ce of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm roe6 - 0wclbdv2 kpscmxq27 nrp6*p /)xx68dzf clls without slipping down a 35e incline that is 7.0 m long. Assl6 c0 )qd86dx/px sw x7nce*b2pzmkfr2c-6vpume 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 momentum changed:ewpoh/lk0,p6gv +l-rxw s9s 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 inerti+cdo d,r w1,bma 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 l ;anm k8p55dkrad/s with arms extended has a moment of inertia oampl5kn ;d85kf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?