Angular displacement is usually expres o hf/6;ja-beq6 p./vck0zrdss in units of

  Angular velocity is expressed in unit1 hncnn8sszzpb/ 1m5w/h/7ros of

  Angular acceleration is exp9p g:i27uqknv 49i)mvf cyj5sressed in units of

  A boy and a girl are riding on a merry-go-rouf0kwj n9z7 +evnd which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater +7k09 jfzwven angular displacement?

  A boy and a girl are riding on a merry-go-round 2bqtpb )ngr /4we7s0 vf7m qc;which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ar7q ft24;)bp gswb/7 mq ce0vnngular speed?

  A boy and a girl are riding on a merry-go-rer604biodt2mvc2 vk ;ound which is turning at a constant rate. The boy is near the outer edm2ivv6t24eod;cb 0rkge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant raten6 v+:2tcle;y-oycxwj9r sh5 . The boy is near the l5t-6yxr o +2 jc9nevh:; cywsouter edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a consta3a d3 a0zazy-apqf e3j3z;cq +qv9;qunt rate. The boy is near the j30a9zda- qqzu3; ;a zc3aepf+vqyq3 outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating.r6tx*k g.hw 9q Which of the following is an accurate statg9.6k* tqxwrhement?

  Rolling without sliptn j 2hlto7x;; wm/py0ping depends on

  Two equal forces are applied to a door. Tq8swb*r k ;;eshe first force 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;k s*8er ;wbqs the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forcenb )yozgig+yt0lb9dt2w jm s*;.c3 2z is applieyw *g ; j l)9ig0csz bmt322nzby+t.odd perpendicular to the door; the second force 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. The fiuljw. m;c/9yurst force is twice as c9m.l ;u/wuyj 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 resis *2ru hxqe6f0jtance to changes in rotation?0 hjx fq2r6u*e

  Consider two uniform solid spheres where both have the same diame az3crd+9d*fspu 8it: o(/tz6um 5xnfter, but one has tffd/tzmiuup *r8a c 6359x:snd(t o+ zwice the 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 haveul-b4j.s q6nj the same mass, but one has twice the radius of the other. The ratio of the larger sphere's mn64 qjj.-lbus oment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass .qw *e eo3a/ay6z/1kgat sp1n and twice the diameter of the other. The ratio of the larger momen k1e36t.ana oyapwe* /zgq1/st of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incrj d/-a5lcsm6 sk,bgb ;eased to 2M and 3R, what happens to the sphere's moment of ine,kcsdb b 5lm -ja/s6g;rtia about a central axis?

  If a constant net torque is applied to an objp:q in- ki4tw*spj (+wect, that object will

  The moment of inertia of a solid cylinderk0u.*vk ujns7(qc9 oo7wfo 2 d about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its r fo7 wdnu7kc* (s9kj.ov0uq o2otational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a zhfq( )jv95* drsun)gmass of 10 kg and a radius of 30 cm. What is the9v)*n(5r zu sgh)qfj d ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid spher*:uxr7qq*8 ;e aexpn.*gz f g6fj ;hdqe of mass M and radius R rolls without slipping down an inclined plane starting from rest. T;fgz:hf; p6 x dqu*nrjage* x.7*8eqq he linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slw/fa4 w-df/u8 m +knmee(g5u tipping down an inclined plane starting from rest. The angular velocity of -w /+k8 mgfdeamue( tn u4f5w/the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of p k5bkgsb30eq+articles changes when a net external force ac+e q35kskbbg0 ts on the system." This statement is

  In what circumstances 9ft7cg,:m ,iw0a qnu xcan the angular velocity of system of particles change without any change in the system':ag7wx,cutn,i0mq 9f s angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore an ase:ceu c)b5+y friction which may be present. What happens over time to the Earth's angular m+escb:5uec )a omentum about the Sun?

  The Earth moves about the Sun in an ellix -wgyn 0tvd34ptical orbit. As the Earth moves close to the Sun, then which of the f3dnx4-0wtvg y ollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in i4ojw5 1.chqciap.0h h(9dca scu:0dhis outstretched arms close to hii ch.s( ci0wh0: dccduq. 1h9ap4jao5s body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hi96o:qzmtt95 t b:sycps outstretched arms close to his body. What happens to hist 5s9p6q:tz: cmo9ytb rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast sp)q;cm z-lf, erin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rota -)z;fmr,leqction?

State the law of conservation of ang01n: ;kwqkj nxular momentum.

  What arc length does the Earth travel irku2sl1b ch;4vx m .u7n a three month period in its nearly circular orbmbu2 l7k.uv;c s1rx4hit 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. Wha 0.qdbb51cu xst distance does the tip of the second hand sweep through in 3 minutes and 1suc xdbb.0q5 45 seconds?

  How many rad/s is 25 revolutions per minute equival s /k)pci1uw)dent to?

  A bicycle wheel rotates uniformly through 2.0 revoluhh .c2v)(kdjitions in 4.0 s. What is the(kiv2j .h)dh c frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 gwpg0lnd0 :y+ ,m0khhkHz. The period of its gg 0km :0,lhd+nwhy 0protation is

  A phonograph record rotates at 45 rpm3 yck7dz4 i o:jwn90xcb9cx+ o. Through what angle does it turn in 0.20 sx40cb7 ni cd 99:ozok+3jwcyx?

  A wheel of diameter 26 cm turns at 1500 rpmd / -ou rxow,bhdqn5;(. How far will a point on the outer rim move in ,xw r d-;qo(bo/dnhu52.1 s?

  A bicycle wheel rotates uniformly thro9 b.bbfouh+xp 7v*4+jbo,imn ugh 2.0 revolutions in 4.0 s. What is the average angubp9.f,7 b+bioub*xjm4v oh+ nlar speed of the wheel?

  A bicycle wheel rotates uniform-sc1qg3dgvpho 41o7a,o-bz*0 zjw xgly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the whgps 0jo 14g,gd*wz x-3aov7bcq1oz- heel?

  A cable car at a ski resort carries skiers a distance of 6.8 kncf9mvj ujdv/)xdx:rk;- zz0f 7, a2hm. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuj);vfmx dzzf d0,c v/:hnr 29ju a7k-xming 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 constant angular spe;0xgd6q; ol zqgtra(1ed of 2.0 rad/s. What is the linear speed of a point on the wheel's ri1 qg0d gz(;rqo6;alx tm?

  The cutting cord on a gas-powered weed cutter is / e,*vhocy9ad n45njj 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what ivcd4o5 ,/ha*enn j9y js 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 :/n m. cp *w3ttegc/w93vvvzirad/s. Wh.9 nmv3g:wt v*/w 3czpvtic/e at is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceler q co/)8ly *5xsmm-ojkation of a point on the perimeter of a bicycle wheel of diameter 70)mcjlmxs58-o o/ q ky*.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulam),s / h4l.cum q/pkplr, rotating space station (rm/l./c ,)mp4 k hqulsp = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating ad0o 0+c2g0spj2 qy n/jar;yoo5y +ifh flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force+ 2io;/djn ysoqgy052 o0afhy+ r 0jpc (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a f 9ig4ly/-lbislat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by st4bllis 9gyi -/atic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to thema:i. 4l2c.6xnubkg u end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that tb gu .2un4:k .6liamcxhe 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 kg and radius 9.0 cm rolls withh4zy2 nvl34teout slipping 10 m down a lane at 4.4 vh4 nlz32yet3 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 constanhy ;,kwhum2cb /2 v;let 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 acc2u5bh7p 83 fedcga 1m4v3kh8r k4xwsveleration 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 rad7iz0vfv4 jl,1s2zb1 iw uln,eius automobile tire rotate after starting from rest and ac1j41swvue0iil v lz 2,f n,zb7celerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest 9p i p44;.xin8jyimo*6s ecyn, 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 (t bev+d6g 25xud:dhf20 rad/s decelerates with a constant angular acceleration of(geuh2+:d xbfd6t 5dv $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an anguqsq -pqrr 19a.fe4 o0ilar speed of 6.0 rad/s while turning through 2.0 revol4reoifqs0 .1a- pqr9qutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.6cj/3tl5up.uav0ztoqtp9pq48ew8 kx s(o ,z0 cm slows down uniformly from 8.40 m/s to rest over a distance owp5tv 8tu 3po 8 qup ajkz4clxt9(s.e6oz,0q/f 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unq* rn m9fpld:e2k(: 3ymrea/x iformly from 8.40 m/s to rest over a distance of dx3/ f9e rlqn:e*yapk2 :mmr( 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 +r7ufg5(v 6-w7u e,den upbxjcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it takuwg+r- bned6 ( pf,v 7jueux75e for the wheel to come to the stop?

  A centrifuge in a medi.zix/s 1)ecqp q-k /(b(y egvycal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before cy(iqs qgzy- pevx/) (.1be/ckoming 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 5o fdvtq6v/e3hdc:i// b kde4require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitu/e / fcdqhve3t 6dbdv4k/o i:5de of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening tob7+c+vs)l4nu6trg xao*o g ijq d +2v8 a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requ jg cb8ui*rl vov+dnt+xs)g7 6+a42q oired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of isd sh8 4i/gzf7nertia $3.00 \; kgm^{2}$ 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 origin, mas*b9s ja4dc)x wh3f) ifs 2m is at x = a, and, mass 3m is at hd)j4w bac9i3fx )fs* x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is piv*;;bhgfasn o* 0yxkg :i 5mr+5qpi+zgoted 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 F2fsz gigk5 *rm xg*i:5 qop0b; n+ha+y; = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted j:5r cpxn9jk8 3 wnt1tabout 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. How many radians does the cylinder rotate throu jc :wjk5t3t8nrp1x n9gh 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 i6qi yxm09r- oynitially held in the horizontal position, and then released as the free end is -yx9 rq y6m0ioallowed 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 cmb v;lh 04+a7hm hmpgg; and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket og7a+bg; mvlmh4 p 0;hhf 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 frictionless disk pulley csl,e o+: ,iu+wmi+zjrv ;3gdof mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of wojci+r,lumz;: , gd+si3e +vthe pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p, l p+*alzcbw5ulley of mass5b ap*l,zc +lw 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requiredx 9 btmtm,q4y- 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 ine (/jc-xk xtm.irtia 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 massu 8c mwj+,,g:cdvvo8 j 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined p8du:mc wvo+jj8,vcg, lane?

  A solid sphere of mass 1.0 kg and ra7qjiy;cr z8+h.n1p+pd p,6 kmia6mlmca ;o j7dius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb befjm+;podcz6p.a67m ric7 ,l hj8iqykm a1n +p; ore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest andu ,7 tr6jtuik zoat03qma:*z- allowed to roll down an inclined plane. How fast is it moving after dropping a vertical disuat qo a-r7k :z*j3mi0,6u ztttance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls with rnbc,z7)ml 65wi6vkxout slipping down a 35e incline that is 7.0 m long. Assume it started from r6rb ,6 vli ckm7x5wzn)est. 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 moml()4 77wqxxf l/ortrmentum 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 momejx qgqt:)6 6j c*ueyy m7za)w0nt 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 has a mome qoqx.)tv4*iz)ez. dd nt of inertia )q. ev)dxz .o *tiqz4dof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?