Angular displacement is usually exprestm v a4olp3w41s in units of

  Angular velocity is expred5bk+ .iyh4l *eil ,trssed in units of

  Angular acceleration is expressedtkvwo (3quf39 in units of

  A boy and a girl are riding on a merry-go-round which is turnilp;w+ 8q p,wc:efi:5 vj itcl(+doib0ng at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular disp+oi ;+p,:(jvt8:iiw f bwd 0ccqlp5lelacement?

  A boy and a girl are riding on a mufymkx-/ j8o.1 h)kr-rv0ta ierry-go-round which is turning at a constant rate. Therx0 i-v -uo)m8.tyjk1afrh /k 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-xpmd.)d6vc rw7-,nivp yz /1 vround which is turning at a constant rate. The boy is near .)vdvrw nd,vimpz 6x1cp y -7/the outer edge, 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 ae(z quqv x*wm m7.2hf:t a constant rate. The boy is near the outer edge, while the girl is closer to the center. Wz *mq2w.(q vf :umxhe7ho has the greater centripetal acceleration?

  A boy and a girl are rxcxmz rfglv4tsfk7:)ee4d*1/ s +1d viding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is csz x/vfm+ 1v*4fe ck:er4 gsx)17dldtloser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followokt)xh4/sg0 zing is an accurate statemen)4 /kg xszt0oht?

  Rolling without slipping depends oql 0o ourti a6pa*)-le84; 2kibgnu/dn

  Two equal forces are applied to a door. The first force is applied atl r4mc9i-iq b7 the midpoint of the door; the secondr ib-m7il9 cq4 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 the doorknob. Thi7qu bshs,) /ie first force is applied perpendicular to the door; the second force is applied at 30i7u is)b/,qhse to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknobv oy*) 7fd;tcb, perpendicular 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);cfbd7vot y*e of the second is

  What is the quantity used to measure an object's resistance to chaj2pll/rr m b .vwi(5,knges in rotation?,2 .r5bvil prlm/w j(k

  Consider two uniform solid spfb22lle/ lvve-di v 7dne 5a)v245q-aj -ptegheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that 2 n e-qv4vfg2ivplb 55-ted la jvl27)-/e daeof the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice nc6nrkg5lxv6kf wyc 6d,:i *.the radius of the other xw6clvdi kcf:6 6nk5* ng,.ry. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid snmu 3b7zcb2 za.uotbq,(l72x pheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inerti q7ul,bbu7 c3.(2za zx2motb na to that of the smaller moment of inertia is

  A uniform solid sphere has mass f;t* quit(80,qc vjdn M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central qjicutqd*, ;(t 8f nv0axis?

  If a constant net torqu)3 hip kcpx xfa747wn9:-g orfe is applied to an object, that object will

  The moment of inertia of a sole6pxk,,(s e t5k(lv*pe op s u2dpv8n3.l9valid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its 6eodn2,pa 95l3.pupl8xevpsvtek*( sl, vk ( rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mu:s c2rsv;3l i0pk br9xkvlgcb1+y . 9t b+js:ass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheelp;yl +v ji bc9rrbs9ls.+kbts0:g:1u32k cv xs are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippinf ox) 83oi69z upg(j dbwgs(hisa w;86g down an inclined plane starting from rest. The linear velocity o)g(os6as6;3w9hf88x zgo djiw p uib( f the sphere at the bottom of the incline depends on

  Suppose a solid sphereg,wpd ) v:*s:dnef, sa,qdh4x of mass M and radius R rolls without slipping down an inclined plane starting f :sd,4d, xd qwg*eapfhnvs:),rom 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 externa/hhlbx7u+b )4e-a0a4u c8 sykp2*zu h umqu4ul zm uhh*)u4b 4p07ayk ucxl-4bh/s8ue2aqu+u force acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles ga8k;d(9 jjrwchange without any change in the system's aw(k8 jrd;a9jg ngular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction,ft4pfln;m:o,fwi d1 cdwf;1 which may be present. What happens over time to the Earth's angular momentw:4m1l1;pwfcdn , of t ,f;fdium about the Sun?

  The Earth moves about the Sun in an3ul6 eclmjd-k/ qa4 q* elliptical orbit. As the Earth moves close to the Sun, then which of the following best descmlc lq3*4 j-qa/udk e6ribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast s/tyq9eax m*)0p cxp9hkcr 8x 7pin) by pulling in his outstretched arqp7ex h98aykx)/pc rc tmx*90ms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouettebrn8 9bsk qb:e)xl7 g1 (a fast spin) by pulling in his outstretched arms close to his body. What happens to h7lxk:b e bs8bg)q1 nr9is rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchej,g 9vxjtqt2an 1; s6ns 5+glgd arms close to his body. What happens to his moment of inertia aboutj vqat;x 5 st n,j6lng12sg9g+ the axis of rotation?

State the law of conservat a up-gw9f+xb 9 0ojq;*cr-mlxion of angular momentum.

  What arc length does the Earth travel in a three month period in its*i,b(uu,-c w2wit,0j .dukh4 oba ns q nearly circular orbit abosb a iwq.(j,bnh ,*-uu2ti,kc 0dwou 4ut the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length opr ,s7ef5i3+t jjj6 sdf 0.30 m. What distance does the tip of the second hand sweepfed+j r,s3t j jspi756 through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per m(a0*qqvh1z tqinute equivalent to?

  A bicycle wheel rotates uniformly q+ /se8ap;bk ethrough 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotat;kp/ ee+b s8qaion?

  A pulsar (a rotating neutron star) emits pulses at ;aybehb n)0+h4srf5)t 8 n qbma frequency of 0.40 kHz. The period of its rotation iqbe b 8;0t5 hrhby+a4)nf )nmss

  A phonograph record rotates.u;dh d(mh ;fq at 45 rpm. Through what angle does it turn in 0.20 hduf; .(d;h qms?

  A wheel of diameter 2tjlje;*f ude;tvi04q w: wr856 cm turns at 1500 rpm. How far will a point on the outer rim move in *05deq ljr8u; 4feviw;jt:t w2.1 s?

  A bicycle wheel rotates uniformly througho ob,r6z;sa85oe ins/ 2.0 revolutions in 4.0 s. What is the average angular ,n8 i6;s oborzsaoe5/speed of the wheel?

  A bicycle wheel rotates uniformly thc b u4l0:z p4n(sfziy7rough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.7 u pfnybzli0c4(:sz 410 m from the center of the wheel?

  A cable car at a ski resort coi/:+xy -c u.b+tbh icny/8fp arries skiers 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 car to mauf/i.-p+yhcc8nxt b + :o/ byike the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed o0 13ju7id3zps7rw hj cf:veg*f 2.0 rad/s. What is the linear speed of a j7ipc*3 sfzhe37rj0 d1gv:uw point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If tzuw4nir *cl .cp8b9)nhe motor rotates at the rate of 20 98n4bruczn*i.)c w l prev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotad71jw8iub1ps*s.dc-iz ;a 5nza2ze7rnl g*m ting with a constant angular speed of 2.0 rad/s. What is the centre8nz gmjsr1b 1npua7l7 . zw2d;a-d i*sz*5icipetal acceleration of a point on the wheel's rim?

  What is the centripetal accelerakx +b9phar:dv 2 z3al)tion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is zr3dva xp9kh l:2) a+bmoving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotamaqg;r/ .m 66srkxk: cting space station (r xk6mcq:rkg/r ;s .m6a= 1000 m) rotate to produce an 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/s zdlu8n6lf g;ta z98l0. The maximum centripetal force (provided by static88z6 nlazl;l9 df gtu0 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 radius -p6 , eemsbr,a50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction)er6p,b,am-se is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to oy;eiax ex0 99the end of a 0.750-m string, is whirled around in a smooth level ta9xyx ae9 oie0;ble. 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 kg and radius 9.0o6jy+,vex/j k cm rolls without slipping 10 m down a / oj+ xvj,e6kylane 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 angulv 4 49zr/iqgolar 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 constad7zj upp2r ;o 0kv ks4(rh4ork:z7x/znt angular 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 0.300-m radius automobi y6i*tghfd-: ple tire rotate after starting from rest and accelerating a f6ygd*th-i: pt a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest etp8c; 2y:+7xcd ztgt, 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 decelerat5mnk wscx*(5res with a constant angular acceleration ox 5( cr*wk5nmsf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6kg9 q-oii1*vu k9k ya5.0 rad/s while turning through 2.0 revolutions. What is the aveikkvog5y1ik*9u9q- a rage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dow:x novy2etq( 0(cs l1cn uniformly from 8.40 m/s to rest over a distance of 115 m.(2ylcts:q( nc e0vx1o What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest 4ars ze ycy346etck/x:8: d-2oe, yuz ue 0cvdover a distance of 115 m. What is the angul83os :yeuctc, 4 xr6e2 /kee:y-4dz uy0 zcadvar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 l klmx3ma 8.*9gv t1,ep lo*ykm/s to rest over a distance of 115 m. How long does it take for the wheel t ylmkl9 8okxl apg* .e31*tvm,o come to the stop?

  A centrifuge in a medical laboratc dx,sp /a7 tqusl6+7eory rotates at a rotational speed of 3600 rev/min. When switched off, it rotatu,6d7qx cp t7e/ssa+l es 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 whep2j4 ,p9qm2)vugzn zpel require tightening to 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 perpeu pqz 9gp,2mz2j4 )pnvndicular to the wrench?

  The bolts on a car wheel require tighteningo +et0+ekcsen0 7yl+6d bln- e to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required whlyen-n6s tec+00k++doe 7lbeen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of9ybmwg j9mmd;- z 23ej 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 t4 wivq+ it-7; 9v/n 0qjgbqupmodeled 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 origin n4v ;jq79/giw-tv+buq0pit q?

  A solid cylinder of mass 10 kg is pivoted about a frictionlesn )waggt51 o:n5f 0ipvs axis thought the center O. A rope wrapped around the outer radius R1 = 1.anwn )to 0gpv: 1f55ig0 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 angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pdip wkneo-s.v.s;nqzd)ec: u v12 .m3ivoted about a frictionless axis thought the center O. A rope wrapped around the outer radi;. .omszdnv.):v3i qkpn-2d1 wceuse us 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 rod is initially held in yeufrp8e)u/- y37 r btthe horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertiar /pyr)8e ueb 37-yfut of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a rq k-2 ez-vu)i,mlciep3 us no3t0q:i 1ing of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a f: isuquc 0pik-l t3oq),ez m2-vin3e1orce 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 frictio2zy-9 48m jz6s kj8uceo+shrxnless disk pulley of mass 7.07 kg and radius oh2j4c8mxr8ey+sz- 6 9jkzsu66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pul (s1/jrf-0cve j4a rrsley of mass jfvr /(as4ejrcr1 0-s7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used tc.: 1rwzi5b vdo 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 inbm 2zd1n 0gu(bertia 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 kgu8zj c mro;85,brgw0 j 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 plane?b j;or g08,crz85mujw

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a sp3ddam1f.bk 7fzgd. 4h eed of 10 m/s. How high 1gdfd7z h .bda.3 4fkmup an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fr ivsr 4vrhjxwg lcdzt82f28q xbi05;)n ;t,q1om rest and allowed to roll down an inclined plane. How fast is it movitiql d02wc ;ibxq,;t5s1 4x g8h)fznr8rvv j2ng after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm ron 8w)fk.nk7e+dd +qcvlls without slipping down a 35e incline that is 7.0 m long. Assume it started frnnd)vek+fk q8w+.c7 dom 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 mowhkp)/ si61ac mentum 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 inertirr qczxtz (any*a+(15a 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/6uatx va/g( 5fs with arms extended has a moment of inertia ofvxa gaf/(56u t
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?