Angular displacement is usually er34w 4jw av95 aijlisq im5 t,b3d+mf-xpress in units of

  Angular velocity is expressed in units onoqo 26un+z+6 qnpkc.p j)p9z f

  Angular acceleration is expre,dmir,pw7z -fj 0ra4g ssed in units of

  A boy and a girl are riding on a merry-go-round which is tury2g su w( s3q45zai:vfning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ai: zfq wa(5vy 4ssu32gngular displacement?

  A boy and a girl are riding on a merry-go-round whikos0 ni7lcx 8/ch is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has ti0 /sk8nc7 loxhe greater angular speed?

  A boy and a girl are riding on a merry-gofa +7,h9dy mglr4egph84(lo jd w1 at.-round which is turning at a constant rate. The boy is near the outer edger( 1+7 dg4fawg84.e ymtplj,a do9h lh, 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 turniljs4hri: umgpvg4l ua;d48(, ng at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who (4 8,hgvlrm4g4u ipuj:al ;sdhas the greater centripetal acceleration?

  A boy and a girl are riding a merry7ff;dstp c,e1wc9) y4rvmam 8 -go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cente)ctf4a p98c7;res1 fyvmm d,wr. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an acp if+bwzgk4u5 p,6ln:p nw**ctka5+* sufnr ,curate sta4*,zwg c 5+:in*k*w ,pfrnuubtapkfs6n+p 5 ltement?

  Rolling without slipping depends onle4bf.wo c-:u4 )h lbw

  Two equal forces are applied to a door. The first force is applied at the midp0u7zs*os nne-n/86w 7 n urrh 9quium2oint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerm8s7e/hnn9 uqzu0 nrwu7 -2 n riuos*6ts the greater torque?

  Two equal forces are applied to a door at thecov5y8 / uvfm8 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 gmu/v8co fvy 85reater torque?

  Two forces are applied to a doork6y/ v5 zwr+cbs t8mcx,nob, 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 torque6 + wzmrc/sv8x5,yc tb of the second is

  What is the quantity used to measure an object's resistance to changes in r1ezz 3roiana)71ih2u otation?zeu7 z1r)3ni1a oh ai2

  Consider two uniform solid spheres where both have the same diameter, but o-x)lxr 2nl ezlq0 j0e(ne has twice the mass of the other. Tzxl0 le-e( jl)0rqxn2 he 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 twicpw1f s3bbv;rx 0 .e1xke the radius of the other. The ratio of the larger sphere's moment of inertirxv031 e b.wfb 1xs;pka to that of the smaller sphere is

  Consider two uniform h 9+/.s/e3llh fhjot ysolid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment o+lf jo hehy.h/39/tlsf inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are i;1v l*cq)f7zb+s / phb: xsselncreased to 2M and 3R, what happens to the sphere's moment of inertia about a central *1hs;p xsvb7e/:fslc)b +zql axis?

  If a constant net torque is applied to an object, that objecgw 986/ 9e/stfdni.pd+gxs ekt will

  The moment of inertia of a solid cylinder about its axis iu tmr *,q gt-cb q(n4aue0hs.0s given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of.(0ga0 bt es4mchu tn,q- *uqr its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg and3bec i/yc-s 13gr4ahib(bz( t 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 wheels arezte41( -is3bgc/ir bahb (3cy uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withob wgeroux;;0c0+9ir uut slipping down an inclined plane e uri cg;r90+obu;x0wstarting from rest. The 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 slipp,ss+0ll4a +r xs 2b/ bdnt,gazing down an inclined plane starting from rest. The an/zgl0b d+a2lx,4tsnrab+ ,s sgular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chanxnd:ln up sz 0eva*) 3.g2ylh6ges when a net external force acts on the system." This stad6u)g l.y0 l3:2exz phnvnsa*tement is

  In what circumstances can the angular velocity of system of particles 8u5exh v*i no40yp .inchange without any change in the 4.hipn8x y oe*50nuvi system's angular momentum?

  The Earth orbits the Sun in an elliptich rhi7t9/ed5 bh;gow 3al orbit. Ignore any friction which may be present. What happens over time to the Earth's angulario drw h935e/7hgbt h; momentum about the Sun?

  The Earth moves about tad/jt 21t 5qrh2wa)ap*jv jc;he Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of tvaa thwtc r5 p;/j21j*aq2)djhe Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his oumqe * 8rw7 q2tiyy9h ng)bjc)-tstretched arms close to his body. What happens to his ang8qthrc 7*9j) qyb) imewnyg2-ular momentum about the axis of rotation?

  An ice skater performs a pit;pssi- f oa20rouette (a fast spin) by pulling in his outstretched arms close to his body. What happenp aios 0tf-2;ss to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b nobyfo ht0+2h t)ol 9cb-07dl4 r3vqsy pulling in his outstretched arms close to his body. What happens to his momenth q0 n v27l4r)socb+-lo9b 3 yt0hfodt of inertia about the axis of rotation?

State the law of conservation of angular momentx,(l6j unep4wst no+(um.

  What arc length does the Earth j2d v pui74upb8gv, b1travel in a three month period in its nearly circular orbit about the Sun with a radiusbpuv8,i g 7p4vbd1u2j of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thei:ro+cc7m;k n tip of the second hand sweep through icik7 ;:mrc +onn 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equii mv2hg+y 0(nm61t/t:ss ezp) ydl4evvalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is -pq96uzcoaf q 2sf.qf ,)7cjhthe frequency of the wheel's rotation,67zqf cohpqf 2- cu)a s.9fqj?

  A pulsar (a rotating neutron star) emits pulses at a freqfpvc6fd1i7 (bt48 vfwuency of 0.40 kHz. The periobc4 pvvf(wtf7d 8 i16fd of its rotation is

  A phonograph record rotates at 45 :0h/vq:ixyycu tg146a2 cro zrpm. Through what angle does it turn in 0.20 savy1 02:tuzgo h :q6y rcc/i4x?

  A wheel of diameter 26 cm rejlk+nt3/ 7 bturns at 1500 rpm. How far will a point on the outer rim moverk/ln b+j3 e7t in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 2 s:p:w )rjicfWhat is the av2: jcw) f:srpierage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 2ycjy+5 n ( 1y9at6d3augoc ho4.0 s. What is the linear speed of a point 0.10 m from the center and6ocy a(t2c9 y5+yu1j3hgo of the wheel?

  A cable car at a ski reso fn9i 2mvt)jf-rt carries skiers a distance of 6.8 km. The cable which moves the c fv mjin2-9f)tar is driven by 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 w5uaz 5t*3naszxgz6vr. q b02 yith a constant angular speed of 2.0 rad/s. What is t*tn.gy35aa6bx0zsu z z qv2r5 he linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.1 hh6 owc7f(k j+zjf8f w3swhz-,,zr+y6 m in length. If the motor rotates -7c(f+,rwsofhf,68 hjzk hyw 3+wzz jat the rate of 20 rev/s, what is 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 w. )c /(ubxe/, c0ka c3tagrmb3aii,b2.0 rad/s. What is theu wiakmxi ,r33.c ,a)0ec/acg( btb/b centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a t8hq ;mg/: rkvcfc,3rpoint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is m;mg kqhcctfr83/, r :voving 8.00 m/s?

  How many revolutions per minute (rpm)lwe *u9l2w3q1 ji133o eduoqq must a circular, rotating space station (r = 1000 m) rotate to produce auq9 1l djq*2oloeww3q1 eu3 i3n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ozvlj-8y ziwo-2 ;,a euf 20 m/s. The maximum centripetal forc-i8zule; -,yaz2vojw e (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular c /2nv9 l+pzx7p*c0hm ,eaay sjurve of radius 50 m with a speed of 20 m/s. The maximum centripet l9pha20 ,ym /jna+xpsc7v*zeal force (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 the enmf*k75o+4 pxlv ca8wr d of a 0.750-m string, is whirled around in a saco8*7+v kf54lrpmw xmooth 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 kg and radius 9.0 cm rollspkuh-:m/ls. v without slipping 10 m down a lane mkpl sh/.-:uvat 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 angular 8o: shtc/--cz.hezk wc)aal0h 36 yonacceleration 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 cq cke( *t:-ybxonstant 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 0u r5qd6-d6fn l n39z 9ign:5hl5ov p ivj)bp-q.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration gh- iq b9 6jzf ln3i dn9-6:pv5oun)p5dlrvq 5of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular anv;7dg792 sixwz-46incj) krdzln.ck9- yo xcceleration 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 a constant angular accelerbkqfrj1-) . xsar.s 1)xfbq- kjtion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from res dm 5kn,x7 f8bsholc(3t and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the 5ocksb8(,73 lxd mnfh wheel?

  A wheel of diameter of 68.0 cm slows down h 8cfw22rpi 19nidd5 huniformly from 8.40 m/s to rest over a distance of 115 m. What is the to82 fd2h crnh1w95d iiptal number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifoi(ag;zbg.9 gr nah;66dzgve 8rmly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceler6g 8iaehr;z.n;gvd9gbz( g6 aation?

  A wheel of diameter of 68.0 vh d)9qf 9c; bevc/) upth0)ptcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take fo)phth )dcb9;qp t9vf)/ecv u 0r the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speeddy i ,d*wo9/wr of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angularwd,*/wdi9r yo 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 to a torque of 90 Nm. If a 30 f9cd q)k*5hpdcm long wrench is used, what is the magnitude of the force required when the fcpfdd k5qh)* 9orce is perpendicular to the wrench?

  The bolts on a car wheer meh *zf7b.s0l require tightening to a torque of 90 Nm. If a 30 cm long wrench is . fb* srzm0he7used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i ,(igoby +l6pnr*amq8ptqr 1;nertia $3.00 \; kgm^{2}$ 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, mass 2m iizbbpq.qz96(*2b x/;5mcm4zji)gqm 5gx hsis at x = a, and, mass 3m ismi;q. 954sg m*x2qzi65)xzbm qc(/jz gpbi bh at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fricti glfjf8 q0*b3aqha 0s4f:lm7 e6d3zhoonless 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 t0d l8qq m3he40b a7gz a:hl3sfjf*f6ohe angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought tp-ufdqg ..(*uyy+ask f9 z,j phe 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 arounu zq.(uf d.f +-kypspj,ga9*yd 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 initialv;ztt)c)g, vmbd h(*hly held in the horizontal position, and then released as the free end is allowed; )zh)t(d g,bht*vvc m 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. mhjr*2iu hhqo3h36.btchr82 Neglect the mass of the axle and sprocket. If a force 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 slippingh63qtj m h2hco.8bh2i*hr 3ru ?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ehzsr* ,2t/wwg8ov ag0g9)x f of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration xah,wgftg0rz gw/8e)*os 9 v2 of the pulley?

  A 1.53-kg mass hangs on a rope wrsnwvp5e u tap81fkhh36 *d.gbsy91 e,apped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratiefn56t.v kpup1 hs9yd3gb,*w h 1e 8ason of the mass?

  A rotating flywheel can be used to store energy. If it is required lw jlcalm.83.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 ofz r2zlm. ki/0zjdjm; : inertia 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 fro .7 4yk lijye;v4ej8 c2-u+ryw b6.dhce0pclrm rest and rolls without slipping down a 1.0-m high inclinewk6 4c jp28.yiee 7r;dc.ul j lebry4c0-yv+hd 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 wv e:9vq nwlc3-tka0, cyga*l8:4 mu wm rolls with a speed of 10 m/s. How high up an inclined p,lv*gc9:3c aa-: t84uw w lymnqewvk 0lane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rew9ot + qatr+h*leased from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of h qtto+9 *ar+w3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 37q- x1ovuh8vn5e incline that is 7.0 m long.v8 17-qhovxu n 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 mom n0f) *8.oktf id)ndcsentum 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 momegk* 1w*vps* nnnt 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 moment .nhse9hp 6o/kvv+7anw)xm d9) ru.u wof inertisr7wvm)/ ap nh+)ku.69.9dwxh uon vea 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?