Angular displacementf2dh l8.b t-pb9kl c(d is usually express in units of

  Angular velocity is expressed inxb;eiqof)izp6 1jm0+qhj3m / units of

  Angular acceleration is expressem0m mx zjb3 m)ohrq:f5*z7x r9d in units of

  A boy and a girl are riding on a merry-go-round which is turning at a con+wyr-6zg *. c9*vdf6js ddzal stant rate. The boy is near the outer edge, and the girl is closer to the cen vrcjwy.9-s*dd6z fl+* 6g azdter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant j. fnmpn h;z:xz0;vs w51qw)mrate. The boy is near thnqmpnmw1 hz swx:z. ;f0)v5; je 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 tur s.lpiy.r(qx3 vu49 l*dwaa j9ning at a constant rate. The boy is near the outerrylu 4 li *(.a.3dvpaqs9xjw9 edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a mer fhwt /ga,9b-x,cwp;d ry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girlf- ,xw,/gbc dahpwt9; is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which imio7 s8cw c+j9s turning at a constant rate. The bo 8w iojc7cms+9y is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the fm8 o5;1 +gkqb;1vx3by eaavhxollowing is an accurate sta8qa 1ebk ag;xb+vm5yo3x1 ;h vtement?

  Rolling without slipping depenim s54cvo;z3ids on

  Two equal forces are applied to a door. The firs znvx, 792dwfst force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicu d2z n,fx79wvslar to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the dur t w6wyr922)(ype7yde p/ mloorknob. The first force is applied perpendicular to the door; the second force is appliedep( l/7mud2py26wyy rt wer9 ) at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, z) 0hdse(f1. ta,49l qsz xrreperpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first trx4zalsr d0,et.1e 9)z(hq fs o the torque of the second is

  What is the quantity used ;qr .fpx:.rbdx2m2l a to measure an object's resistance to changes in rotationfp. 2maq;lr2 .:rxdxb ?

  Consider two uniform solid spheres where both have the same diiei(km,t l63 xameter, but one has twice the mass of the other. The ratio of the larger mim( ,ix t6kl3eoment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same masqal., ralzuv w t3.c;ahcsx*1 r6(ch-s, but one has twice the radius of the other. The ratio of the larger spheshlhwa6(- vc xlcta3 ;uqa.r. ,*rcz1re's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twm* rbbi*, ogus fodpc5x/c)cnz18-l * ice the mass and twice the diu/) rc-xfpz b*ds cmo5cgl*o8n,1b * iameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M ange :,)abhdv-o d 3R, what happens to the sphere's moment vg):ba - ed,hoof inertia about a central axis?

  If a constant net torque is applied to an object, 8lxyoz0xe-/zeah :0tyu5 jzz,g g+n5that object will

  The moment of inertia of a solid cylinder about8t )t)xvz g//trnl yr/ its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy t)8 tlyzg)tvnrr/ // xto its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whe, hiwa,t/. .eql)tu hich has a mass of 10 kg and a radius of 30 cm. What is the ratwulhta),, t. .qeieh /io 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 sphere of mass M and radius R rolls without slh1uvzf*-zor l6 2iuy,ipping down an inclined plane starting from rest. The linear velocofylr 1u2hvi-zz*u, 6ity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mfrd6y vx 93(m:rep3yj0n y-jbass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the spheryp(m-306ndvjjfx9:ber3 ryy e at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net( wmye)1f3 jm4d kkfm* external fork*e3kfwm1 )m4 df(ymjce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles1osw7gq34sk /vc4 ahs change without any change in th/a ch1sqsgsv k4 374owe system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fr zj1 wb+:jveb a: x4znblt61.oiction which may be present. What happens over time to t:6x jb +ow1 ez 1l:.bzavbtjn4he Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ear b+i* c1osly9w0yin/ )tux1jxth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about theyxoi+wl 1 nib/jt1c s9y )x0*u Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his :s/tt 93ig ucdn3r(x qoutstretched arms ccqi3 9ntr:gxu dt3s/(lose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin; kprq :.pnbl9) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis ofbr:p9lqk. ; np rotation?

  An ice skater performs a pirouette (a fast spin) by pulling d66mlb;/h .k hdzv;n1jr v7h ain his outstretched arms cl1 jvr h/6; znmb6vhhadd l7k.;ose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angula j +/n(v(3b95ykyq .6jh; jeqors tmpbr momentum.

  What arc length does the Earth travel in a thrdn)ktl 5 o(li y/j.uq,ee month period in its nearly circular orbit about the Sun wit ui(.k)ylld5jt/qno, h a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lx1i63nfb c1 b l vy/onl).o ep9ymc273*c diidength of 0.30 m. What distance does the tip of the second hcilcv)3 n726 bc e1x /9o1o dbnp3 i*mlifdy.yand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolwk0tryy)woqk50wnx j - h7 i1+utions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sggr;u fyd)3.l oqf e.9. What is the frequency of the wheel's rotat. 3 urq9fy.ed fg)glo;ion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHutm97li* lwt .0k qiwm1 0mlgml9 j:z0z. The peiwm*t19z7i.9t gulml:lm0w0mlq 0 k jriod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20oz avy f7-/bz6n9 rnpgrl/ 2(xun/ 9dr -zo9arlvu7xnrr/b6 d 2zn/n(fgpy9 /s?

  A wheel of diameter 26 cm turns at 1500 rpm. How faht ju98f( ztsv+n. e4ar will a point on the outer rim move it.(+u hez89n f4jstvan 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions inuh8m)8gs r)3,uxg sbh 4.0 s. What is the average angular speedsmhhugu)bsrxg 8, 38) of the wheel?

  A bicycle wheel rotatesvxsm)ss3:b4t s/vs:tj2uz: h uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a possvh tjsu:2 :vb s 4stz)x3:m/int 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The w0b (ride q h4(yayuv)a/6lxjv:i8zvj 0k+t: cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming qd/6iv4hklibaetvy w( y rj(j:) :a80zvxu+ 0no 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 withvv9infs7l+w8: -yx wv a constant angular speed of 2.0 rad/s. What is the xn l -8vw7iyfwvvs9:+linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is3 xszsh j+h2o hah ,9j9:b/ix)* gchlh 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of x hx2l9i:osjzb+sha hh)hj9/,h*c 3 gthe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0: oefn o7 qzs 9)sp5r*+lj+sk8ree5q e rad/s. What is the centripetal acceleration of a point on the wheelr eeskn *8os+p7 )e5j 5frqs:l e+o9qz's rim?

  What is the centripetal acceleration of a poiqtaz n -zk532j30d b6r1,htz aoel*mv:aa 7 ycnt on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike 31ta zrkmyz02,o-a5dl thcv n zj a*eq63b7a: is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station xk1hi cb;*vv.(r = 1000 m) rotate to produce an artificial gr ch*;i1k.bvxv avity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cka0j4dyjw roxjtig9q((+n( . urve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided byry0j gxk woj(.(9 +aniqtd4(j static 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 50 m with a speed of x+ocro 6f6g.t 4re mb00ptdere 8t:) m20 m/s. The maximum centripetal force (provided by0)0o +e o rr8x.tetm tc4 p6:fdgrbme6 static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is xkvyk+f n s85 +7-6p0zapak zge55ibbwhirled 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 i+v n7 zb0yie zas6pbkkf p- 85+5gk5xaf the string is not to break?

  A bowling ball of mass im cr ykpil161-)web+7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane e6+wb11ycpli-i r mk) 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 angular accepctk5lrrsw;x-;3 our)*r ( osleration 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 angu mu35 ,t,tj) xn8em* pyfwse3flar 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 m:; f; mta4eyedl*-zs0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration o*tfmd :a;eme4;y-lz s f $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, kn4a ka.6s3e +pz 7bqko1m k4hl3urw 0and 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 decelerates with a constanpey8k*t35 -2b -o w0caf gd)eyb8 gscut angular acceleration of-g 8 y5d ebyuf8 0e3sgwc-kpo2)b*tac $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest a/1l, olxck0ww w(dvg;x/hu 7 dnd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What d uw/dvo7( w/0lkw;chgxl1 x,is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 4eakl/g) z)(z- d;zwrc9j4 b hv;yre6easbd98.40 m/s to rest over a distance of 115 m. What is the tot4;6bkw s h(elzezbaycdvrd9 )e4/)razj9-g;al number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter 0yql/zbqb 76uazsf7/of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerati z/qb 0aqs7fyzu/7l b6on?

  A wheel of diameter of 68.0 cm slows down uniformly fr0xm;x 5 g b,dify+k.by 5cg7zlom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to k 7y5mz;+bfl 0ci5dx,xgyg b. the stop?

  A centrifuge in a medical laboratory rotates at a rotatixjbd,y3 j foodkkw ).j5.vg; ;onal speed of 3600 rev/min. When swxjf .);jbd3yv gdo,j 5;.wo kkitched off, it rotates 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 wheel req (1g g+ltkr(,iunlh5 fuire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rgf(nlrh,+tk u5l1ig (equired when the force is perpendicular to the wrench?

  The bolts on a car wheel requte yan0)h dr. p-c* i+7zgzl a7of3+swire tightening to a torque of 90 Nm. If a 30 cm longpezsa)7zl +fwniytad ro gc3h+.-* 70 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 o iysi,jj/4pdw)x f pcj68(e2 hf 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 modeled as follows: mass m is at the origin, maiu0+fqbm)r ,e2rb/iass 2m is at x = a, and, mass 3m is at x = 2a /u)2 bai0+,br fqimer. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg* b ixr9k07ql()gfuba 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 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 accel0xubr 9*k alfibg(q 7)eration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a fr -dlhif x-4si8(ung/ t*mhjb 3ictionless 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 through in the first 5-j ixu th8-h3g4(/ns *dmbi fl.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at j-wpc5d :) z*tqnizb0zs 3k6bone end. The rod is initially held in the 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 iz3szd) zbbk:*-iw j 0qn65ptcnertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius x9hczp.*wc39 u)i v pv : o3xd62fpcfr30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangf i2ouc 69w3 zfp)c3v*hvp dcr:.p9xx entially 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 i4 ueffhap+9rbmw* 3ga5-)upa frictionless disk pulley of mass 7.07 kg and radius frb )gmpau -wu+9*3fah ep45i66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of masph fnve0/). qnt- udq)s 7.07 kg an0/.vp deqn fq th)nu-)d radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If ib/yrf0 tt huao7 ;phv;r12fb, t 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 oc)ixmt.,uvic.h) +3jt; a n.2gdrdd r7dny b:f $5.00 \; kgm^{2}$ 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 from rest and rq0 el 1x9fuvk0f1uc3j olls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reacheseu10 9ff x31kj0vqulc the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. dk lf-(e3hyk/4x6ri3qtiv 8kHow high up an inclined plane can it climb before coming to restf (q kk-lt/vx3kd386ir ehiy 4?

  A hoop of radius 0.50 9a2*nbfrna)ng ixum9 (8p)q-e-axl k m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance-2li )xarn nqnmb-g99k)ua (p*fe8xa of 3.0 m?

A solid sphere of mass 1.5 kg and radiusf:u r yc4mroug-f(m2ros .)rzvp,2 8t 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started f8o:rm rc (2s tfuz gr,r-pmy)42ovuf .rom 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 momengin45;fry 21m ci;sovtum 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 inexeqx 0zo9g 6l:zef ;6nrtia 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 q3zw yd,7 (gg0z*hq(mwmv-mbextended has a moment of inertia gdg7 wb yw,-zq*(3 (vmh mz0qmof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?