Angular displacement is usually express z 0(hujupr x -bmm7)6 qp,k:kyin units of

  Angular velocity is expressed in unqcnk63pe ;f(e its of

  Angular acceleration is expressebgd83x+tmh qyn ,3z;wkpz5x.d in units of

  A boy and a girl are riding on a merbaa i,xakk ej)6+hqjo t.k39b 9zep/r5goi .;ry-go-round 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 angular displacemenz;k5+9rkiajx9kb t6i ba e, e3./q.oo)h ja pgt?

  A boy and a girl are riding on a merry-go-round which is turning at a, cp7x-.7uz *px ihxg /+koh3;lgtfuw constant rate. The boy is near the outer edge, and the girl is closer to the cent*xz-gp37huig7ptu; clx .ko/h fx w+,er. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constnje 9wt2 e njo6*c4g9tant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the gre4ow9tej nj 2c*g6e9tnater linear speed?

  A boy and a girl are riding ap. sh*e uo t0cc+p+nz, merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who ht+c0o*u ,csz p n.pe+has the greater centripetal acceleration?

  A boy and a girl are r njmm .n*ei)x;whwmw(xd-a 9/iding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is chim nwnmj-xex/wm;(9*.w) d a loser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follo)4 i*j pqrfc.r0q (pjawing is an accurate statemer*jqq.(crp if pa0)j4nt?

  Rolling without slippimj+)tvfu/ cl+ ng depends on

  Two equal forces are gljh(6 z34;w.wjpp n sapplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces 3 jpl6wwh j(g .;4zpnsare applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are a s7 b6vvb2-ldy m:wct/pplied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane om7 t/:v-b2 ywbl6 cdsvf the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to thn g )vkq6 xtl1eah*4pqpj (-;iw hr9*le door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque (x 1hq6 qle hjvtwl)rk*g-9n4 p;ap* iof the second is

  What is the quantity used to meagp o9a 4agk,gs/ym3+g sure an object's resistance to changes in rotati93/ ,apm g+goagsg ky4on?

  Consider two uniform solid spheres w07.ivz 9k pcd vh pl9.eum6,9;stxspu here both have the same diameter, but one has0 p,ze vct6;.m vp d9.su 9phs7k9ilux twice 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 have the same mass, but one has twice .o:igh2ah rr jk;7(ifsx0p-zthe radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere h. a ;2 i-jh0okgzfp:(xrsi7 ris

  Consider two uniform solid spheres where one has twice the mass and t79 l87qrhv )z8;vlenlmuwu14hlyo p +wice the diameter of the other. The ratio of the larger mome1lpo9u 7u;rvwm8)4n y7l+zl8e hqlvhnt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M zxhfs3ne3*- yczvk8n* g hgzlb1s+(0and radius R. If these are increased to 2M and 3R 3h z kf*se(s+8g v0gzhlx 1yb-3zcn*n, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, dn+ : kwlji +35b( 5iskkcnch*that object will

  The moment of inertia of a solid cylinder about its axis is given 5bit. )beo6ul9 oj fynwv24rx*8ag d;by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy gwbjn v8)y4eot b.62 ulr9ifo;ax * d5is

  Consider a motorcycle of mass 150 kg, one wheel of which h-o8c)w:i sqc jas a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total jiw8:s cc)qo -translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without yr f2r ):nyjvu j1g;jo*8ptr m*-1frfslipping down an inclined plane starting from rest. The linear velocff u*ym8*vr;-j grj)tj:oy1rr f2p 1nity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wi mji3u0 af,c;m wwjilbvxy3ho w+9982thout slipping down an inclined plane starting from rest. The angular velocity of the sphere at thju9mww30lv bo8yicwx a,h92+3fm;j ie bottom of the incline depends on

  "The total angular momentum of a system of particles changes when dyz96i yczhf,h/*)ghcp0q +x4 brre3a net external force acts on the system." Thzep*)f3yd/xqb+,96r0gy4cc hrih hzis statement is

  In what circumstances t3umemsyx :ogj7c+h1vwx 07 6can the angular velocity of system of particles change without any change in the system's angular momentucgtvm70 jx1w 7s6 xy3muo h+:em?

  The Earth orbits the Sun in an elliptical orc-8 wt)ioc.e(8 yptv vz)o +azvl-zx*bit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Suvytl -vxcpva*zzo .ote iw 8)8-+c (z)n?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clo xz b*,og4l3 5h3vezksse to the Sun, then which of the following best describe hxzsgz,b534k*ov e3l s the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pbo.v0l/q up(wuxb 7s /:wwf3wulling in his outstretched arms close to his body. What happen/u( bf x:.3/lpwbo 07sw wwquvs to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) 0f5j9kaa hi8m y5:fay by pulling in his outstretched aiy 5a:fj5m98kyh0fa arms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a o3xr jy62bu6g pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment g36jxy ruob62of inertia about the axis of rotation?

State the law of conservation of angulr j2n ,3l5o4vlqf2fi var momentum.

  What arc length does the Earth travel in a three month period in its nearly c h4+v5 ,jmzm5e7sa tphircular orbit about the Sun with a radius o4a mzptj5s 5m+hhev ,7f $1.5 \times 10^{11} \; m$?

  The second hand of a cloch 43;qbntn ,8oa4ig9dt-a ktfk has a length of 0.30 m. What distance does the tip o 4k iq 4,d-nb8nfo9t3a t;ghatf the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revo: hr/2 2 erfjpmfmyh5-lutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolut dd*t55;y4fs1p aj ohgions in 4.0 s. What is the frequency of the jd1yfgp4tod55a;*s h wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency h)ez1 hsj2o0w of 0.40 kHz. Theh1ze hos0 2)wj period of its rotation is

  A phonograph record rotates at 45 rpm. Thr +)r f;d4tvs(pxp q5-(na pcizough what angle does it turn in 0.20 s?p vqa( ;)dxtp4c n+(p-s5ir zf

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer 7pmlzlhk9 bxzj+:pcs(p 03a8ripzp08pxja 9 :( sck37lbzh ml+m move in 2.1 s?

  A bicycle wheel rotates uniformly thro 6skkd 0tn6t**zi8ryrugh 2.0 revolutions in 4.0 s. What is the average angulaz 6d08rtrk6nst* yi*k r speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolution a;g(nty6oqe 4ima0q-2kym /9jlud o/s in 4.0 s. What is the linear speed of a point 0.10 m from the center of 96 al qka do/20u( ngt e/momqy;y4-jithe wheel?

  A cable car at a ski resor/smouxi boc 566,ek4 /or0mbut carries 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 make the trip in 12 min,bcmr0siuo 5omux 6/4b /ke6 outes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.u 0x.n5 g ml(t6ewnb/n0 rad/s. What is the linear speed t5en un6(xm/wnl0 .bgof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0 u-tn cjca1z;:bh . bn-g3td:x.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cg:.:3d tjhbatnz-x-; 1 bncucord?

  A wheel of radius 1.0 m is rotating with a constant 8,p qd(* hj:lmrsj+ flwg4(qm angular speed of 2.0 rad/s. What is the centripetal acceh ms,pd w8r*+4 q(m:ljj gf(qlleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of anb: emm(5kpr-jaov. : bicycle wheel of diameter 70.0 cm when the .:jpbn-(e km a r:5ovmbike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stat vu5bq, ng7l,mion (r = 1000 m) rotate to produce an art7gvl muq,,b 5nificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wio,or 1irisrl6wsp o)ti)9w52th a speed of 20 m/s. The maximum centripetal foro,sio9 i 6w l)t)rr wis5rop12ce (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 cirbv;x)ia:/b zawlqra1. ) jdqte/c o67 cular curve of radius 50 m with a speed of 20 m/s. The maximum centripeta6;xlweqb.r/at 7jcq)d 1 oi): /za abvl 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- 5brw, pu5hki the end of a 0.750-m string, is whirled 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 k5b5p- h iu,rwif the string is not to break?

  A bowling ball of masscpgtxweb94(c3 z6 g, u 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.u (cw9g 6,x4zpcgtbe3
(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 accelerativ+w /0 j/h xtelym60dlon 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 qzqt g sf9v8 -4v+fxynge-j9/ a constant 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 3 8c2-a klltf)t hbv)oautomobile tire rotate after starting from rest and a)b )2v to8l-tf3klach ccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, an27x/kn qz,nz8f9xx vk fkt 262a*a bfmd 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 constant angulj:sp( of se-:lar acceleration ofp-ejs(:o s:fl $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angulacfsuu3l v5w +ad pv80u 8/3snur speed of 6.0 rad/s while turning through 2.0 revolutions. Whatafpw+uc n/ 3u8d8ssv 3vu0ul5 is the average angular acceleration of the wheel?

  A wheel of diameter of 6m5uoe7tzeju(nw. id.6g/rd n8m b1 r58.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Who(8 mm5d n.ui1zg ewtre./75 urb jn6dat 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 bz; * )68da7gf+fo32qxuhtcmzdfr x,rest over a distance of 115 m. What is the angularad3bxzfgtxf, 7 o6)rf +82 ;udqmc* zh acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fq 7e0l)9ggcvvube* *op/ t3y erom 8.40 m/s to rest over a distance of 115 m. How*) cevp*7q0e l9oe g t/vuybg3 long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at l6bh:.a+ptfu6 urs;a a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befo ;:fpaut+bl u.6s6har re 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 tighterdu +0/g8r9rdkd)-t vhq g*rlning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of thetlrd r-)/0+9q kdr* hgvugdr8 force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to aug f htdo8i-)nufyxk(w:y8 k*ug665 n torque of 90 Nm. If a 30 cm long wrench is :k)k 6*6yx8 hngf-dif(n5uuwtyg 8 uo used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inert 5vqmreq 4rst9p: z5p1ia $3.00 \; kgm^{2}$ 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 qr72f1 j 73xgp: 2nft mnvx ,*el;yrzsis at x = a, and, mass 3m is at x = 2a. What is the mxp qjr1,vnfzs73 t;nex:2gl*y72 m froment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axi:48c gp-td pcvs thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exer8p c tp:gv-4dcts 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 pivoted about a frico c:g:c,j;rty8* gz sptionless 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 ropeps;zg8 cty::ro *c g,j 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 i zy7gee()1o ksu(1hz(q wjii0nitially held in the horizontal position, and then reli7w )jhoue k0sye(i(gz 1q(1z eased as the free end 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 wheel to be a ring of radius 30 cm 7dfaz h6 q d1;)s5)scgmu gca9and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force ucsggad d7hs ) )c1zfq59;6maof 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 avxam me hi4eg,wv; 8v0lvj;3es), rnug4 v;v1round a frictionless disk pulley of mass 7.07 kg and radius 66. r )ejvvl ;ivu1e4v,e vw8mg,hg3;; 4v0msxna0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wraptqvaens/,e p()iq*;u ped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accel ;*t/ieuv) , eaqp(qnseration of the mass?

  A rotating flywheel can be used to store energy. k-c4a x2 av3o .rf2iyi 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 inerti e3:veejh2m5ja 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 from rest and rolls g0+tqtu zgk+ rfgh /xux(,o*.without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches thqh x gtxggrk+u/,+f0 * z(ot.ue bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed ok 4rs1jus8h7k5b /pbof 10 m/s. How high up an inclineksr5 hbs81u4k7jp / bod plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released frous kvt,7sv i9.sd5x(+wduw5 om rest and allowed to roll down an inclined plane. How fast is it moving au sk7,stv xsou ww5dv(. id59+fter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without.jm+wyb9ysb , a j5ezvl)o(1 x slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is givezjbol. sva,+wy5ejyb)x (19mn 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 changes w9kd n5m,g*l, fmuncukvl- 61by $20 \; kgm^{2}/s$ 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 i)9p 0gi5aluie +fc2p nnertia 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 exs m-f (2uo2aswtended has a moment of inertia ofs( -os2a m2wuf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?