Angular displacement is usuxmo6tlbm+0 s *ally express in units of

  Angular velocity is expressed4 hg8j54/hwl /qzvhhi i g;ta0 in units of

  Angular acceleration is entf .hl5uzy 1/xpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a con7he h2mlt/hu5u+p ue90y.0amobi fz0 stant rate. The boy is near the outer ed0p2 hb5./0f9u ae hmutz 0iel hym7ou+ge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry/;7.gjw p hf4c:kmsim-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 speem.g:f m 74i hpk/;jswcd?

  A boy and a girl are riding9ca j )nlq/l nrll/m6,kx+kt3 on a merry-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 grel9+ )tlm/ljxrlq,ac k 3nk/ 6nater linear speed?

  A boy and a girl are riding a m3-yw fls7nfm;kan 7 z4erry-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 h snk4n-73ylfm ;wa7 zfas the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant r5(upxzw ,gjnqguzz8 s)k8j, 2ate. The boy is near t wz5zz(2 ,8,x) uguspq 8kjngjhe outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. qdvn/ y*5e ne1e5imx +Which of the following is an accurate ste5xv+/ 5in1q*mneye datement?

  Rolling without slipping dependsi f b*.cqjr8n9 - d1 +ija.hu9sjw2uzp on

  Two equal forces are applied to a door. Thby:)w gu;ge r9e 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 the )wuy9 ;e: grgbgreater torque?

  Two equal forces are applied to a door at the doorknob. The first for qtti4z1/d5rquq1ra:6f oq1hqp+az8 ce is applied perpendicular to the door; the second f8rfa+1qu56d zq/:zhtatqr io4p1 qq 1orce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpend) 6va) vu )r v3d4c2l6f.lfn tgxt-gksicular to the door. The first force is twice as large as the second force. The ratio of the .dfcga)n-fu vrl)6v3t xl24)t kvsg 6torque of the first to the torque of the second is

  What is the quantity used to measure an objg,:hz9/,bsiy o i5pipect's resistance to changes in rotatio:i i5h z9yo/igp sbp,,n?

  Consider two uniform solid spheres where both have the o789ba 5uk71gu 6s-m0e st:mqbhdzg esame diameter, but one has twice the mass of the othbh75 u1qa09oz b:g6-m8mke sgseud7 ter. 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 ha8tn4 :pdnh v:j;yc .nos twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphe d;nv4yt8n :ocph:nj.re is

  Consider two uniform solid spheres where one has twice the mass and d,bt(+ n 6fcbtd8 .btttwice the diameter of the other. The ratio of the larger moment of inertia to that of the sma d8( .bt ntc+bd6f,ttbller moment of inertia is

  A uniform solid sphere has mass M and radius Rp e,oh,:0yzbtix 5 c5w. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia ace:wh5 ,5pxyotbz i,0bout a central axis?

  If a constant net to/ex;c l7*3rpn yx 3jpsw;l it)rque is applied to an object, that object will

  The moment of inertia ofv92 l o,qbpq m7cs -tgqi072wu a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the r2,9m wc-q7q igvots0u p2q7lbatio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a; droe /xa,d, gy8od8,q vy6mm mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the mox8;qy,,y gv8r dd ado/,6mewheels 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 slipping zj rbz6p wi4t-*5*aabdown an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends o4wb** i aaj -zbzr56ptn

  Suppose a solid sphere of mass M and radius R rolls wisg c( 1xjb5hh0thout slipping down an inclined plane starting from rest. Th0bgc5shx 1j(he angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of partcask hj-u 66n;a8idl +icles changes when a net external force acts on the system." This statement issha-cud 6k+ a8nlji;6

  In what circumstances can the angular velocity of sysud+0y , uu ,dn ;h+dxdjqxx7y-tem of particles change without any cha7ndx u+;+dh u ,ydqy,d 0xj-xunge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. v5pvrq7xireo; ,0o2i Ignore any friction which may be present. What happenvpi;2 5vr, eq7o rio0xs over time to the Earth's angular momentum about the Sun?

  The Earth moves about twehx:zc1 5n x7l7 g1:r hmt+yhhe Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed wlh::ynzx 57 7r+1mxech h1gt of the Earth about the Sun?

  An ice skater performs a .v jl dqe9fz 9kn+3*ogpc-k6 spirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens qfgoked k+snv. 6 3*lc-99jzp to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette xw6( i(pix-9z c5s g ps*hu2kf(a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotation?xshs -z g 2ci(9u*6pfp kiw5x(

  An ice skater performs a pirouette (a fast spin) by pulling1cv/qxd5ora 4 in his outstretched arms close to his body. What happens td4co / arqv1x5o his moment of inertia about the axis of rotation?

State the law of conservat- bey.cu3fba xg -x07pion of angular momentum.

  What arc length does the Earth travel in a three mont ano2xz 0qd dk8*i979dur-qavk 3wu+qh period in its nearly circ7+-vq2ko kq8 daardqxw 9z i3nu 0ud*9ular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3m;w jrp us1oai.tlh *l5g2v+10 m. What distance does the tip of thegh;u +v5lt11wojpls2rm .ia* second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalentfhu6ec*x+* f b to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the w+ql)nt94br e frequency of the wheelw9 t)4 +lqebnr's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Th e)5- je14j :dv* y)btewnhgvee period of its rotaew4j ) n1e-gee:hvv*jbd5ty) tion is

  A phonograph record rotates /cpbi o3j,39dj1 y wjuat 45 rpm. Through what angle does it turn in 0.20 s?ypj1,i3 u/wb9j o d3cj

  A wheel of diameter 26 cm turns at 1500jqg)- /hagcy jg q;y;6 rpm. How far will a point on the outer rim move j -q;)a;6jgyq/g gchyin 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 htwxp hoa9a )4e(2 h9 g)jaqda.dd-(y s. What is the average angul yj9aa( (a9g4-hp .qhtoe2dd)da)xw har speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0df3og9 ocry -hx3 8m1k revolutions in 4.0 s. What is the 9g-m1ydrxkh o3co83f linear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The2i vkx69pd.mm. gb b6s cable which moves the car is driven by a pulley with diameter 3sv6gmmbpbx k2 i9.d6..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 (+2+ek;hyrd0 )be 5q8j7 qc rq zm1ldpg4 cpprm is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the whehp0e ;drq)epcz(42b+jlkp 5r y8 r m1c dqq7g+el's rim?

  The cutting cord on a gas-po*a7 kxhdat;.u 6sz7f fwered weed cutter is 0.16 m in length. If the motor rotatef.77ux zfkhs 6;a t*ads at 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 *wt(c*p2wsq1qs j jy ap7gfm:m 8fm*4p na.7rwith a constant angular speed of 2.0 rad/s. Whfw 7*1pm4tcf awpqnmjrp7 a:g*8y( *m2s.q js at is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the p(zfjc,g8 g8/ uwv( 7itk h2cvnerimeter of a bicycle wheel of diamu ft(v287i ch(,v /jwc8zggn keter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, roz yj0r+( xjvg5tating space station (r = 1000 m) rotate to produce an artificial gravity of v gr(50 yjx+jz$9.80 \; m/s^2$?

  A car is negotiating a oz;g1b*3ep,mk ixmq.gp e;h:y( n :lsflat circular curve of radius 50 m with a speed of 20 m/s. The maximum m zo,h *;;e3 yeqsln1:p(gib. g:kp mxcentripetal force (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 curve of(,nws7-82chr q awmrg radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided byhwc-m7g,rqr 2(aw s8n 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 ,jjn 3b -+utvzfjah2 a bk4i6: iu38ssstring, is whirled around in a smooth level table. If the maximum tensib:hv, j4njuz u3 8jafi3-sksi6+2abt on 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 /dmnuwn1g +z;mua2id3 2nuqsum-q3;rolls without slipping 10 m down a lane at nquw u;+2n ms u-iadzq31 ; mu2dm3n/g4.3 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 ac0hg/ m 84fomgoceleration 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 an1tj 5,m1 ,oh 6n )ayln7vhkncbgular 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.o1 teg(e u*g0.300-m radius automobile tire rotate after starting from rest and acceleratin( *e1.otgemg ug at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular mglm:9 mvk6j1acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatiy6 2lqz3 dccth 6e/h11 ou:cytng at 20 rad/s decelerates with a constant angular accelerationt1lct6hyzcec:u d21/ 3q yho6 of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rauqzfn,td k7)ft/ m42u5 lq5leaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acf)tnzfk 7m,uq/q l2t45 la5udceleration of the wheel?

  A wheel of diameter of 6rr1 32d1.z tqz5lxcbii8 5zc i8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel ro8zr tci1ci5 db5 .ri3zqlz2x 1tates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 2p2lvx4qw lxu uaf 0,o7;jw4sm/s to rest over a4 2o,;qvw lfx2wl upx7us0aj4 distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to reslt ,.2tgeyg ,lt over a distance of 115 m. How long does itegtlg ,ylt2., take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 r17 (y hpee2dlaev/min. When switched off, it rotatesae7phe( 2l1yd 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 require tightening to a torque of 90 Nm. If1i2,f cj gabn9sxx;z- a 30 cm long wrench is used, what isng;9 ix1jazb- 2cx ,sf the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque ofhc. t/4sj (9io+ lnlsb47th td2pr fd( 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force reddti.(24l9h p7 + tr bs/4(csnlhfotjquired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o-r(e5h9d:wse+e jd)w+ ws wf kf 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, 22,r qkjbph+ ymass 2m is at x = a, and, mass 3m is at x = 2ay,kb+hqr22p j. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fricti50f-(zfwz* m,t mcy+ lzvd k;k*w.lyionless axis thought the center O. A rope wrapped around t l0k; mmfw c5w*tf+ y -y,.i*zdlk(vzzhe 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis th1)13h*f n88wo 24xvwl:xhvyw gna q vgought 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 aroundw lwwyg8 qxv2h11nfv:onh3)4 xa8g *v 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 qdzn jse; 7jb phvh 0(,u9n;wzi 7pp(/hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed pbj/u(zj;0q(vpd9 iw 7hn,ehpz;7 sn 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 30mqhjn 08n .+z1m0fo xa,8 ;izxbbr e(d cm 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 of radius 4.0 cm for 4.1 s, what linear spee1m0hbj0( 8 ;,x8+ibqnezr mxzdn.o afd does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope -v6rxfenlfc/e ih:(8wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular cfh8ne-:x l6re/fv i( acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arouzi+:7jx/ 0cy 0q amfjend a frictionless disk pulley of mass 7.07 kg and radius 66.0aj qycijfx0+ 7/ :zme0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to sen77wf rk8yden8b .t, a 1xdtme,9z) otore 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 inertia of boy, 3 pmua7/uxykh7/g 0i(dq$5.00 \; kgm^{2}$ 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 (/+tvij/d3hr f.iiz vand rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it rea +dtj/v3i hz(ii./ frvches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 qy8(cafa;*/oz57 i )nlufez sm rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rfz) nui(y al*fq85;zsoeca /7est?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and alloudlvdn ;gbmt5j* f)+a)i)x6 twed to roll down an inclined plane. How fast is it moving after dr+; dm)a fxunl)5 *tvji6dtgb) opping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping downolq2f u e0yq11a)kmo4e uvl q-)e1bs0 a 35e incline that is 7.0 m long. Assume it m1yuvofq eo10 -0e)1e2u)q asl4bqkl 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 momentum chqxnv2 mql p-5q-omu:5anges 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 inertia t9spz q4ua-1 5 opry9fnbb8*kof $5.0 \; kgm^{2}$ 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 extendei/9 6r 0z/od q63 ize-pozvcovd has a moment of inertia op-o /z69o0qr/c6iz i od3ve vzf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?