Angular displacement is ua/mub-5kk.,d t.f1oh7gqh n +x/dl h dsually express in units of

  Angular velocity is expressed llckk-4/6)n c nym8kyin units of

  Angular acceleration is expr5/yoz jfy v:4lessed in units of

  A boy and a girl are npravp8 b/a+- riding 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 centenrp+/a-v8 ab pr. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round wh l0pck8 .e1zflpo)iqu0 ( a(+t eqp*ohich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cet p + .1*((loeu8hq)oacpf p 0q0lzikenter. Who has the greater angular speed?

  A boy and a girl are riding on al0+t9ykd+han h86aq o merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girkay06+t hnh l9a+qo8dl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which i bxj2q1c*0vqz s turning at a constant rate. Thqjbvxq 2 c1*0ze boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridingo gty+lzkj;uy)pc+ clr80o )) a 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 has the greater tangential accelerat+)jlzu0tlygcpo ; 8y)c)k+o rion?

  Consider a rigid body that is rotating. Which of the following ial+-sxzml2 / d7lw, cir),s cls an accurate stml/w i +ca, z)rxllds-72l,csatement?

  Rolling without slipping o1z )szj+zg j7uv,yd7c* ahl6 depends on

  Two equal forces are applied to a door. The first foru (q8zngqavb-yh 2pr 0c6m(0 nce 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 greater torque? a2pb(6mq hzn-rnguq 0(vy80 c

  Two equal forces are applied;()sf uvqg ;lpn(vcy9 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 of the door. Which force exerts the greater torqueq() g(;sl fup;9v nvyc?

  Two forces are applied to a doorknob, perpendicular to the doorop3eq w*gyo,9 . The first force is twice as large as the second force. The ratio of the torque yq 9ogw o,p*e3of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes inmm *c *fqnvd92 rotatiom f2cd**m 9vqnn?

  Consider two uniform solid spheres wh-pdgg 0az -q xjda/h8 8q9dn1mere both have the same diameter, but one has twice the mass of the other. The ratio of the larger dd-j za a8 8g-qmdq9xg01/nhpmoment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, b)sd g 9wz)/e22 tt8 wnczngib7ut one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the sg7d wi) 8z cb/2enwn2zt9)s tgmaller sphere is

  Consider two uniform sebjs1sw /n jy56 u2t5holid spheres where one has twice the mass and twice the diameter of the other. The ratio of j2sw b1eu65hn/yts5j the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid spherem89ul5f2, w7psmd tiz has mass M and radius R. If these are increased to 2M and 3R, what happens to the sp,2lmt 89wp i5zufds 7mhere's moment of inertia about a central axis?

  If a constant net torque is applied to an obj:i k(i 3hdgox9fyq (f.ect, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MRo us-ch p6fp6.2. If this cylinder rolls without slipping, the raf6u.h-cpo 6 sptio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of wc y7-zr*b , f3da.h*ib+gt( kg-fcqw mhich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy o,kgimy gd(-w qra *. 7cb-ht +fc*bfz3f the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid spher 9rzrmm( cv.x00 /xjkwe of mass M and radius R rolls without slipping down an inc(r9 mx w0c.vk/m0rjzxlined plane starting 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 slipping dowvq8 l c75;crxwn an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends l cc7rv8qx w;5on

  "The total angular momentum of a system of particles changes when a net82*uq pk0;bpen sm5 dwf+5zlo external force acts on the system." This stat+ 5pdofq0ue b; wsl8m*pzk52 nement is

  In what circumstances can the angsswa ;ii1 e9eq:+ :yayular velocity of system of particles change without any change in the system's angular 1q+ya:i y9swea s ;ie:momentum?

  The Earth orbits the Sun in an elliptical orbit-rj -l/6b4lf (y3:z vexpdrvr. Ignore any friction which may be present. What happens ovef6rlv/4pbj3e -(rr yz-lx :d vr time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. z ldi5k.vi7tv)l1b867tcug aAs the Earth moves close to the Sun, then which iadt t)l77gvk5l ibz1u cv68 .of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hivzef/e2 e+zl 5s outstretched arms close to his bozvle5+ 2efe /zdy. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling4:u-.u d*gr8 rfj,d7 kjlxatcf33sh1 exci:g in his outstretched arms close to his body. What happens to his rotational kinetic energy about t u,xrad4*3rd81xgf3 :js hc-j.cg7ufet:kil he axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pul0-.hek.lpkb o)yy, wcm:5dq0 cym fl7 ling in his outstretched arms close to his body. What l )f: wodc5y.qhy-bpmyk0km.0l, c7e happens to his moment of inertia about the axis of rotation?

State the law of conservation of aylok : k4sn 6;hpp/.ojngular momentum.

  What arc length does the Earth travel in a three month period in 7( mesj) x(n g9fs5dk). (iy+ikixnfq its nearly circular orbit about the Sun with aikij(nx f.k7 y e(sxn)9(gs+midq5)f radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What disk5h o83iymxt+ on2 gea+uq:d0tance does the tip of the second hand sweep through in 3+ 8 qymke o+i:hn0au2dg o3xt5 minutes and 45 seconds?

  How many rad/s is 25 revolutions pe/s),;wsv c7w1ih x+e0zrp vwn ,m gj(or minute equivalent to?

  A bicycle wheel rotates uniformly throug assd -m1um+w65cjq1 jwzqt *cu180rt h 2.0 revolutions in 4.0 s. What is the frequentjwmut +0duza mqs1 r*5s8 w16-1c jqccy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. The2d azz; oiv 7f;6yeee5 periee2;v7;e zyioad5f z6od of its rotation is

  A phonograph record rotates at 45 rpjyz qj-sn332k qxh /.cm. Through what angle does it turn in 0.20 sz3 c-n .qqj3 2jxy/hks?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poqbn*f 2id 7lb3int on the outer rim mfn*i 3d27 qblbove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.xy429 a bh*zp qt o27kml)kbm*0 revolutions in 4.0 s. What is the average angular s)by a24*7mqmpk l hbt2x oz*9kpeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluti/5x;32 jjzqrszee 5 meb0tkc(wpc. .* mbo-swons in 4.0 s. What is the linear speed of a point 0.10 m from czw/z5bm 2mqtj(ewbe;sx0oe .p5s3.*- rk jcthe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. b;. e )f vh.l:-tnikomThe cable which moves the car is driven by a pubo ei;t.vl:nm h.f-) klley 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 with awjkg mmr3 (kk9;6mxseev. h83 constant angular speed of 2.0 rad/s. What is the linear speed of a g8vr6 kkmkmm9h jxse ;3.w(3epoint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16t4zl:nq5z7s8 *s gmxl m in length. If the motor rotates at the rate of 20 rev/s, what isz sgmqlnz4t*sl58x:7 the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant4q):+ 4;dck ejn1lcmdh 2x5fq jjo6af angular speed of 2.0 rad/s. What is the centri4f:jna 1dhj6 cl5 edj q;x4k)o+q mf2cpetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a3 rzx)4a ,k:rog vhx*v point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is m*hgvvr)o,43rxaxkz : oving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rota.w zbll, aotrv64uz1 1ting space station (r = 1000 m) rotate to produce an artificial gravity b zzw,va t6l4o.r1ul1of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of)c2wumcp(6a; qv sismbgv:5f2 8o:zc radius 50 m with a speed of 20 m/s. The maximum2pqu8f )wv s562b i ;zog:: acccvmm(s centripetal 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 circu3zj l6+ud+po .i,hl h)+vd0fo pidl*wlar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictio. +d3hv+, lpli 0ud+z po)jdhif* 6wlon) 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 whwv zbap s:s)(-irled around in a smooth level table. If thz- b ()svwpsa:e 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; lo3q x:*i8jcrux:pl cm rolls without slipping 10 m down3lxx li :* :u;pc8jrqo a lane 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 angul xm2 px; vmhf5brys825ar 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 7 dtspedtby89 /5:ekxconstant 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 automobh,kx8(4 z* geje zg+zeile tire rotate after starting from rest and accele8zj4ghegke,z+e*x (zrating 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 an+rubmu --st *j9:c luvi)zw :ugular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad6p0iy6 gj 8bap/s decelerates with a constant angular acceleration ofpa6ijy80pg b 6 $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reazh+4q9opcal,5n a// /vj tudsches an angular speed of 6.0 rad/s while turning ta/nd qphs, 5o +vlz4tc/9 /ujahrough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest2hhsv8hf x2x3,l/r fa over a distance of 115 m. What is the total number oar /vh ,2 2h3lfshxfx8f revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s 2zg1wg iwn, i4to rest over a distance of 115 mw ,4nzwig 1gi2. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slowmfi( 84i0tztt s down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to thzi0f4i(m8 ttte stop?

  A centrifuge in a medica5h/b zr cjl fgd5,j8bpl.n2;nl laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 c,8df5hbrjp z5ngbnll /j2; .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 tv m7p1eq6ea/0.axqeo 0iaq c( o a torque of 90 Nm. If a 30 cm long wrench is useq10qme qaae o0i7e.x(pcv /6ad, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a to ohg9u+y7c- u,b0q. sis 3ueyirque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcs 73yq-.9iuy0c uosbge+ui, he applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia f wsev 55o m.d,pdd )/rg)mkj.$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:,)yoj (: j3sqhjj6pa d mass m is at the origin, mass 2m is at x = a, and, mass 3m isq6ao h,3(pjyj: jds )j at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted av qspn+p4(g(. qv 2iz1gqgc-g bout 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 rpg42( qvvpg+1sqqzn -(gi.c gope 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 frictioyk z 0tmc(4:ea(dc+4vo9 urimnless axis thought the center O. A rope wrapped around the outer radi4cvcimz0 +(y d(o9 :m eraktu4us 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 7oom9+yxri.9 q*zqam8 *f3h m nihqi 0hinged at one 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 relea8y 0or.hni q*zq ai*iq979hmfxo3m+ msed? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 3qe 5g wa wr;+xe*,kwqyrg74t+0 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 speed does the wheel achi eg;7q k5 rwqe +r+a,tw4ywxg*eve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley m4 x 05:tnnmf mm)0ehbp uw;3nof mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pul )w hxnbm m0t3m5pu;0mef:nn4ley?

  A 1.53-kg mass hangs opo/ a-dp -ck*tk+z :qb.0kole1l on2gn a rope wrapped around a frictionless disk pulley of mass 7.07 kg an- oaeb2/0+oq .:pd*oktkz-l ln cp1gkd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to sto2 4cqr39hyg.7jodi(xn yv i7 x5t bmo4re 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 o0.vv d ige50p$5.00 \; kgm^{2}$ 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 withbc a -a :xplxt;5pxs6;out slipping down a 1.0-m high inclined plane. What is the speed of the sphere when i sb6;5xct:a xp-xpal ;t reaches the bottom of the inclined plane?

  A solid sphere of mac:,skmm5 oe-x.vecb . ss 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comeck v:,m -cmse5.b x.oing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released froml-4 g r5t i;1k rdhg:(j.xwgfm rest and allowed to roll down an inclined plane.l m:5gh4rwrf (g .tk;g-1jdix How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiu.e*(x 4eat)oxuqnh.qes;2grzc t 2l3s 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from )x. z2tx .lunehtoe q3a*qs;4 (2ecg rrest. 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 changes b2cjgkiy j af(w27 u:v,y $20 \; kgm^{2}/s$ 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 l.uld)ja q./l 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 5.0cdxnd g:2vn8 n-q25)h:/; / fy, jtvry wfvglx0 rad/s with arms extended has a moment of inertia ofyxl8q )/dn- vyjcx 2nf tvg:dfn,:r/hv w;2 g5
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?