Angular displacement is usually express in u( hj/oe0 vr3fvdnt s/8nits of

  Angular velocity is e d8nvzr d/ f3hmw78ev.xpressed in units of

  Angular acceleration is ey(lq/-y ug;3uzmf0y yxpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at bjtg f1ityr32t l/i,,a constant rate. The boy is near the oute tit,lbtjy2,3fi /1g rr edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whi39 tcmgrl ms3h3:ln3vch is turning at a constant rate. The boy is near the outer edge, a9ghl r 33:nst3 mlvcm3nd 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 e ;hd2snq1u;aning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed an2d 1qush;;e?

  A boy and a girl are ri*ozjn sg9gz zpak2e8.+zlx7 5 ding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while thjg7lgnoez +2* 5sap9k. zzzx8 e girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a me0n5c6rsyj h g-rry-go-round which is turning at a constant rate. The boy is near the outer edge, w 5ns6- c0hrygjhile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which:5e aib gutj)) of the following is an accurate s5e jg ):uiab)ttatement?

  Rolling without slipping de+tfyibbl2xs 55c,uzx 6hw+ o*pends on

  Two equal forces are applied to a door. Tht0dw .wtc xjxth3 -soses-65; e first force is applied at the midpoint of the door; the second force is applied at.ot3; 0dtxx-wesch j-t5ws6s the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at ti7h7k0k /+klhfy 0bpo he doorknob. The first force is applied perpendicular tokp07 hf+k0okbl7h i /y the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The 67 q oe6gotootd72 r7nzg,v1 cfirst force is twice as large as the second force. The ratio of the27otro t7gv c7o q,god66nze1 torque of the first to the torque of the second is

  What is the quantity us (ta2)6x5 bw7pqfzi5cl6sr,c kh5noeed to measure an object's resistance to changes in rotation?(zkn,)tcrcof56ep 5i2x7 6hlas qw5b

  Consider two uniform solid spheres where both have the same diamete3bno29j g-g jgkgg-dhng j*39r, but one has twice the mass of the other. The ratio of the larger momentggg9njgg d3 h3j9j*- b-2o nkg of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twicevd)uxgk mc*6 1ld9hw4 the radius of the ldcv16)* gum9kxw 4 dhother. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid6t:hvdhfb: z8 spheres where one has twice the mass and twice the diameter of the othert: hdbfv8z:h6. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hahpbru 75 c ,s(,u;mvds0ha qa9s mass M and radius R. If these are increased to 2M and 3sh 07qdbsuua 9,hvp ;m5r(,caR, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applie.noo pln2sz rf5e1 ;e(qw jrl5h,s),xd to an object, that object will

  The moment of inertia of a solid cyli; 4vmgkl2,x wc0zds2nnder about its axis is given by 0.5 MR2. Ikg4s2 dxz v2l0nwcm;,f this cylinder rolls without slipping, the ratio of 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 a; f lsn8od+o,jnko*7jnd a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic edlfs onoj kj+7*n ;,8onergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls wi5evo -j(c c91rcgz u6vthout slipping down an inclined plane starting from restv 6c591roev(jcug - cz. 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 slippinggl4-,v.4a 34yxp vj faoe,lyu down an inclined plane starting from rest. The angular vea4ul, evavf.x4py l3y -,4ogj locity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externalbdbtaq5as)1 3vq05 sj+ ,er al force acts on tb 5j0sbqart5daqe ,)sla1 + v3he system." This statement is

  In what circumstances can msh+ d8ya 95sy 0xlb;x* p3wbothe angular velocity of system of particles change without any change in the system's a 9y*3xa +y8x0 s5mwsh;bopbldngular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignd.t.w.; rho8 yxr u.r uux(2lgore any friction which may be prese(ru.g.rt.w ; xhur.xud l 2yo8nt. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elli;*1 x8nl7unoa cgta1ic*zd kk8fqw* 1ptical orbit. As the Earth moves close to the Sun, thed*c* ik qg1;z8ou a lwt8a1k*n 1xnf7cn which 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 his outstretche coebn ar-x6-2tno ..nd arms close to his body. What happens to his angular momentum about6xto eo n- -nracn.2b. the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchyh3w pqc,b 7v7ed arms close to his body. What happens to hic 3vw7h,yqbp7 s rotational kinetic energy about the axis of rotation?

  An ice skater performs i m*.k1jwnf ,ktt4n 7ua pirouette (a fast spin) by pulling in his outstretched ar1 ukj7.itm *wn, 4nkftms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of cons5va-i-9 w r /zw 8(+sffh*zby tqi*pndervation of angular momentum.

  What arc length does the Earth travel in a three month period in itmht9;qyz w1+x (*7hozoxrd9j s nearly circular orbit about the Sujhotxzmy *(;+r1 woz9dx h9 7qn with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length y sr -sr*-flh+ 5v 7gjj.qko-pof 0.30 m. What distance does the tip of the second hand sk-oqlp5-j sr .yf r7*-jhv+gsweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutihg noo/0x.e 8 f ob44vz--htmcons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.. 7q(p6 jb1pgyiq8gga1vu ze10 s. What is the frequency of the wheel's roab.81p jqq evggz16(p7g i1y utation?

  A pulsar (a rotating neu9*jj2e oddo4s sljtvku/ :f+:tron star) emits pulses at a frequency of 0.40 kHz. The period of its rotationjj/9:sj*k2dle:4 dof +tou vs is

  A phonograph record rotatespigj7o(w+ r6 6st6afp at 45 rpm. Through what angle does it turn in 0.20 s6 pr6(aj7w fgtp i6+so?

  A wheel of diameter 26 cm turns at 1500 rpm. H d+/6 ym7zfao zziucl8/01d8,fam vv kow far will a point on the outer rim move in /a8ik87mzz dvvl+y/0d fo1c6 fuzm,a 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thea3x3ek,tapa/ ns, ;ehh pw4+nv*)e9j d4pjye averagwt );h3n /,e+kah a *3evespeax4n,9yp4djjpe angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What vlg3 uh6ngu9lj3n0 z8jf q 02pis the linear speed of a point 0.10 m from the ce308 nlpf32v6 glhgujnzj 09uqnter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cableqw:dr+ +; o1offx8bpc, n.s)o/ rkgcq 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 td/ bsq;.p8cw1 +f)k+n cgo,oro:qxf rrip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a ewk0o n qat:w2 pz 5, .z4q2qqoy)mf,0gauus/constant angular speed of 2.0 rad/s. What is the linear sp k t,q0:2zq4 owzqy.wuauo) am5s fen,q/gp02 eed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in w3-:ntcn7:h .gpvldo dvd( 9y4l.jcq length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed o :t(d9w cyq l h7-l.:pj3d dn.vcgvno4f the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 radow df f+it:)qj*ulh *+/s. What is the centripetal accelera+j wt*)i+ldhuof :q*ftion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter+-c) rddya weh*2js9b ..mxcx of a bicycle wheel of dieb.cmad) y -j s2rhxx+dw.*9 cameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatd6ilwi j.j b4/3 z f0tvy fhxu/;o.jo+ing space station (r = 1000 m) rotate to produce/x wuif /h3ov0z.l o6dtj;yj .jbif4+ an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed odr57k )ll92v2p lttm ef 20 m/s. The maximum centripetal force (provided by stalpvdlrt l27k9 t )5em2tic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cic b :rm ) rox*flc/:.n;d bmr;35mzwccrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pro m:or;cwzmm; .rb5*:c f/bxccd)r 3lnvided 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 end of a 0.750-m strinzpa9uv j*:wpf2xp3p z80ty (hg, 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 if the strinua2( y9pp3hpf 0pwz*xz v jt8:g is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without sq dpmto+dr pw 2bi4i2o009x+ rlipping 10 m down a lane at 20p d b9q+o o2r+dp4mi0tirwx 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 acceleration k-tw2mjff.wl dl :x z0gn4kv4v0z1z) 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 p cg14 j4u7oqjbo ,1lv-nfk z: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 automobile tire rotate aftr 64//hw bjtuqs e51 y1vthoxk5n9;vs er starting from rest and acceleratx t s seyhn;jv9wtb5/uok /16v154rhqing 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 adu/jm69tek kdpi5 kz1-rh,g7cceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating ax xlm *b,5w.: rf.om,hh f66qtxxp,lu t 20 rad/s decelerates with a constant angular acceleration o*tl 5:qmh.xx. 6r,f f,hwoxpx,ul6bmf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches cct iq;*mkp s./ )mod0an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of tmq*pcdtsco/).k m;i 0he wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oow95c(p/a cewver a distance of 115 m. What is the total number of revolutiow w(cpaoe 5c/9ns the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to regg6 epbfzb v)xfk9q3-9tj(xxcw ;vh)gz5 *a0st over a distaz6hzcxv)b 3wf fjg0bx;k9g (*q 9) epa-vtg5x nce of 115 m. What is the angular acceleration?

  A wheel of diameter ofb2-ln* *fplv/ x1coiz 68.0 cm slows down uniformly from 8.40 m/s to rest over a dis-lnofix vc2*/plbz1*tance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rdi;)k7a*u t:m.+ zg fwszvnp0otational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acces+:zt).mp;*7 dui 0kaf gv wznleration 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 wheeldgup9mi, ,d.g gmehuz44f 7y:qjz);v require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendiculf,ggevmu hu9:d ipqy,zzd4.j );7m4g ar to the wrench?

  The bolts on a car wheel require tightening to a torque51nfr) fibhovv)+ ,xv of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required wh+b f ) )vofvixh,15rvnen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertid/c6 a bwo5ro 1ze/6,pfwxjxa)o 1l8 l;dr j3xa $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is model9loolwy 7kboi1z*mt1 /l-fs ;ed as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia a kl sf-bool tiz;yl* o7/1m91wbout the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictio+eogxr3dqw: sy)ei1 hh++,o wnless 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 sx:++oheg1yd 3wwh , r qe)o+ianother 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 a*r 4hnj115k2rfws esf xis 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 wraf1f nss5 21hwk er4r*jpped 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 hing6s34 79,qv 4 lpbmdy a0xruhv5l-ntrm ed 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 released? (The mvxv rus,l 3r4nm l7a9-b4md0yp 5h6tqoment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wvop/tcpt/ob vh . z;e6kn h ec73:er76heel to be a ring of radius 30 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 achieve, assuming it rolls terzpt.6/3v/vnhebecoh ;c :7 o6p7kwithout slipping?

  A 1.53-kg mass hangs on nxyl( c0,k2q wajr)w2a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration o, knwl jqxw(0)r2y 2caf the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley o6c (pw fqjghz-d3 :z/s b39hxif mass 7.07 kgdzhz (-/s: fj6g9h bqpic33xw and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to se 4m..wny psm1tore $1.00 \times 10^{6} \; J$ 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 x*4:af zpdwyu) pc26 yof $5.00 \; kgm^{2}$ 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 sxuthzo(pr0n9fvct.o4 : e4;rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphert4tx zf(. pno :ev h9;sc0oru4e when it reaches 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 e qamkw/jtywt5d(i 1 eos jzt/,2iut+ g541c6 m/s. How high up an inclined plane can it climb before coming to re +5tgcm w/otad51zj i2swe,q t1yk(eui64 jt/st?

  A hoop of radius 0.50 m a. .h- ve)cdxdph4w 8ywnd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving afterdh.ye8 wx.)c4 hv-pd w dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls w; uo(oclcq9j 0ithout slipping down a 35e incline that is 7.0 m long. Ascu9 ; jo(olc0qsume 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 momentum changes cfgy2+20m p6sh ) hrlcby $20 \; kgm^{2}/s$ 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;b)abr;nl o .y 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 k5c5 /+(nlxf)tucfrc with arms extended has a moment of inertia ofx/cnc5rkt l)fc +f(5 u
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?