Angular displacement is usually exsy/:,e(uf ky 4l rhw:vpress in units of

  Angular velocity is expressedt7iqbb j-1l id*5:lfb in units of

  Angular acceleration nowe1 g a:x4qd+cy:t8 8uo (omis expressed in units of

  A boy and a girl are riy 8gy:d8jw3)kt ; fnlyding 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 j3 :wyy)l;kyt d8fng8 greater angular displacement?

  A boy and a girl are riding on a merry-go-ro 4cc y;.exe,d.ex(w gwund 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 speed.g x,w.ey e;xc4( ecdw?

  A boy and a girl are riding on a merry-go-round which is turning at a constant r a wlc9 ;pjow)8mw(3teate. The boy is near the outer edge, and the girl is closer to the center. Who has the9m3p)j ww waleco(t8; greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a cons nmm*hq+ r2czy f0+nm(tant rate. The boy is near the outer edge, while the girl is cl mmnq2+ 0cm(+yzf r*nhoser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridj/yd96. hybni gnfv2 )ing 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 acceleranv/bj629 f nyhd)y.gition?

  Consider a rigid body that is rotating. Which of t ,t/mp7/foa(b 0 fwjsche following is an accurate statemen,bwcp/fftm 7sj(a /o0t?

  Rolling without slipping de::ztc( a y:yku3p0ino pends on

  Two equal forces are applied to a door. The gqry 9n 1ec2 1hsju(0ifirst force is applied at the midpoint of the door; the second force is applied at the doorknoqse( nhi 0g21r1cj y9ub. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is apr/qb5v qszhw421r w ,dplied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater tor/ 2qrhwb ,rvz4w15qds que?

  Two forces are applied to j ac,nrbw0y25 a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the 5yw,2a 0bnjc rtorque of the second is

  What is the quantity used to measure an objecj zw:xus 8km,9mhd;izu98o p:t's resistance to changes in rotationp:zzmuo9 :w;9d8uxmhjk8s , i?

  Consider two uniform so af-d lflp;h68lid spheres where both have the same diameter, but one has twice the mass of the otherl hfp;-8dl f6a. 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, buggp9b6(9le1d 0 slsys9 2afsyt one has twice the radius of the other. The ratio o se9g1yl90gb9lds sf(sya26p f the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the masia(j , ib ux4/.8yfkins and twice the diameter of the other. The ratio of the largexy4 jbi8( .i,inufk/ ar moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If thepo/;s)gky6,o:oq8 pt jamx qagu 3*:dse are increased to 2M and 3R, what happens to the sphere's momeomp8j/:3p)ta uo dks:o*qy x;6gq,g a nt of inertia about a central axis?

  If a constant net torque is applied to an object, that o4i-c y9c4ao l1- ay(mnkyvet4ea a7x /bject will

  The moment of inertia of a solid cylinder about 98n50d :*.iqpv1hz0qv znd b8ggecv3*jj ttbits axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio b*v5dqgpvcn 0 8 3iv9j.j: 0htq1bnzez*8gtd 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 +a76 q epfb,rfn9ypb 2aru35 c10 kg and a radius of 30 cm. What is the ratio of the rotationalr 7cbpnb236 uffr9e+ a,a5pqy 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 zidmu:eu1 / :hrolls without slipping down an inclined plane starting uhuei/d:: 1mz from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass kxn4;rrq/zswdj:ra-)-w-b gp ,x 5 hvM and radius R rolls without slipping down an inclined plane startragn );jr4sz/k: ,wb-5qx- pdx rwh -ving from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net extern53v yi rl(9lbzal force actz y(ibrv l5l39s on the system." This statement is

  In what circumstances can the angular veloci+ j3tye)a v6uibmds7vu t*c .;ter1h9 ty of system of particles change without)7 *1.d9tcbv vi+euhast rmyj6t3u;e any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction wp 9 cp:/ux5xwphich may be present. What happens over time to the Eartxw:p p 9c5xup/h's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves closepqb;u5j*peij3+ z kgwz9 sb/) to the Sun, then which of the following best describes the orbiting speed qjzj9kgpe uis;z)b 5 *b/p+ 3wof the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hi pjnj.6 )cyol2w ka ocwi77x9-s outstretched arms close to his body. W-o297a c.ciwnol)pjj w 7kxy6hat happens to his angular momentum about the axis of rotation?

  An ice skater performs a:tbt a4t:sz( qni.4l 9bby+ iv pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy abont.9:b :tsq4zt 4ay (v+ilb ibut the axis of rotation?

  An ice skater performs a pirouette gmm m8;e knczo2m ,*fo9 ;5per(a fast spin) by pulling in his outstretched arms close to his body. What happens e 9m m2;zg5kmm,o ef*n pro8c;to his moment of inertia about the axis of rotation?

State the law of consery-jy jgef+a5e 2u4 nrcj 66bx o9s6xl3vation of angular momentum.

  What arc length does the Earth travel in f4;p; gb9rlwc)c5v*x zw90rhqqq x h )a three month period in its nearly circular orbit axr9;rb c)q 4 lg 5xqhwf*vw p;)c0qzh9bout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3t pq7d)hhr p.0dt7 05w bboze,0 m. What distance does the tip of the second hand sweep through in 3 minwd0)pe t.r7qb,0htp5 7ozd b hutes and 45 seconds?

  How many rad/s is 25 revolutionxsjf//w h57ids per minute equivalent to?

  A bicycle wheel rotates unifp 4p gbvgyo07/hfa8ly6 kr qn ;1*s2ftormly through 2.0 revolutions in 4.0 s. What is the f*y46y vop; 1kfa8b7r0ftpng2 h/qg slrequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thet 4 i/g0pcllyp)h/q.y i:sz ;.5fjrsr period of its rotation ip /hlgfps;r 4jqy:/.c5zl)ir .i0y ts s

  A phonograph record rotates at 45 rpm. Through what angle does it turn i z7o. cqci;q0in 0.20 s70iqcqoz ;ic.?

  A wheel of diameter 26 cm turns at 15r:lc77bwk ke4,i2mw tz2x n4he(vdb000 rpm. How far will a point on the outer rim move in 244rve2,be 7htk(bl7xwm 2in:dc 0zw k.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isz vlb7 3 sy8hbqn3;bnv5,i-is the average angular spsib8h 7 v-3yv5,q;bnlb nz si3eed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolu8ty2m y*lq 8d1) red7x+q8tfsdnb*o 9tz9 v tntions in 4.0 s. What is the linear speed of a pnv todltsx d1tzm*n 8btf97q8e+y)89 q d2r*yoint 0.10 m from the center of the wheel?

  A cable car at a ski r+ bjur n wn,*4dk53jyzpl26nzesort carries skiers a distance of 6.8 km. The cable which moves the car is*zpl 4+nb23k u6j njw5,zr ynd 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 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. *2nk-(jozugfm zvd: 6 What is the linear speed of a point on the wheel's(dz-2*6ju:nozgv k mf rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in len,m,(x,x rz+:c lq quatgth. If the motor t(q+xcrzx:q mlau, ,,rotates 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 with a constant an rhglzaw,bv/;( e s-( ,gn.vufgular speed of 2.0 rad/s. What is the centripa,rv(vh/gn;blw g ,s e-u.fz(etal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle ( jl9+gmt7.gsmg q o9zwheel of s ( m 9+7lqgtgzg9.omjdiameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute o5 t (kj g.::yd:q rto1zkde5v(rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an art k ( zdkegt:v:5oy5t:odrj. 1qificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m withezlw84c66 iam5 u0e oe a speed of 20 m/s. The maximum c0i68 owz me6 54laueecentripetal 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 radik2 lh t1j1(mrbus 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fril12tb1kjmrh ( ction) 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 wuet7 8rhlx; c*hirled around in a se87r x*u;lthc mooth 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 string is not to break?

  A bowling ball of mass 7.5 vty 7/ swo1 1*nzz-.4 snywcobkg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 ywnzyt* sow c z-vn s/b17.o41m/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 angulamw3 iord-mvtzuagm 7l:++ 8q6r 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 constant angcwp hl;6e;gi, ular 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 automow j clb v62,68skxo xa(.aci/eu --zcqbile tire rotate after starting from rest and accelerating at a cok6c ezccas/i2qxx86w -vo-, .ua(jbl nstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and ha /y1hg0 -nim)08d(pkiobkge ms 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 angular accel8b03oxauu+t rerationxb a3out0+8ru of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.000hb. 80 shg frhsjcxkw3 yru8m0qx,* rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the whes*rxhm.b00g0xh83yhs w8j, rq u0fckel?

  A wheel of diameter of 68.0 cm slowxcnk.3u d9 xo7;0ehphs down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to resn9p;cx 3od .7ekxu0hht?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over a;jrg-s , ,elcjcr3ekw+ l,5qp distance of 115 m. What is the angular acceleration?l5lrgk-j pew ;,cj3sq+, ce,r

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s7eip, xrh:mwsxg3i 5l9;hj/ p to rest over a distance of 115 m. How long does it takei h93lexg;, 7/ms5h:ixrw pjp for the wheel to come to the stop?

  A centrifuge in a medical labora 0l):9 yi9a-itylseq atory rotates at a rotational speed of 3600 rev/min. Wh i9 :0-ti)syleaa9yql en switched 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 require tilp*n -3wx *vnsp,h:vdbs8sr. ghtening 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 perpendiculad s3nrp pvh:snws*,. 8x* b-lvr to the wrench?

  The bolts on a car wheel require tightening to a torqurtn qg xmu0f0; x++ j7d7rw,xge of 90 Nm. If a 30 cm long wrench is used, what is the magnid rngr,umj0+0fwq+g 7 xx7 x;ttude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment abvny()+ kx3dof 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 folp(nm 7rm5ht f:lows: 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 about the m (p5mfrhtn7:origin?

  A solid cylinder of mass 10 kg is pivoted about a fs+41wuk v( h xw40*be)d lrsmu)7dj wqrictionless 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 foru4k e)jds*lm7(v hx4suw1d w w0+r)bqce 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 thought txww08 q.9omh:p+ewr dhe 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 iwqhdxmp9r 0eo w8+w:.n the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in the8lss-ow 0)k)pxlpk d* horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration adx sksl)o-0kp pw8l )*s 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 and mass 1.5 kg.qw*4xejne udwly4tj- 1;r.0q Neglect the mass of the axle and sprocket. If a force of 20 N is applied tan twude4l*41 qjryxqj-w0en ; .gentially 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 a frictionless disk pultl (pm.xahzful9u s- o:-m7kyil m nx+.gb 0/,ley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerbgy(pl-/ 0.t z: ,um9. mlo xufmxsaih-k7nl+ ation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictlkme57rb; oa2,(se5vjpu 9bb ya5 bark 0z* p9ionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceler ykr7b590e,o 5s rupavpbaa lkez; 92bm b(j*5ation of the mass?

  A rotating flywheel can be used to store energy. Ig l d8sg w/e.uqw::x.xf 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 inr *,szzie*x/ jertia 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 k4qqzyk/ tm(w*g and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reac*( 4q /tyqkzmwhes the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with wqr*3d j2uuwpm ;(q-8p blrn: a speed of 10 m/s. How high up an inclinedb;8l3qm qw-ruu dj*prn 2:(wp plane can it climb before coming to rest?

  A hoop of radius 0.5y7mc.0r j-s pic.qrn, 0 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined .- y0qns7 jr icr.m,cpplane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiu omwt: wb+wc9pgpr* :-s 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from restw-pptbo :w9+m w:*gr c. 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 ce56e2m vnc8s,g: z ikmhanges 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 qyio+*t)vkod5xwu 4q:q- sm7e8 q3 qr of inertia 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 extended has a momenc ii5k1,sankv)/g5r z t of inertia ofvg5 r15iz a/k)i nks,c
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?