Angular displacement is ucj ;kz ,rqbt xih0.;0c* ufcv3sually express in units of

  Angular velocity is expres:p6mkk qy/ne; sed in units of

  Angular acceleration is expressed in unitsrlr u, 5w;hv;*)kpdu u of

  A boy and a girl are riding on a merry-go-round which is turning at a const i5ucyf6 9.bsv 3ropj)kdh /1t fnd6n2ant rate. The boy is near the outer edge,fo9j.tu)pn/d 3y1csnr i5 dk6f v bh26 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 which)y3t4-zo/yt nz xpzmaq 7u c2- is turning at a constant rate. The boy is near the outer edge, and z2 pn4y--c t3 zuomq zaxy7)/tthe 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 t ,p0 gq;lutj4 hg1nw2d+;tnoburning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenp 1wto h qt +ljnubd2g0,;gn;4ter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turningr a4slc:z9ku . at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who 4:ak c lrz9su.has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is c7* 5cl:h/ygn,)*fxgtvk w nrturning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential accelnc7vnxkhc )wg*t/yl rg5: ,f *eration?

  Consider a rigid body that is rotating. Which tojs n9altmx/,bp3.( of the following is an accurate statement?sb/ tal(m 3o. jxtn,9p

  Rolling without slipping depends ohvrv.p5bc334saa6/ a zsxc a 9n

  Two equal forces are applied to a door. The fiuf8tc1-5 ba5;cfyopmw pm0 2m rst 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. Wh mfm58mc 0p2-u1 wcp bfyt;a5oich force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The f hp n7ts5rn3gyp*rb hdc b-5xe1 *)0lpi8d0ojirst force is applied perpendicular to the door; the second force is appliehs px 3b r5hln-o*ntg85)p7cdey1 jbi0p*r0d d 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 first bi5g yh);pd,yhqtx 5( yo17uqforce is twice as large as the second force. The ratio of the torque of the first to tq,oiuqyd t5 7bxy)g;ph1 yh(5 he torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotg:ugzl +5 7ur:f px2u7asbk/oatiougx 725opu b:fz+ r/ klgaus7:n?

  Consider two uniform solid spheres where both have the same diameto2sn)vf77kxv6k)pgc er, but one has twice the mass of the othec) 2)fknps67go7 vxk vr. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have thyxlqq0(-bezg998nq d k;n m ,de same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia 0-xdd8;qb 9ze9q(n mq ngk,yl to that of the smaller sphere is

  Consider two uniform solid spherem*igsmq)s 4kfs y(ne5vp(6w 2s where one has twice the mass and twice the diameter of the other. The ratio oefnmms5gwvpik6( sq 4y 2*)(sf the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M anb(1oi , xhb*ej1if 1pjd 3R, what happens to the sphere's moment j(1h11 p jebxio, b*fiof inertia about a central axis?

  If a constant net torque is applied to an object, that ow2po-dg*law 2 bject will

  The moment of inertia of a solid cylinder abz .q hsp+pm(8yt etu,:out its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle ofvq1qrq+7/n9zm8trqx mqz:s kssd*/ 9 mass 150 kg, one wheel of which has 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 trans// 9str*:m7mrq 1 szqd+qzx9 qnk8s qvlational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an idru d xmsz22lpovb-pa8.+e ;2nclined plane starting from rest. The linear velocity of the ;mabdx.lvors z-ppd 282u2+e sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R o jz(kt ji50z2vu7s7srolls without slipping down an inclined plane starting from rest2zsk(v tjj70z 5u7iso . The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentp x2zo -z w30 .llqk7q 1zpjhh/5ds0uaum of a system of particles changes when a net external force acts on the system." This statement ipz-qh w0o3 x2q dk017ph/ a.zllu5j zss

  In what circumstances can the angular velocity of sikxjn 9p(e u2/ystem of particles change without any change in the system's angulpx (ij/uekn29 ar momentum?

  The Earth orbits the Sun in an elliptica0dc4zt)xsqi-u4r :ts7 ,f tf s8(bh oil orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentxdqri7 zch)s(0s:4b,it8 ut 4ofts-f um about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As th3g8 onz ho uti);7:sxpe Earth moves close to the Sun, then which of the following best describes the orbitingng 3;z o7so tui8xh:p) speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by b.-l gxkl*9bypulling in his outstretched a blbl-kgx*9y. rms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast s exqx6(f8 g/xupin) by pulling in his outstretched arms close to his body. What happens to his rotf(quxxeg6 x/8ational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullj 2e6-)b:bh +ciuraqy ing in his outstretched arms close to his body. What happens to his moment of inertia about the aa bb)-:6rqheyi 2ju+cxis of rotation?

State the law of conservation of angular momene -inv fvr64bo*ghk3p/ b+h3c tum.

  What arc length does the Earth travel in a three month period ie qzfe .l.uzq2y7x3e(2 bdrir8*/ apfn its nearly circular orbit about the Sun with a radiuxed*z u3br7 yp.eqff(ie z2.ra 82/lq s of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.gd2: 4t ah1njy30 m. What distance does the tip of the second hand sweep throu2h g1natjy4d :gh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eqam*uuvki+nkt z- ),r 7vlyh33uivalent to?

  A bicycle wheel rotates uniformly vpu/8 l)og8c-fes*q qthrough 2.0 revolutions in 4.0 s. What is the frequency oep/ 8qfvug )-qc8sl*of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fsj kfzphb5b7*3ie) .xrequency of 0.40 kHz. The period of ith fe pzxi.b7j5sb3*)ks rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn tg,rx iw5s,;3 5m7ep8 in)ifj- cndjcin 0.20 s ;-mdp 8xnc,tj)esngwiji7f ic,3 r55?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poi:u/ bde4 tf,wnnt on the outer rim move in 2.1 s? :enb/wdt,4u f

  A bicycle wheel rotates uni- u7k8 s(hr.yc g-t 9xtahiw0gformly through 2.0 revolutions in 4.0 s. What is the average a7saw0k .itcx8 gyu9th--g( rhngular speed of the wheel?

  A bicycle wheel rotates unifo, mvf( c7isms1rmly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the cem1s, fs7c v(minter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whicdug z/w z3sum,5g(v 7fh moves the car is driven by a pulley with diameter 3guv/ 5zzf d(s,wum7 g3.0 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 spegaii6fe0 8 g)isi9a+ eed of 2.0 rad/s. What isggai)e9 8e fiis+ a60i the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0m5foui3mi: esp wii/p9 prq6 t18* z8r.16 m in length. If the motor rotates at the ratef5qpr6i 9pms1uz8r3i :e i/i*mo w8pt 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 at o*icov u.,z2 constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a .c ,*uoz2vtoipoint on the wheel's rim?

  What is the centripetal acceleration c dyx-gng9 u1( ez9us3of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moy1uuc sg e3(z-9 nd9gxving 8.00 m/s?

  How many revolutions per minute (rpm) must a cir fdu1pxzp(7n1/hh3 tag*g ys.cular, rotating space station (r = 1000 m) rotate to produce an artifici1 st upzd /3aghxy*gf(71hnp.al gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 h)tck6ahp3pox0hght)/0zq)s : c3t im/s. The maximum centripetal force (provided by static friction) is a)pc xch)3 ghito:/zs qh3k0th 0pt 6)$1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiatingdjzm1g;nd/ d, a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided b/d;ndm,g1 jdzy static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attacho8w-sl ..- pjsuyntd;ed to 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 if the strswl..ud-;o 8tnj sy -ping is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 isfw5 / n: +k2p) eqe n,-f*udl9altunm down a lane at 4.3lfeu /wq ldeni)a:pn, *29ts fn 5+uk- 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 acce hr6z utz9h3+uwpk/ s/6tb md;leration 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 angular abr*2lxnzglu-amp)p2o g ; ;e; cceleration 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 rota ;wa x8yez9k*nc(8k fzte after starting from rest and accelerating at a constant angular acceleration*8kwzkaz( x8 nc ye;9f of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, ansmkxgf(6y)b7in . mqy /g38ai d 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 v+ lgu8wd*0c lrad/s decelerates with a constant angular acceleration ofvd 0*cluwlg+8 $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachve*wewf2w 3*o/ 9dzh0 fj-y yres an angular speed of 6.0 rad/s while turning through 2.0 revolutions. Whh0 fw j2 f3 ewy*z9v/o*-dryewat is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uj5wn5lda ez+ ht k)q.1 ;soux+niformly from 8.40 m/s to rest over a distance oadu tk+ +n15;)qho wxl 5jez.sf 115 m. What 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/c(xrex) )w0ev( cl*3kqj*qh- t2 f rvks to rest over a distance o0jl ))x(*v3xeve*kr(w -hqqtcr2fk c f 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifo,5l-z*zl b q7knj/kkv .4v 1n(ckkzymrmly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to comebv 54y- km7c.z jlvk* kq,k1/nl(znzk to the stop?

  A centrifuge in a medical laboratory clt c+6mbsaukx5f 3p x+ lwk(--p+j c+rotates at a rotational speed of 3600 rev/min. Whmb aws-6-x+jk3 p u lfccpck+5 +(x+tlen 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 hao -p05bms +vrequire 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 p0samo-h +b5v is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque 0*cd /v6jy7wy mlkkosh (8e)mof 90 Nm. If a 30 cm long wrench is used, what is the h8y omc6kyd(*svl0wje/) 7mk magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner*5kviszq-5 twtia $3.00 \; kgm^{2}$ 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, f- bg7p8 (rk taica,p .e2mb,xmass 2m is at x = a, and, masap.kp2(fbxib 8 rg-7atmc , e,s 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg p/t:;*jc/w jrcb k;i uis pivoted about a frictionless axis thought the center O. A rope wrapped around t r*tpi/kw:cj;/cj u;b he outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tuddmxx6 2ujoo c (+0-a9bbq-+eav xh6hought the center O. A rope wrapped around the x6x2 -0heb6+db umoc9 o- vdxaqa+(ujouter radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 initially hlv wgw,:52 mg8ql0d 0(agahwteld in the horizontal position, an0wh0w2lm ,gg w: lvgdt8 5(qaad then released 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 and mass 1.5 kg. Neglegryf m0q583j* hg qoex0)4ejx ct 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 rolj *m08j x egfq4eg)03r5hoyqxls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fr:o. l d2 cj/ol/g lbr+e9ny*lvictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulleol.y/r2g nevl9/cbld:oj * +l y?

  A 1.53-kg mass hangs on a rope wrapped aroo.j)z6+*0ocr p e)sdmiq orjj9/ r(ca und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm.mp. )/oz aq()s9rj+ji0cd* ro 6orcej What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it ihc2m76 f m54 skeeulu+s 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 ofmily)uyl;+s96zh 1db $5.00 \; kgm^{2}$ 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 m-xg (wv.xuf qf(l7 s:0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the spherqm-w g :x7f(lsx.fu (ve when it reaches the bottom of the inclined plane?

  A solid sphere of ma nk5f-; kyc3phw+yhty w/no5 0ss 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can ic f5-pk wo5hntwyy+0/yk;3nh t climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from(0xlpsds(8 49q4g0 krucoudhj -5hj a rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical diusjd8 od-g9 04xk5rh uj( 4(qhclp0asstance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolgonuyzj;8 q .)do26q yls without slipping down a 35e incline tj8zg 6yyq) ;ndu. ooq2hat is 7.0 m long. Assume 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 o :9hznm.2h o:(wgytnchanges 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 4 :r/b1zrbxkrinertia 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 momen4d1y4:m vi2n 0v9ufj1kosvc at of inertik:v0fs1nij d49co y vm14vu2a a of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?