Angular displacement is umrybj 1v):ilo )yv 76usually express in units of

  Angular velocity is expressed in usji k.g( z)ua2nits of

  Angular acceleration is expressed in un* cgy12re;h2w) h lpkzits of

  A boy and a girl are riding on a merrru vru-kb)6* kpcy(6aqxs +dhfi8: p, j.,eosy-go-round which is turning at a constant rate. The boy is near the outer edge, -f),js.orp y*xkd i:hrc6,p ueua v+(68kqb sand 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 is turning af0g*lq+up;re , mwce5 t a constant rate. The boy is near the ouqe5 ;rcwm0 *+efp, gluter edge, and 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 turning at a cyncpx.-hx-hz wi/ 18c onstant rate. The boy is near the outer edge, and z nch/iyxw xh-.p8- c1the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are cbub 26, nz2hlriding 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 centripetal accelera, hbcl62 bz2untion?

  A boy and a girl are riding a merry-go-round whicezv su.pf6. pqeyrj :m(pkj- sa 27y77h is turning at a constant rate. The boy is near the outer edge, while the gir fj7:vmq27ypsa 7e(-zpupjye6.r k .sl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the foi6pr0sbn (e m8llowing is an accurate statementibpm nrse86 0(?

  Rolling without slipping depends 3o+i 7* jw2fty,qashnon

  Two equal forces are applied to a door. The firsrg(n vqao61 9mt force is applied at the midpoin 19nq(6gvmaort 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?

  Two equal forces are applied to a door at the doq4zgz1ifnhmk, ; ck0 )7wpj1morknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exertgqf )wpzk410c;n,mj zkm h1i7s the greater torque?

  Two forces are applied to a doorknob, perpendicular tb)gd v4- b-0i 1v8bu 4gbfv9k2 jngdsso the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second i bv2d-gf4susb)n8ibb4kgg 9 v 1vjd 0-s

  What is the quantity used to measure an object's resistance t.ls t0nhgw 0;po changes in rotati.l;gs tn h00wpon?

  Consider two uniform solid sphere 6o6b g a5og 94jb l0ztj3tej9s07xhmrs where both have the same diameter, but one has twice the mass of the other. The ratio of the loje rx a6glo7m s0ghj0 659j43bt9ztbarger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sphp. .iv 6uo f*r -jhini,wzh(.oeres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller-pzo6 j*h(.h onu iw,f.ri.vi sphere is

  Consider two uniform solip sc( 6wrh.*ckd spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of tps*cr 6. cwkh(he smaller moment of inertia is

  A uniform solid sphere has md z5plvm4ei*. il)y .f-fs9s nass M and radius R. If these are increased to 2M and 3R, what happensfsyf-.9)i d i4ml5ev. *szlpn to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to agpkq q0 5abs66ixc/ 5xr+0 uqysr11ctn object, that object will

  The moment of inertia oya4*5u p0o ntct2 qbb:f a solid cylinder about 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 of mass 150 kg, one w)(o be nk6e4 hivakd4;heel 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 translational kinetic energy of the bike? Assume the wheels are uniform disks.46hd k(a4 ; obi)veenk

  Suppose a solid sphere ofix xp1 1bdaw06 mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incxp id0a11b wx6line depends on

  Suppose a solid sphere ofnegrh.4 .bh .e mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of hn.b4.grhe .e the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net0iq3ybcg (t.aa v(h0o external force acts on the system." This statemeb(tghv0yo (a.3ac0qint is

  In what circumstances can the angular velocity oxc3km2 b yc)o( k5kz0kf system of particles change without any change in the system's angulo b)kk k0c2kc3 zm(5yxar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whuv): 7u7 5 k qn)q ivprmbexu)r+,+ipoich may be present. What happens over time to the Earth's angular +) 7)kiuur:75e xv vri b,n)+qpp mqoumomentum about the Sun?

  The Earth moves about the Sun in ano p/r elq5tq +vhx,.;o elliptical orbit. As the Earth moves close to the Sun, then whico,qo h 5lex+;vp.r qt/h of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullv-sycodrd 3 / -1ids.ming in his outstretched arms close to his body. What happens to his angular m voms3 i /-cr-sd.yd1domentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) bx( cfnwt 72e,qy pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rote27( wct,n xqfation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched x)uu:2cc4h qic* +ztb arms close to his body. Wbx +ztcu c u4)c*hi:q2hat happens to his moment of inertia about the axis of rotation?

State the law of conjbl+p8(-93 cvxzefar7 ht +gpservation of angular momentum.

  What arc length does the Earth travel in a three month period in iz 0+lx:xpg o j/d ir/2w7k.mzhts nearly circular orbit about th.2+ilgj/7w 0dxrzmh /o:xpk ze Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng8i6,zys,3vybkv(r5che+ e f7x 7tywrth of 0.30 m. What distance does the tip of the second hand sweep through in ic6x3 v7 ,8(z+vftwkrh,y57ybys re e3 minutes and 45 seconds?

  How many rad/s is 25 revoluti+ ,hlpt6e/iyc n5, qpeons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutvvdt 1ma gk94rkt /-k7ions in 4.0 s. What is the frequency of thvg kk1a9 v/m4 tt-rk7de wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. x8ufl6 :gprdtoz. 5z pbj7-2hThe period of its rotation isou :7.8grpzh-p dxz5 fbt6j2l

  A phonograph record rotates at 45 rpm. Through what angle does it 8pf1nz2mp gard9 3,q pturn in 0.20 s32 ng mqpzf8pdpr,9a1?

  A wheel of diameter 26 cm turns at 1500 szwvho +kze2g/b69r4kl z+ d0rpm. How far will a point on the outer rim move insr94 oe+b0z2zk6 dw+lvzk/ hg 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolua; u2: /i9qekhnkh4z jw bw.c39-ektb tions in 4.0 s. What is thet qa9-kkbnjkheiw : 942.z3h u w/;ceb average angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.00xwy o4q cstr12vn(r: s. What is the linear speed of a point 0.10 m from the ceys14 :tvrc( w0oxn2qrnter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 kxmudc yr6;tw.t2+ w0mig2n a*oq d*/o m. The cable which move oy2.wg*iqw m /do xtraud2+;6n0mt*c s 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 trip in 12 minutes?

  A wheel of radius 1.0 m is rotating wi,a5r4xzu0 n bsth a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's risurzb n4x0a ,5m?

  The cutting cord on a ga 1wi6dl0 bkep :vys;y;s-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed oy6ik s;d ;:0evywl1pbf the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angul bks4,mi0rfel2r8e12 z hp(sdar speed of 2.0 rad/s. What is the cent, k8r210h2 r si bsme(plzf4deripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyc )1w)nwjhi co(le wheel of iwhw)oc( 1j)n diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stamz .8 7kfiynb :h9zalj(km0 )ption (r = 1000mpkhy 7z f(ab:)i08lzn m.kj9 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spennt 4n/2lckg+5 tl 3q 4qsauhs*p)y08xix6b oed of 20 m/s. The maximum centripetal force (provided0nb48o nq sp2txuy)6aq 4n s53+gl /*xclh itk 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 v+v: g2dqxy wei 814ojradius 50 m with a speed of 20 m/s.wjy:8d2g 1oqv 4 ex+iv The maximum centripetal force (provided 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 string, is whirled around in:l.p fqzu +j ,t8cz6tp 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 stringp+jqzf utptc: lz. ,68 is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm uy2q3m)bo- 1ck0 /vevmp ub:drolls without slipping 10 m down a lane at )1uu3pck0vb/ybdqveom2 m:- 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 wi 87lvjx8 g,oj4/ z tov(qxh(onth a constant angular 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 constant6xo4:-s d3hbid ik/ yzw6dw4a 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 0.347gnc6trg :f7 eoa/dl00-m radius automobile tire rotate after starting from rest and accelerftlonc67g4:/a 7 re gdating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has -(5ntdam-7 v8lr4.v bnh vwva 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 decehxqfb;1 q,9 ktlerates with a constant angular accelera;fbx1t ,khq9q tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from restajqe w hys0239 and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of tah3qj 209 ywsehe wheel?

  A wheel of diameter of 68.0 cm slows do jf-2opn8ccqw)1incn ixj(ml */w2xhd+ *v+ own uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel wion8ixv-n f* +c mc2qn2* o+l1chjp/(dw) jxrotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to 1x(fzcd;**me(:s: q6 xb 8 kkts chblq))gryy rest over a distance of 115 m. What isx:)(:x s;rkmh sz6qg yqk*(bf)ccl* tyd8 1be the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unif1 l46uhy; mdheormly from 8.40 m/s to rest over adh64l1e;uym h distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates /dd,ouu1di8m *q/cx -v5 ltz hat a rotational speed of 3600 rev/min. When switched off, it r xocth *dli1,8uz/ mdd/q-vu5otates 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. If a 30 cdsvi 4 fqg6use)5n2b, l,ye(/tpa tsmbe ):8 gm long wrench is mnst(4b6 ie 2gt)v e 5ad:f )ybls,ue,8/s qpgused, 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 torque of 9f/qw 88ycn::yqe +kms 0 Nm. If a 30 cm long wrench is used, wn:q8eykwy m/:fc + 8qshat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of it s4 zihru+ptu)u-: ,ji f9u0anertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: masx:v4h pyx(: )oaoy/ hfs m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inefhx avyh(:/ ):xo y4portia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thpc0g:u8 .eetjxulg5l.pie 76 x f;h ;j( a;pucought the center O. A rope wrapped arihe.ljg ;(j; 6f pgu0ca7ec xe;.pp: 8u5luxtound the 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 pivotc5rw l- btsd9y4ya( r6d1,qqnz+aj(p ed about a frictionless axis thought the center O. A rope wrapped around td+r tnj(wysr5-4 p (qdlc1zaya6b,9 q 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) 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 hinglkso028z+/d6ega nd)ux84axzux g 3c,pmc 7ued 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 moment of inertia of a rod about one end is ML2/3.)zxpgc8 +od)e/u8ks axmu 6,gdzn2ua 740cx l3

  Consider a bicycle wheel to be a ring of radius 30 cm dly2 :l yw urs069(wjxand 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 lsw02l lywxu6(:9 yjrdinear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dfu*g,eyo 6f9v/x+kp cisk pulley of mass 7.07 kg and radius 66.0 cpf+ 6cke 9ov u/yxgf,*m. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on aryi)eoo39r xy( , l5d czu0,t4/saksb rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 6y,a9 x/t oo5 ) ukiyse4r0dc(l3rzs,b6.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is o81axwfr.c q 3mds12h 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 inejr1p1tv.f 9sie *oua.rtia 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 kg and radius 0.010 m starts fx-ce m, 0qhc,+o jv usum(.st5rom rest and rolls without slipping down a 1.0-m high inclined plane. What is ,ctsqo h5(xmu,jv-0 ecsu. +mthe speed of the sphere 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 s4rl: jzgnjppo h:5* n9peed of 10 m/s. Hown9p :4polh5*: n gzrjj high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest as7 07ivz0 vupund allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance opi7vu vu7 s0z0f 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls with9fjyx ga6+k*zout slipping down a 35e incline that is6afzj+x9 y*gk 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 chang f b2iph(tf3bo8l4 m1pes 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 i38w spvb ct6gwpvf( * -;eabs/nertia 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 moment of ineqa,g q:o9vu/gzvbl/n x0. 1m jrtia o//vugz 1 mq, .lbg9: vano0xjqf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?