Angular displacement is usuadamdv awmy6e8 73(q,v-j4u.m) hjhmr lly express in units of

  Angular velocity is expressed in ;i-a*n hk.4uibobcj lh 5vh.7units of

  Angular acceleration is expressed in unitvmyuaj na90aq0ov (/me2 8 rn;s of

  A boy and a girl are riding on dm 1+qaan2s- jh6 q2idk*pv/a a merry-go-round which is turning at a constant rate. The sd/-hqv+kdn1mq aa 2p26i j*aboy is near the outer 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 which is(p /j-ani*kpk turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center.-(apkp/n*j ki Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a f 2x4mg8;chyt constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear s;84ftmcgh 2 xypeed?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratelj uu1s tvs(+q4 .g/lx. The boy is near the outer ed+ vjx4s . qlu1/tu(slgge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at -1 b qq mkr0y8iz,dmf*a constant rate. The boy is near the outer edge, while the girl is closer to the center. miz*mq, yf0-rkqd 81b Who has the greater tangential acceleration?

  Consider a rigid body that is rotating.:g lhblmgt/lhg+2l/c 1)c n0:5 vum ed Which of the following is an accurate sta:gvg :e 02ctmllb+lgmd1c/h hlu/5n)tement?

  Rolling without slipping depepaqer7a ;shz3mr :w2dv+u9 * mx):hqxnds on

  Two equal forces are applied to a doo x 3t i16bwek2mhn29vcr. The first force is applied at the midpoint of the door; the second force is applie239w6 in hbtk21xecmv d 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 doorknobp-o53ef) mpumil*es 7. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of th7ui sp -e3)m5 peo*lfme door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiculx3u,1ix)zmuoq)13d sdr x+z jar to the door. The first force r1x)mdd j3x3,sqzzi uu)1x + ois twice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's 6l6 bprzb+w9r l3s/:gc y; jqoresistance to changes in rotatio6gcob / rrlw;s:6pq3j9+bzl yn?

  Consider two uniform solid spheres where both have the same diamet76 yq:mf2b0xq4g ihhser, but one has twice the mhq7 sh :f6b024 gyqmxiass of the other. 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, but one haej ms84 9x8tnqs twice the radius of thq 8n49xem8jst e other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twin8oj3f1 bsp;hn 4b5iiukaz4;ce the diametb3p84bzan 5sun;jki4 ohf;i 1er of the other. The ratio of 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 argpgc( v db:;. pnvhris mmi81-k92cf1e increased to 2M and 3k 1 i c29csmm8(frgh1: ;bdp nigvv.p-R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, i0idwt wzo.e: /h0yc5; 3k c+8wisointhat object will

  The moment of inertia of a solid cylinder about its axi4stcy6qsdm(gi(o 1vm9;8 zx tdns7wz1 ) sn-is 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, on,/ -q ugofkt+me wheel of which has a mass of 10 kg and a radius of 30 cm+kg -uq,/fto m. 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.

  Suppose a solid sphere of mass M and rad1t2lfl )sf9 pyl lx:f/ius R rolls without slipping down an incp2l1 llt/9f flf: ysx)lined 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 withhjn-0)mi ya2qqx i *r.out slipping down an inclined plane starting fromy-a*.q nhrx2i q mj)i0 rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a :rh.+y;dt 9dtw 6z hfxsystem of particles changes when a net externalxd6t:d .h+ t;hz f9wyr force acts on the system." This statement is

  In what circumstances can the angular velocity of system of( vqg-xwcq8+dg6lwf 89+ 4ad 4yygxps particles change without a -axyg 8g9ylc p8 4+gdxdws(qw vqf46+ny change in the system's angular momentum?

  The Earth orbits the S xd rlboaw07+r 5+q:coun in an elliptical orbit. Ignore any friction which may be present. What happens over time to +rw +aq5 xbcl:r07doo the Earth's angular momentum about the Sun?

  The Earth moves about the fh*k 89mc b:xlmf86np Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following bk86p fm m 8:ncblx*9hfest describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by hfzzgv +0lz/+my6+vppulling in his outstretched arms close to his body. What happens to his hfz0gvzzlv +m + 6+py/angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) bb(8wl2rm*w gky pulling in his outstretched arms closem ( blr8*ww2kg to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin 4s6 s3q7er t2rvzl,p hbu..ufg in his outstretched arms close .7 z,rq s2ust4 u l6vf.h3brpeto his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mivhtc )umu3ueg 0,lj71s7fj f gaa*7/aix +x7omentum.

  What arc length does the Earth travel in a three m*51 iasrlu 4j1g z;vo mp6.nhuonth period in its nearly circular orbit about the Sun with a zhg s l6n mur i;.a*j1u4v51poradius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. 6pwg-y+uvaz7c hm ) 8bWhat distance does the tip of the second hand sweep thr7bz-h gu )y wcp8+a6mvough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per m k t6n3cx(bnoizb3 mpeef0ttn;w54/9inute equivalent to?

  A bicycle wheel rotates mgexjz lmo :08 /cm(;ynsm 3v7uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatiomjg 8x/;em mz3o sv7n0(c: lmyn?

  A pulsar (a rotating neutron star) +b 9aza;9bdb+ xpn.eu emits pulses at a frequency of 0.40 kHz. The period 9a+p.edab ;9u+bnxzbof its rotation is

  A phonograph record rotates at 45 rpm. Throzo6r k4x9p1ogvwsz9 7ugh what angle does it turn in 0.20 s799r64 gpow ozs kz1xv?

  A wheel of diameter 26 cm turns at 1500 rpm. -qbxg -kthxzhr6/5l) f (skb/ How far will a point on the outer rim move in 2.1 s qk5 bfsgz bx6/r/khl--x(h)t?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. q1wv10ba0n r hw/d2boisb . tcy-bv97 What is the average anguby bb bvtso12 h d /9.iv0r-wcw7na1q0lar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.s( p -z,6 lb2jveq:zhdu6*wmr0 s. What is the linear speed of a point 0.10 m from the ce62lhsu mv,q6bjz wd: pz- re(*nter of the wheel?

  A cable car at a ski resort carries skiers 3ue)ckj*tkve lp;t5 6 a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming e vt6)cj k*3kltpe5;u 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 roeq xgp n2(v,i(tating with a constant angular speed of 2.0 rad/s. What is the linear spee2 px(,i qgv(end of a point on the wheel's rim?

  The cutting cord on a gas- lnsg) (r ,afira j6(.oml*-hgpowered weed cutter is 0.16 m in length. If the motor ro-m6grn sghrai)lf jloa,( *.(tates 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 dx +r/spp k3yo/sf.6cq s3:rvis rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheelss+rp36:o v pqxr3d/c f/y sk.'s rim?

  What is the centripetal acceleration of a point on the perimetbzt -eci3n*5d j hmo46er of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00eh4j3 b*-onzi 5t6m dc m/s?

  How many revolutions per m feh utn f+xt4v8t,v;8inute (rpm) must a circular, rotating space station (r = 1000 m) rotate t8;f+nvttetv,hx4 8f u o produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a 2ozl *odf)+yf speed of 20 m/s. The maximum centripetal force (provided by static y+fdozl*of)2 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 radius 50 m with a s0p3p6iu xh3q +ip lhu-ejk(1 *kd. iktpeed of 20 m/s. The maximum centripetal forchdk3.ux0 i 1p k 6i(eih*p kp3t+lujq-e (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 lnn;s-h0;v ej: 3d6a:bojhql)nl9j wa 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 maxionj6;nj -9wv3 0d):llenh: qajhsl ;b mum 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 cm rolls without slipping 10ma xwyy27m,yu:1 iqx4 m down a lane ata4 y qm7x12xiy:ywum, 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 ofa+. :j,de6u 2 ncxakfc $4.5 rad/s^2$. 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 consti dld61o mo2loi6-ua* ant 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 a-6 hvxa- ls0 yq.4hh)a)ugwhkfter starting from r6l v-.s4x -ahhukhh g0wqy))a est and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and har3-c;hpf29,owdk r1a) *cy n sdllwp8s 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 witee(+-j w 0n9qvg.w* cgdx o)q grg,2qgh a constant angular acceleration x* 2 e wggg0,-cdg) qrgnojvw9.+ eqq(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 6.0 rad/s while tu9fo m8;r-vwv/ w.fuporning through 2.0 revolutions. What is the average angular acceler ;f.v o/ vompw-89fuwration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to resk.n ewv0h1 rd6v 3bl3tt over a distance of 115 m. What is the total number of revol 0kr1 6b.vwetlhv n3d3utions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/ mqfi f2aj2v)-s to rest over a dis jq)2am vif2-ftance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dow 9ybrjc+ eb4*krn)j -un uniformly from 8.40 m/s to rest over a distance of 115 m. How long doe -uj c+9k)rjnyr*b4 bes it take for the wheel to come to the stop?

  A centrifuge in a medical la a9r2bw ;ugp(d.cyh1r -pjcv2boratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before -;9bdjrp2 c (h p2c.1varg uywcoming 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 t6o dx if9w6p4 -4vkfzoo a torque of 90 Nm. If a 30 cm long wrench is used, what is - 6vpk4fd94ow xzoif6 the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening b jp 9m,0 i2v ioi0iaf5 f*lbh;1jvtdwh7*uf1to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requi1ihl jf hb dti,9awijuv25;i0mb7*v*o1fp 0fred when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofkv7 (c 4-en: b 6wyodae y430xf/np6nxjeqf/h 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 follows: mass m is at t (1q llal7 34g.vnpipjhe origin, mass 2m is at x = a, and, (a7.g4ip llq31lpvnjmass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a49*(vqux . d(vzhujiu frictionless axis thought the center O. A rope wrapped around the(u. quvvu*d49hxzj i( 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 pivotm; kd9i( 0-,nwup 7f bg)osnried about a frictionless axis thought the center O. A rope wrapped around thib-7ifps) o;gr9m, knn0u w d(e 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 hinged at one end. The rod is initially held/c6; zq+ -kuosual jk1 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 icq- lz a;uouj k1+/ks6nertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a r8vsmekgyb *hx2s3z4 /ow j( b,ing 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 tangentiallyem83 sv o bxh4*z(/b,gw2jysk 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 wr mjr*. j;e2nwfapped around a frictionless disk pulley of mass jfem;rjn2w* .7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fri,mgjad kn) -n+. 0ep(3h1idkyr jeib;ctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratihk1 );pnr-0k g+dyj,dmb.ea j3 (ine ion of the mass?

  A rotating flywheel can be used to store energy. If it is required ton8-t9w yygcb4 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 in8l(3zlfqc zf7,c vxl:pqby pvif7+ :4ertia 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 from rest 73poe; x efua/lr(h;qand rolls without slipping down a hlpare7uo(fx; ;q 3e/1.0-m high inclined plane. What is the 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 ajcq bf5s8tg;4h;tz o5 speed of 10 m/s. How high up an inclined plane can ;cz;s hf tbqg4tj 5o85it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is ;knudes;-/ 6ugvjx- vreleased from rest and allowed to roll down an inclined plane. How fast is i6;uvd/ ;j -vukgnx es-t moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg ands. fx:1g xshx. radius 15 cm rolls without slipping down a 35e1s.g hx:f x.xs incline that 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 changes 9ef6y;jg qgcdn+h+ /wz7w 7 bcby $20 \; kgm^{2}/s$ 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 26;gm jr y hpvtn: rb-sfj9w86of $5.0 \; kgm^{2}$ 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 momezj3/) i ,ycy j /p-x2eufb 0gbrrkv-8ynt of inertia ofbrjf/p gib/v0-82e , y3)jxc-zkuy ry
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?