Angular displacement is usually express in units of6*lmko gy0d i8

  Angular velocity is expresse7i+kbbplin ,dt0s,t6xf) 5s)fo:a b fd in units of

  Angular acceleration issk iq,;(tjkzfw . ;wq+ expressed in units of

  A boy and a girl are riding on a merry-go-j1k79*q okm* i lyx:bu;ll 7wlround 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 greaterul7k*l ; wb:o* imj7 1lqkx9yl angular displacement?

  A boy and a girl are rid4)ha azp5f y en;-7vqz 0ckely b,oh6+ing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, andazazke;,y7v0elb pqn+f6yh-5 )h oc4 the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a mersspz s-8i.zhpzuiw5 9epyi7 :v7 p-h-ry-go-round which is turning at a constant rate. The boy h- psz7:pzspyie-u i h8sw -59pzi7v.is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a meri2k1b dh g4hq7hw/ rz2ry-go-round which is turning at a constant rate. The boy is near the outer edge, while the giwkh/dz 41b2r2 hi g7qhrl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turningl- -s7 fzg(hvas c5y3e at a constant rate. Th -lc( ssg5v-fh az37eye boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating.nhegl0 umoyid+4q 76 h:x+iy/ Which of the following is an accurate smh :g+6yi+u0 /dq yxleh 4oin7tatement?

  Rolling without slippin/5ufgye n;ch *g depends on

  Two equal forces are applied to a door. The first force is applie1; vcaf88 eax x*/qfaid at the midpoint of the door; aa* xxc8vaqff8;e 1/ithe 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 ,25c c20p*m udp uonv99s uswtkpnk. 5a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 3n5dwk u c9unus2s2k0omv9c5 *tp, p.p0e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pez6o,y 0q5.zi5)s )fls4npi v xh+bdj qrpendicular to the door. The first force is twice as large as thh xv)0y +sjlp) 6s nqbz,5if4zo.iqd5e 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 objece86b02jq(+vq +n0 ujupp;wijjew rv(t's resistance to changes in rotationerp2 j 0e;8+qb(u6pivqvju +0wj w( jn?

  Consider two uniform solid sphere lqmkctz6:*p- s where both have the same diameter, but one has twice the mass of the other. The ratio of thekl * m:qtz6pc- larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radi6z6wg /er xn -v*9ci ditsr2,dus of the other. The ratio of the larger sphere's moment of inertia to that of th6dgne/ vrrx* tw92cdzs ,i-i6e smaller sphere is

  Consider two uniform solid spheres w2g:)1 audvx;fhb ai:+ k;ncb ihere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment g +iavu2n;abif b ; )ckh::xd1of inertia is

  A uniform solid sphere hmt8r ) ,d(fyyv(gp.dqn/ z 1raas mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia aboutg.zd ),ry(m1nqtayd rfp v/8( a central axis?

  If a constant net torque is applied to an object, that object) s1g*zr bdewfw(ez3o; ) 4e w9gxw1e)jiy( vt will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 ;evjwif9f cur2g5sc;jf2 )1 u MR2. If this cylinder rolls without slipping, the ratio of its rotat12uf2fj;fisjw 9g r c v;c5e)uional kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one2llw -tqatz7k.3(b st wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatiotbl.(l tqs3a7- wk2tz nal 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 masq (sip8l)u)xa s M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere a)lu sp i8a(q)xt the bottom of the incline depends on

  Suppose a solid sphere of mass M and rau 4t.l la/y bdo/1-phhdius R rolls without slipping down an inclined p/1h-ou/pt4 ybd.h lal lane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systeoa :tgdxcgb 6*9xi( 3mm of particles changes when a net external force acts on the system." This statx*dggb6 ci:mto3(x 9aement is

  In what circumstancesibh5)v urel)x , za*w: can the angular velocity of system of particles change without any change in the system's angh,uw rx:e ) *b5al)izvular momentum?

  The Earth orbits the Sunzlp721rcaz: +c0b;jwhrhof ; in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth';; 1fh c+blj02zprw:czha 7ors angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves close o. +jicqe0(zp ;h/larb;nziz/e7f6it 5.j tr to the Sun, then which of the following best des ic+6;// jn0q 5ezz.iaro7h.tfel ;(zb tp jricribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fam-48 xq -omn+8rvia, wai: athst spin) by pulling in his outstretched armsi- :o-twq4aa+mn,8m8va xhir close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pi uhy--4z c6ppnrouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic eny n-c6hp p4uz-ergy about the axis of rotation?

  An ice skater performs a pirouette (a fastrms;1srtx 3q(nann7 3 spin) by pulling in his outstretched arms close to his body. What happens tnqn;a73rs mr (sn1xt3o his moment of inertia about the axis of rotation?

State the law of conservation of angu +7p9 kd5eqv5qckr 9 twurel87lar momentum.

  What arc length does the Earth travel in a three month period in its nearly2(m5b lax dn*k (jhon) circular orbit about the jml)d(noa kx2n(h5 *bSun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length q kd+db7tzx ey8/il hg(l27j(cx: ta .of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 seconds?x8:h (jzy a7i2/g tke.( lc +bdqxl7dt

  How many rad/s is 25 revolutions per minute equivalent to:72gfqzqwt b*i ogv 3:?

  A bicycle wheel rotates uniformly through 2.0 revolu n6:(rq+1ijtv0jfflc tions in 4.0 s. What is the frequency of tt: qnc6r j0(1+vljffihe wheel's rotation?

  A pulsar (a rotating neutron star4s f(s ;oumtzt+;vu 8k) emits pulses at a frequency of 0.40 kHz. The period ovo;zs; (mk4ust8tu f+f its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn ide q0umbe i-wnihd0d c:;w0*6n 0.20 bde;u*0 d:mi0i6-wc q eh0 wnds?

  A wheel of diameter 26 cm turns at 1500 r v nn3hy)-shky/ (z0zb gs:ar/pm. How far will a point on the outer rim move in 2.1 sns(0kv:/h - bz g3/hya y)snzr?

  A bicycle wheel rotat) c6 jexqyw ; 0a+wnk9zamg4u70a2ijres uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the +m40qcuw7y jn; kj2awi )r a0x6a9zgewheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What2*isqv-xi jy.c bif v1mbo2ev:6 r67y is the linear speed of a poiebmfvbix:ic jyvv 7y21*-s .2q6 or6int 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of u(90kwnq; mgjte 56cn6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate 5ejg6(9k 0w mct;u qnnfor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating(h*, /rqgq ydu with a constant angular speed of 2.0 rad/s. What is the linear suy ,h*qrdg /q(peed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Ifrv x72a7ufhj + the motor rotates at the rate of 20 rev/s, what is the approximate fa7xhr v 72u+jlinear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 08flvu urb:t fu.l-v/rad/s. What uuv/v-0f .tb:f8 rul lis the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a pointeu/ash5r o4l2g qt0r z;0 on3c on the perimeter of a bicycle wheel of diameter 70.0 cm whe4 0 octaoz3 qe/ 0l2rnruh;sg5n the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulxji-kny6i7 ;t ar, rotating space station (r = 1000 m) rotate to produce yn; 7-kix6t jian artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radshvr; (1. d:eris 7ydmius 50 m with a speed of 20 m/s. The maximum7 s hedm. srrv:yid(1; centripetal 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 radius 50 m ww fye5:n,z.j3hb svf3ith a speed of 20 m/s. The maximum centripetal fohze ,fn35jfbs .yw:3 vrce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached t at)-. 3 y:dhu6-iu63hzbeh xnq/ 5zlhgruzo*o the end of a 0.750-m string, is whirled around in a smooth level table. If 6bz z*qdrhhh5 t6z:oyhl-a u/ ).eni 3-xg3uuthe 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 kg and radius 9.0 cm rolls without slipping 10 m dowshrk *4b od7;mn a lane at 4.3 m/;ms r4*kod bh7s.
(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 rqa, c9ahfs oz15u3o6 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 constd0g.au1ynhgi eo +nm6 1k6ll.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 4ckznb/c2 jfu*(l) jlqhn5i;tire rotate after starting from rest and accelerating at a consq(zb4c)ju;5lfi* h/2lcjn n ktant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has x *vx 9)umi4luan 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 con9 9*bz/sqczas s0 h2udstant angular accelerationqzz09bu2dh /ss c*sa9 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 turning cy q hlt35(yf4(lvip* through 2.0 revolutions. What is the average angular acceleration of the whehy 3yf vqti5(*l4pc(lel?

  A wheel of diameter of 68.0 cm slows down uniformly fjj7xh )x3kfuk0u e:0qn +lws; rom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel)ewk u07jxk :0s;+fln j3qxhu rotates in coming to rest?

  A wheel of diameter of 6:ocm;46:vqu;nzv xh c8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angulaomx;6:;4nh czc vvq u:r acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40/c rpgf (e;:dg m/s to rest over a distance of 115 m. How long does it take for the wheel to c d p:(;/gerfgcome to the stop?

  A centrifuge in a medical laboratory rotates .cjhlpei)2g : at a rotational speed of 3600 rev/min. Whi l:gp )h2.ecjen 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 whe aqd5 9;wyxsz-1a f;lykr ac52el 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 perpendicu asrl a5q -dyx91;f;azwkc2y5lar to the wrench?

  The bolts on a car wheel require tightening to rewzj) k00g(qa torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required wheje(q) 00gzwrk n the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment bq ym7n**b9f i,q r7xxof 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 f)bor7 .fmujp:h2 xl +bollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the p7:jb )lb +x.2umhofr moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axisah e 5*pi)nsj cts8 6-*oezyc98 taz4u thought the center O. A rope wrapped aroe jn4csat-8 ze zo *8sih c)*96uyt5paund 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless 8+wlfmdum0r )2,ryqp 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 y0 l+,q mudpr8mfrw2) 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 hinged at one ed.rz4a5*ese; 6-uxurmxs: j3x(k k yend. The rod is initially held in the horizontal position, and then released as the free end a x5 .4e*s; dxx3uuyjseer k-k mrz6(: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 b (gtjtp f7pwcqd u(ps .x*25r)rz(s: we 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 f*(d :2)5.pp(ruwgpj (7 zfw x rtsctqsor 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 a 9p rkkyfnzp/98i5m / hi3t;jkround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angulark8/kj/rfp m zypk3t ;h5i n9i9 acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk punf/xikr rciqx(*1o *;1i7g.dmtvqc. lley of mass 7.07 kg and radius 66.0 cm. What is 1fk ino.*xm/rq1v(rt iic *c.x;qgd7 the acceleration of the mass?

  A rotating flywheel can be used to store en ga8u20emiwv +ergy. If 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 inertia ofe 572xx uosg2 5upz-zd $5.00 \; kgm^{2}$ 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 1 1u7 zbh i;8ou)(pzlw7yjym(go9hew 5algx*and rolls without slipping down a 1.0-m high incl 79y7 o8uhzi1 )1ep ;mj(al*ygw (oblzgxhuw5ined 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 a speed of 10 mhn(7sg z0tj(z/s. How high up an inhsn((tzz70j gclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is relevd/xn0c*w,h1 k,kc otased from rest and allowed to roll down an inclined plane. How fast 0 wvk*,c1d/nxk h,cotis it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wwc*ku i2*s/d 4 -mnvfvithout slipping down a 35e incline that is 7.0 m long. As-2u4 ndv wks*m*fcv/isume 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; nlh+(,ip 3.sw.r kzskenf0x changes 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 :w 9cjq+z 0 nhhhek6 i(cj*b3kmoment 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 wgjcsga nn*,7:b0vx*o cj1g 7 extended has a moment of inertia 1 0 7bogn7w,c*ajcg *sxngjv :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?