Angular displacement ioa77a d2 ppd5vm:cr x7s usually express in units of

  Angular velocity is expressed in unih* qxpqrk5b35e kc;jb-re 3y9ts of

  Angular acceleration a+b ;lfh4l.ejis expressed in units of

  A boy and a girl are kg*0gm/70 h8p;lctk6 : rltaeyqux6eriding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is :t;/axym60e7l 0k 8 g teg6qhul*ck rpcloser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant 8i)q pq(nm 0ya x-uyp;rate. The boy is near the outer edge, and the girl is closer to the center. Who hau ipy-a;n)qm p8( qy0xs the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a zmui7r. n i(vzk9x4r r9.io7vconstant rate. The boy is near the outer edge, and t v7zn97imkri9z(. xov.iru4 r he girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which gay idz85.li z;: x(07 guluziis turning at a constant rate. The boy is near the outei 75u z:g0di8(.uaxlzgi lyz;r edge, 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 turni2 +ef:/hjsonhng at a constant rate. Th: nhfso2e/jh+e 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. Which of the follown* :rv85 cj psnu,vcl:ing is an accurate s8 v,p*lrnv :: jusn5cctatement?

  Rolling without slippi:uq jtjwssh mr u7-+36ng depends on

  Two equal forces are applied to a aqo4o p*ad:y 8lnvzx9+yw5(r door. The first 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. Which fo*ov+ry894o l ap y(xa5zqwdn:rce exerts the greater torque?

  Two equal forces are applied to a door at the d mannx237l*0nui+x +6dzoevh)wna3 ooorknob. The first force is applied pe) x+and h a2lxo* nounew6n03mvz3i7+rpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pe ctq.;pgsba*he4 u56olr f.u+rpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque g bof5.c6t4ehpuq + lu.asr*; of the second is

  What is the quantity used to measure an object's resistance to changes in rotoy xsm ne*1; zgic:-*iation?m*zci- yn*;1o:g xe si

  Consider two uniform solid spheres where both have the same dia a e+p+lrrj73emeter, but one has twice the mass of the other. The ratio of the e7raj+r+le3 plarger 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 radi1x0:w: wmt k;p*oim,dmpa8 m *bj wzs8us of the other. The ratio of the larger sphere's moment of inert p :bw0mwk:i8dpsa;,mtj8* m*om1xzwia to that of the smaller sphere is

  Consider two uniform solid spheres whmyod.z4cx 4ax 94:fe rv )rmu7ere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to th4cxy. omd7 fmruze 49)4 :ravxat of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. dba/pl* w qhs;g22 46nry v8umIf these are increased to 2M and 3R, what happens to the sphere's moment of in h2sp/dry vwa4gq;2unlbm 8* 6ertia about a central axis?

  If a constant net torque is applied to an object, that object w qp* feh:; 9it2cbe2(-pzs koiill

  The moment of inertia of a solid cylinder about ivn62 (c pvbs7c30sgo8sp 0y yb;hyt2 zts axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinep( vo gysyh076ct2 np0ybs3; 8bs2vc ztic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a 62z :ypnhhv)j mass of 10 kg and a radiusjhz y62v) pn:h 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.

  Suppose a solid sphere of mass M and radius R rolls without slipadydav4)dk0c ,2cp (.udhcg /ping down an inclined plane starting from rest. )0cakd ga4 y.dc/,2chdvpu ( dThe linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius 2c- +dl( 5rf)p4hbx,we.hqtbv mh6 nfR rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclinb e+)h5 d(wh6pcb -,tfv .x4m2nhrfqle depends on

  "The total angular momentum of a system of partq(wac*h+p-y,mq lk pzz6k)0bunr ; 4 fi.nn9qicles changes when a net external force acts on the system." This state4w(;ur-*k+9faz0 bihqpqz k), yln6c. nmpnqment is

  In what circumstances can the angular velocity of system o b-+h r7i;0/rs8jzcol t 9h;jwnmddq7f particles change without any change in the system;tz-0or br7 sj dhmi 8h/j+n9lq ;dw7c's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction ny+yyq.qde7 9 which may be present. What happens ny e+q.79qdyyover time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. +grcs m77k.m n As the Earth moves close to the Sun, then whic msn.7+rkmcg 7h of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (*(f(ig hya 5aea fast spin) by pulling in his outstretched a( *iaga eyf(h5rms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast ,w1 npjqvyi 50f h,o6bspin) by pulling in his outstretched arms close to,1 jq nfyoh,56ivw0bp his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outst.wl0vp7qe,/1kdi d5qwgj 2 rsretched arms close to his body. What happens to his moment of inertia about theglq.vdsr dkwjwep i75/02, 1q axis of rotation?

State the law of conservation of angula9 ssf-pbc7ium ):*ik oi.c.8zlpbjy ,r momentum.

  What arc length does the Earth travel in a three month period ilyc qk2btp0 k)s v5 q+ei0,c-on its nearly circular orbit aob ykc,q)ekis t0 0+cq-5l2pvbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tiz4l1 /m1ij upap of the second hand sweep through in 3 minutes and 45 secj1mz4l /piau1 onds?

  How many rad/s is 25 revolutions per minute eq8(woj8tg 5k xul4 q1kzuivalent to?

  A bicycle wheel rotates uniformly thofu*z-)eqp v ji9np)9 rough 2.0 revolutions in 4.0 s. What is the frequency of the*nj-ze9)ivfqpp u9o ) wheel's rotation?

  A pulsar (a rotating ;t:ghr9a gl+v neutron star) emits pulses at a frequency of 0.40 kHz. The period of itsgth g;v9:l +ra rotation is

  A phonograph record rotates at 45 rpm. Through whbj 0-1hwqpzc prwfw+v5z9rp sx :,0y*at angle does it turn in 0.20 s?j0wz 5 w:0sp zrxph,c+ybrp1v-wf*q 9

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pkn u5(zy( gg ia,)mskj4c8 ,w-brcg 0ooint on the outer rim move in 2.1 s?gms8r5n jkkcoc -,wzbg0 a ug(i)(4y,

  A bicycle wheel rotao8d j 5 bl/zsej0afl0ah rh 9r:pkshf8.+ri+ 3tes uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wheasp8l0/5l.0 dar8 3j+oh9r e:kfrz h +bfhji sel?

  A bicycle wheel rotates uniformly through 2.0 r: )e.zhr 2sal*u jda0revolutions in 4.0 s. What is the linear speed of a poinlr0.azedh) :us ar2j* t 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a dikn ool7/bd i(6stance of 6.8 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 for the cable car to manob/l 76id k(oke the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rl ,sr:tv4 hnk/y)g/xaad/s. What is the linear speed of a point on the whrtx, 4shk gn):// valyeel's rim?

  The cutting cord on a gas-powered weed cutter is 0ezs x p-8 3.f;wbgs 24zfg2lsn.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the appn;pz3szxgg-28 w f l .4ssfeb2roximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a cofjdu5ce(f5gsb c,+4 ga/1 ouqnstant angular speed of 2.0 rad/s. Wha1 5g4(s ,q c gju/cofeb+fd5uat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle whz 1.bz+wt-qmdm- jct eq e-*i8eel of diameter 70.0 cm when the bike is moving 8.00 m/scti ze-.w+m- debt*qjm8 1z-q?

  How many revolutions per minute (rpm) must a circular, rotating space station (rd/:e,gd2ayd 5zq0 wyp = 1000 m) rotate to p2:d,0d egdzy awq5y/produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating(73m4w+4h 2of uzlt jz2lf wb2*hbysv a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal forcs bzzuwowj*vhl4 m43tb2h7yl2 +(ff2 e (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 p5:obf3+a h.yr bip(;h vhsu:radius 50 m with a speed of 20 m/s. T5 y 3ao:u: f+h;isbpb r(.hpvhhe 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 sz 5*d c+m(twearound in a smooth level table. If the maximum tension that the string can withstand is 250 N, c(tms5ezd*w +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 slivpy7,c:l/;njx7hs f qpping 10 m down a lane at 4s;pcyxvl /nfj qh, 7:7.3 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 cond5(8fzq)nz )us u d-f 5a-m my)(ecscnstant 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 constant angular kfz9hg)rc 0z /0dsp5p 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 au6lll5ul4 td+ q)he l.jtomobile tire rotate after starting from rest and accel6.l4)lull + 5hldqej terating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerationw:ddjcgmy ob+9 )qv*j)(nel3 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 afpmd* 8plkn.(7g3w ybngular acceleration ofb7p 3 dlfp*n(g mk.y8w $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest annxpsjnev0xj ,- 31hf jr1(8eyd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the n-xeh308 j(n 1ysperj , fjxv1wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 w vy+/hrcsfec94 ),vn0mul;lm/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comi 9 n+vl,fc/4)l h vsyc;mr0wueng to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to /h i:6 mlqzfd.rest over a dis .m qil/:6zfhdtance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fro .ahlch h4sds- hh gia+e9h.bo7(sz/ )m 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to e.hhs(7 +ss9bd4ahhh) . zgla o-/hicthe stop?

  A centrifuge in a medical laboratory rotates at 1p-i fx8 9wcikh08ah9: l+t .zidcsepa rotational speed of 3600 rev/min. When switched off, it rotates 50.0 tim:8 idhx-ikzaf sl.9+1hpc0 8wtecip9 es 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 tighte3ljzbt cwd. p .efw+7;5qze .jning to a torque of 90 Nm. If a 30 cm long 7b z.pwj 5 ftq .wjc+z;3le.dewrench is used, 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 906 +0d; gubczlprxi5p4 lii u01 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcgl 5xd c;i 4ui61upp+zrl00bie applied at $53^{\circ}$ to the wrench?

  A wheel with moment of /, bbdsy+ rcgb9pql e3fjg. (.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: p xcs(kd ywdlb6.q7 -/ mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x 6bq(dw7 s/xlcy -kd.p = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis though 47 kbq/qae4rd0 tl(tpt the center O. A rope w4 tpb0l tk74d qeqa(/rrapped 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivot-1ojl eh m/n zb6j25w7vf7p tsed about a frictionless 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 force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts fhteob217j z jw5n f6-m /p7svlrom rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held d catp ;ei8l(gyw+ c69in the horizontal position, and then released as the free end is allowed to fall. What is the angular accgw9 86 d+claie(ctp;yeleration 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. Nt9k(e(fr 2h/uv (3mjh a h+ vowxdm.*ueglect the mass of the axle and sprocket. If a force of 20 N is applied tangentuwomkx2 jv+9d3u* ( a(tem.hvf/ ( rhhially 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 pulley of masho*, cwdf 21w+2h-7 cvjmkgfz s 7.07 kg and radius 66.0 cm. What is th-cfcj+moww 1hz7kf2d2,* gv he angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictioiy3ve8b -xw)sl ;k1n6jcd t.h nless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleb6.yn xsdlkv-c 1 iwh)t3;8 jeration of the mass?

  A rotating flywheel can be used to store energy. If it is requir2fnkw tsu3 p*1ed 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 of nvn7j re8x8 c)$5.00 \; kgm^{2}$ 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 and rolls keelu 6yl.i 80v7 uzi2ldh02l without slipping down a 1.0-m high inclined plane. 8i .2khi70zeu uldv20e 6llyl 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 w3ky rye ohq. q 9mrr60iyb.+/yith a speed of 10 m/s. How high up an inclined plane can it climb before coming to rest?oyyqmy0 9+bi 6er.qr.k 3rh/y

  A hoop of radius 0.50 m and a mass)b nh m.9ytsp+o-it:+k kxga; of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after drop.o-:ntx )hatmbp 9+k+s; kigyping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without d9 mtpyc1 x(2kn.yi8r slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Thecyyxtk1 9.8(ri2dmn p 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 chkut e4 yu8jcv0dp.h ,1anges 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 jwglc vdip(j tk460 +70nw yo2moment 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 ex3b. awp6 ehryi:u8 y1vtended has a moment of inertivh: 3 ie puywr6a8.by1a 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?