Angular displacement is usua+(n v;kiv )kdktt -cy3e5cs/u lly express in units of

  Angular velocity is expresses9(nu1 0as qprhpm40k d in units of

  Angular acceleration is expressed in unjy,oj g9qn 1/:xfyvl2hb+ .yot3pir, its of

  A boy and a girl are ra8s 5jrccz6:yz8cug9 fk7 t +yiding on a merry-go-round 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 greater angular displacementt rg u 6+ycz8k:sj5c98ca y7zf?

  A boy and a girl are riding on a merry-gwph,-d5 ik e.ho-round which is turning at a constant rate. The boy is near the outer edge, and th.hhwi e5,pk-d e girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merryj5dsihi7j l0po40p* q +kb *buiw1w0zqg+ y5n-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has t jng5 wi5bb00ppyq*h4* uq7j+li w+skioz1 d0he greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constan -l qo. foidfnt8wj /)tzp3/0gt rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater cen8 jnoftz)/.wfo0pi/ gld t -3qtripetal acceleration?

  A boy and a girl are riding a merry-go-r s pccx torhf2szrf,+;:un 0)+ound which is turning at a constant rate. The bo)c ;+:x2hprzrcn usft,fos+0 y 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 following ivsg1 hza2.gwh tlz,35*f i(bns an accurate statement, a.itz bz15nh*slw(hggv23 f ?

  Rolling without slippingo( mhs1x fkyib6376q a depends on

  Two equal forces are applied to a door. The first force is appzmvh rd42n2z ,lied at the midpoint of the door; the second force is applied at the doorknob. Both fdhm2 z ,zvrn24orces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at thez(9ivk - itorm3 ;xp0q doorknob. The first force is applied perpendicular tiz0 i- k (9tmrpq3;xovo 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, perpendicular to t6hq xy m*05uxlju/f*phe door. The first force is twice as65fuxh/0*jp ulyq * mx large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantityy/xbv2mz-j09ov-ef j, uo -ab db/b b. used to measure an object's resistance to changes in rotationz9- bdfb2oj0m/vxb-ev/o ba-.,yubj ?

  Consider two uniform solid spheres whey90o3 ojf mqgk9+*dfcre both have the same diameter, but one has twice k cgjd +m0o9of39yf*q the mass 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 onewj9+bjbh 7/m q has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere wm7j9h +jbb/q is

  Consider two uniform solid spheres where ong1+3 )5 u xpgg;cte xykzwf,em47 v2wwe has twice the mass and twice the diameter of the other. The ratio of the largg c;2 e)gw7wg 4pfkuwtz ex, vy13xm5+er moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphes)8 z l8mhbkq0re has mass M and radius R. If these are increased to 2M and 3R, what happens to)80kb qms h8lz the sphere's moment of inertia about a central axis?

  If a constant net to2ltuf tpb e 43nsma w.5i+-4aeo5wd2yrque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axi;vnh:5 oodqo 8cf/;a l nf94qzs is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translationaqoo: fcdlq;9 v/n45ah8fo ;znl kinetic energy is

  Consider a motorcycle of mass 150 kg, one w/-i 4igf7r jeyheel 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 47-irfi yj /egwheels 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 witho7vm30big5 hltg3nzj8f4g h mg,;u,co ut slipping down an inclined plane starting from rest. The linear velocity of the sphere at the botto4gc h5m,ungz80 i 3lbh3gjt7v, ; fgmom of the incline depends on

  Suppose a solid sphere of ma1alr + iaf4xnh.ko2j)2d nom x,t*+ugss M and radius R rolls without slipping down an inclined plane starting oj1) mxu it+hfn gnkx2o,r4 *ad2+ .lafrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of(ymdckn)n7k-+ xzz28 lx ap8c particles changes when a net external )k8- ka c2(p7znzy xdn+ lmx8cforce acts on the system." This statement is

  In what circumstances can t7a8 axa2hcbis v6,nz4 he angular velocity of system of particles change witho8xiv ,bzn a 2s4aah6c7ut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which map73cbf2t +9 9ebaevkty be present. What happens over time to the Earth's angular momentum about the Suna+pt be739vbf e9ckt2 ?

  The Earth moves abours(ue4 bf fmk3.ufz,d m2:y:yt the Sun in an elliptical orbit. As the Earth moves close to the Sudzusmu:y:r(3fkfye2,4 .bf m n, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling inmyws - 0 ;*8wagfmmi*t0fkt)b his outstretched arms close to his body. What happens to his angular momentum about the axwk 80g*)swfi-;tf ymmmta*0 bis of rotation?

  An ice skater performs a pirouette (a fast x +;00 i7xyf ;fl6 op24,-bwxdghvxoyac7pim spin) by pulling in his outstretched arms close to his bg mpfx yyp 7w6f4+cli2;bx o;7,d v0o-xxh0aiody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by.vm ze*j9+q of pulling in his outstretched arms close to his body. What happens to his moment of inertia about the*qm j.vfe +z9o axis of rotation?

State the law of conservation0, li t:jth(+s utm-ne of angular momentum.

  What arc length does the Earth travel i/t5p uvkpje g* g lq.-77orjr7n a three month period in its nearly circular orbit about j7gr*ekl7ut5g - 7r.jpqvo /pthe Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m.dzk/elv9qr 2u7g 7m3l What distance does the tip of the second hand sweep through in 7k73 d2 lerul vzgq/m93 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent toyhxvl:+hxrd.m4c - q1?

  A bicycle wheel rota4n/qtze 6u sr1rj84vk tes uniformly through 2.0 revolutions in 4.0 s. What is the frequency4t/k errquj vz481n6s of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a cnn5ayz:gnfl, kn fx /h(+-;os w)5r dfrequency of 0.40 kHz. The period , k/ +f;azxds5:(nf) nn5ghl- wyrnco of its rotation is

  A phonograph record rota l*udsgv+8.a ites at 45 rpm. Through what angle does it turn in 0.20 s8+ *.li vugsda?

  A wheel of diameter 26 1du9fetw dseq3uk.34 cm turns at 1500 rpm. How far will a point on the outer ridq1e4su3u. 3k ef9d twm move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.4k4dw fq1-c,zih h/yn (sva .u0 revolutions in 4.0 s. What is the average angular speed of the wheel 1u-aqni hkh,v/c swzy.4d(f4?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What .wfb+s,wvf :q;bc :7*lkf 4h9litad yis the linear speed of a point 0.10 m from the center of the wheel 9;fk t4df,s i7+q*vafc wyw.bl:lh:b?

  A cable car at a ski1m( iy38li s;dpnzar( resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley w r(8dpsa mii(;z1nyl 3ith 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 95p;ux6ko ef(o 5 qeq*wyz;ot is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the9z5* eqf(qxk;ooe;t uwpoy65 wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motorlc:2b+or bi )o rotates at the rate of 20 rev/s, what is the approximate linear speed of theob+:2r) o ilbc end of the cord?

  A wheel of radius 1.0 m is rotating with a ce6w m:agu(i2rxpe/m3 onstant angular speed of 2.0 rad/s. What is the centripetal x e/( uwema6p:mgr 3i2acceleration of a point on the wheel's rim?

  What is the centripetalw vc.xq*6/p wz acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movingcqvp /*z6wwx . 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stpxkifxl 3)6gr5ygnyu69v ;1( ya apg)ation (r = 1000 m) rotate to produce an artificial gra x yan6y9)pg( gp )f5u3al1v;6gki ryxvity of $9.80 \; m/s^2$?

  A car is negotiating a flat cirh jgdsnoj98/ njy :xm8 9w,eoy;xob+-cular curve of radius 50 m with a speed of 20 m/s. The maximum,bjjwx9o eod h8mn;8so-n:g/9yx+ jy 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 with -fj y2.,ao)ylw8q)s ktew n s/a speed of 20 m/s. The maximum ys)l- w ywst/fa)qeoj2 ,.8k ncentripetal 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 edc;)ofkunhc ( w7vi+j80obm+ nd of a 0.750-m string, is whirled around in a smooth level table. If the maximum tensionuob(m;vnfkw+hocd8 70 ji)c + 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 rad9qgqyn v9 )mi/ius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/sv9/9n) igymq q.
(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 constancx9*u8kz 6zq:hk- ip 1 3deqeut 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 acceld.urd6*gmyd /eration 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-mvo74f hw ht/yi,v8hu; radius automobile tire rotate after starting from rest and accelerating at a constant angular u/h,ht wyf v4;7i8vhoacceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accd904 9 gymeg8zy 6+lb42yp(qxfl ovfeqz0rr2eleration 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 amvr yy(ho98z1 constant angular acceleration h(y o1 zmyr8v9of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from p ;jmd*;d(h ferest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheefdd mje;*(ph;l?

  A wheel of diameter of 68.0 cm slows down uniformly fhzvmta. si 6+:rom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the w6v.atm +h zi:sheel rotates in coming to rest?

  A wheel of diameter of 6 1s,. j5g0qn j4a*lfkxzivc,h8.0 cm slows down uniformly from 8.40 m/s to rest over a distance x4izv5f,*ck l1qjja, ng s.h0of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4v8fh4 wj5r.yzcbv +v(t:x3z ao l2zv,0 m/s to rest over a distance ocv2 :z+jty 4bfz x58vlrz (wvah,o. v3f 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600xm69*nc :plwn rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before 9cp wxn:6nml* 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,r 0apn:2a 5 xjczciyt:9 oq.ne, rrp( 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 perpendicular(nz , qi,: .:tpeay0rp 2a9nojc5xrrc to the wrench?

  The bolts on a car wheel require tightening fvq8(ryd3j*v*n ,ed2q .d91x ygorbh to a torque of 90 Nm. If a 30 cm long wrench is usedgvf 9qrn1r.d*(ve yyjhdx2,3d 8 b*q o, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia rj tz72a ig;c5$3.00 \; kgm^{2}$ 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, mass 2m(2co4j+(w2 bc 4a j drdzpk(+t,ln eys9bbeu3 is at x = a, and, mass 3m is at x = 2a(ab e ot d4bl(2nw+ cj kz3jc9 du4(bsp2+,rey. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictv5 8oe :mbyh5x eo7eh-ionless 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. (See Fig. 8-1.) What is the e: h 5 oobee5mv-x7y8hangular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionw 10n/n8kdsv fhow0z )less 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 fr/ zh0)1okvnd s0f8nw wom rest?

  A 4.00-m long rod is hinged at one enx :6jo*6ab6nk-luox6 y,tgat d. 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 endjg a al6 x xuo:b6tt*kon6y,-6 is ML2/3.)

  Consider a bicycle wheel to be ai fi.c8kti 8hj6d23l k3+8uomg oort5 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 for 4.1 s, what linear speed doe to28k.ui8+ lt5md63orf8ioi3 hcgjks the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fric nr0we+4f 9a0p )w:nb3fb ztbgtionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angu3zr0w )few0p b:9fantbn4 gb +lar acceleration of the pulley?

  A 1.53-kg mass hangs 4c lw:1-btnq,ua4npk on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is thk q-at:pn4nuc,4lw1b e acceleration of the mass?

  A rotating flywheel can be used topn07sdu8ds b( store energy. 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 ih ip* .+x2g0cypub dr;2yucoh);l , pcnertia 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 re8 culul05g) vdst and rolls without slipping down a 1.0-m high inclc8dgu 5l) luv0ined 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 rolllyjg8r6xcm53a :y yx6s with a speed of 10 m/s. How high up an inclined plane can it climb before coming to restg y3y:86a5yxr6 cxlmj ?

  A hoop of radius 0.50 m and a massf48n (f mgu6yr of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distancf 68ungm(yrf4 e of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withoutkz7vm/ imm k1 b2ty47i slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of kytmmb2m4 i77 kz/vi1a 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 c)ary)bhsu7.2rjx* pn r d e.p,hanges 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 inertia of ymk durkkz6: m+aw:/3 $5.0 \; kgm^{2}$ 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 r229igh veof+gbq+a;hov 3f(fd1u j/h ad/s with arms extended has a moment of inertia o gvfh/oqad9e;hj2f fvo(3 hig12+ub+f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?