Angular displacement is usually expres.7sax:8fxz c kxz+ r(5 l9igc jml/;zwct9g2k s in units of

  Angular velocity is 4v wea(f9*vq;(,7fboa5cdw c 5n.yvvzwlhg8expressed in units of

  Angular acceleration is expressed in unitsxzsz.p0r9t03l4z obz d ;tr .l of

  A boy and a girl are riding on a merry-go-round which is turvv9xk(gh g(8 oning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacg8 vo9k(xvgh(ement?

  A boy and a girl are riding on a merry-go-round which is turning at y+fy 7 w4dfeipg8 )r:ea constant rate. The boy is near the outer edge, and the girl)48 ywdy7fr:fee ig +p is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding ot0kar dz nze/-;dy7x vp:8.rqn a merry-go-round which is turning at a constant rate. The boy is near the outer edge, adnkypxe:z vaqz /07 t;r-dr 8.nd the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridi:vgs tg7(-grm 0l5 hppng a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is cl7gmvg r-p 0(lpg sh:t5oser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are r)fs o ir1:kd)miding a merry-go-round which is turning at a constant rate. The boy is near the outer ed f:om)ksrd i)1ge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of yhtc 3f9 as:3mthe following is an accurate sty9hc m asf33:tatement?

  Rolling without slipping depends pg1ghn;s*ne) )2rqn z on

  Two equal forces are applied to a door. The first force is applied at the midpo5v 9oqv4a2snrint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater t 4r52avqn o9vsorque?

  Two equal forces are applied to a door at the doorknob. The 0l3rtk 94y0mk scbiv7 first force is applied perpendicular to the door; the second force is applied at 30e to the playkvtm00 94c7s 3lkribne of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to tfucx are7):+l,0g g3 *2q us0xir3)wyo kebvmhe door. The first force is twice as large as the second force. The ratio of the ty 2fmuqr:g0ex30lc sxi e,))a7b3k+wg u rov*orque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in 99eva+cfrwbhp hi*/bif23/w )h k,6ww4qdfb rotationb2d* ) whhqpfw 3carbf/+ki64/w 9 h9 bf,iwve?

  Consider two uniform solid spus hu026ziopa;er5 /oheres where both have the same diameter, but one has twice the mass of the otherh2u6o ra;so /z50ip eu. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheresm7qjw3mec-o8xnd w:h:s r y3/ have the same mass, but one has twice the radius of the other. 8 w/ mmnr-o7s3hdwx q: ce3j:y 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 tw7o 2 r/eujot)n+2zwkp3 w5s,yszo(nkice the diameter of the other. The ratio of the larger momk2 ozn7y2 )5w zop,sk+3osjn(et/r uw ent of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. Ift*q wl(h,lit 7yo 5lm3 these are increased to 2M and 3Rm 3,yit7*w( lltlhqo5 , what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque 3 jg r+size dptq +a442c5; mvrtibn,4is applied to an object, that object will

  The moment of inertia of a so gh 9rjl:mcjq:tj)/4hlid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational:rj l9t/jh4hj )gqc m: kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wbk kqq6f*zbegk0n9b ( sk(e*e5nr;. sheel 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 energyekse(g(*zknqbsfe;*kb9 06 q5rn b.k of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping dow4+etuig(qh+6 +5 : fsoowwstdn an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dependewt+5ioq :h+sf6 s o(wtd4+ugs on

  Suppose a solid sphere of mass M andy/iwq+;0o*l. nl dkdv radius R rolls without slipping down an inclin0/y k;ldqvilo .n+w*d ed plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes;g/tjx zqbenzd+8,u +mhh ,*v when a net external +e8z ,+/uxtvzq*;md gb,j nhh force acts on the system." This statement is

  In what circumstances can the angular velocity of dil +7p iyp h41q7wsmm)kz72 hsystem of particles change without any mi dshpwi)l k77y 741+2mqzp hchange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical-*m)mrh1 nl gz orbit. Ignore any friction which may be present. What haprm*h)zg n lm1-pens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an;ajernl2va 3 6 elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting 26 3an;re vjalspeed of the Earth about the Sun?

  An ice skater performs a pirouette (a fanj*8d 2( c.(uy+asmgsb bj ,sgst spin) by pulling in his outstretched ar 8ss2.dyu( +gsgbm*c,jb naj(ms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by 6r rn0dx nj,d.ube6t 0pulling in his outstretched arms close to his body. 60r60tue ,djn.rbn xd 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 outstreqax77yr -c*3m. bg wbptched arms close to his body. What happens to his moment of inertq wm*.7 cx gr37yab-bpia about the axis of rotation?

State the law of conservation of angular moments pty(/ m:o9mrum.

  What arc length does the Earth travel in a three mou 3 ed+qzcn br87/i,unw7aiy 6nth period in its nearly circular orbit abou/nen,iw6yu7r 7zdb+a3qi c 8 ut 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. Wh:mop m m)3tl9 h-8vswj4qfb.yat distance does the tip of the second hand sweep through in 3 minutes and 45 8wb9) hjpy .stv3m4lo: -mmfq seconds?

  How many rad/s is 25 revolu au4w okyi355ytions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4u tsa bv26-e-pthsjl 2bm;0y 8.0 s. What is thebe0sv2 t6albu 8hm s-tj;yp2- frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency ou (t*6s 8+w4dzcfxy fvyi t:s0f 0.40 kHz. The pti z 4sx(v+uysd 60cwty8ff:*eriod of its rotation is

  A phonograph record rotates at 45 qn;eu u (9q r72,qum3zrf8eyp rpm. Through what angle does it turn in 0.20 ep7; 3m y8(ufuz2n, rq9uqerq s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on thbho aj dhq adlw8jg8(ih +h (un0k)/-.e outer rim move inhj ho(h(0add /.qklb i+)wn8agu8-j h 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 2x xjl02 vg0zy4.0 s. What is the average2vlxy0 z02gj x angular speed of the wheel?

  A bicycle wheel rotates uniformly throujp ,zsdw*6)jk: /jqzngh 2.0 revolutions in 4.0 s. What is the linear speed o*z :)njj, wkjqp6s/d zf a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a dist z1fz t9 f*v,3f0exmttance 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 th1f9z t0v*m ,f3fezxtte pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m h 6p)o6mthw14 9p ugtiis rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point 6otp6u4whg hi 9pm1)t on the wheel's rim?

  The cutting cord on a gas-powered weed)4,zr3pzzl3 in6,pwxxgt n *q cutter is 0.16 m in length. If the motor rotates at thl, qztnn3i)3,46 wzx*xpg pzre rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angula4 c+fkm,ogna0r h5n 9br speed of 2.0 rad/s. What is the centripetal accelerati nf5kchg 4b+9o0,rma non of a point on the wheel's rim?

  What is the centripetal acceleration of a poin g4ns.mn5c0wj69h ajit on the perimeter of a bicycle wheel of diameter 70.0 cm50ga ihw jj9n nm6s4c. when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spar8qpq/w q8k ds5,,pc vce station (r = 1000 m) rotate to produce a/ cvq88p5pr s d,qq,wkn artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of b8sp /7q bo(kf20 m/s. The maxi8/pb7( fb skqomum 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 a speedgvdofd n/,fk51 4v0 mb of 20 m/s. The maximum centripetal force (provided by st v nm/g5vk4fd,do fb01atic 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 s m3n ,v hoaqfovhru -65v4iv2 yx2::rytring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is o5qhr3:vnf:6ry 2m-4vx aivyv,2ohu250 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 wsv(j ,q3iv.bdnh 2 /aeithout slipping 10 m down a 2ais .3hje,(/v qvd nblane at 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 accelv3 sbfhu3rnsq 823;byeration 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 accelerati+ jbz7f b-q2+ir(kfxa)u qq 5zon 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 radiucy) +lkqdq,qrtkgg;8elm3a / 0d4e z 5n bt+h4s automobile tire rotate after starting from rest and accelerating at a co+3q 0hm +;5 tqkz4,e nc4del ykg l/qba)t8rgdnstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an an2d9k7h brl(8hrsri t 5gular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatings(qv (ijcfmp,r 39r /u at 20 rad/s decelerates with a constant angular acceleration r( 3qi(up,s/mjr f9vcof $-5.0 \; rad/s^2$. 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 whxm)k-vw )kg:s mef-)yu+y .is;uu:ws ile turning through 2.0 revolutimyys k) w;ik:g:swuu )s+)em-f x v-.uons. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over t3f p v4 qntbnwb7 04/n2qbl:va distance of 115 m. What is the total number of revolutib/37nnpf 4b2qn vbltt04 :wqvons the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove.d8/au lg1d jxr a distance of 115 m. What is thxa.j 1 /8udglde angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.406+q vy0b(jsfe m/s to rest over a distance of 115 m. How long does it e+s0 qv6 (jyfbtake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 4 7ic xr*-csrnrev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to res7s4 *ixn-cr crt.
(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 tigalhap,;qp+-*,e fxr i)r p c;hhtening 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);p+h,apxipefq;ra c-l* r,h is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm ay9 ,yvor9shhn 7 sl++ f7u8fds, kso(long wrench is used, what is the magnitude of theu,hlha +foyf9o+rs 8 y9,( s k7sns7vd force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiak 71s9ou 8febg7bv2s;ug3f8 co)kb ya $3.00 \; kgm^{2}$ 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 vcvgu9;*,ew qthe origin, mass 2m is g;vv w*cu e,9qat x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axs *jw5ocei -v-q s9:ipis 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.) Whe isoc-wp95sqj- v:*i at is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought thei9)vmf d-sb5rmy0p *ug 8 h)om 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 radiusfiu95mhm*symo)) r gdb0- vp 8 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 from rest?

  A 4.00-m long rod is hinged at one end. Th *0(t(cgzxrjj3arois03 9 vvhe rod is initially held in the horizontal position, and then released as the free ena3jxc9 3h(0oizrg* j(0 vv tsrd 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 be a ring of radius 30 cm anc3xwrklg7f o-:1sd. y d mass 1.5 kg. Neglect the mass olw 3 1-froky7sdg.x :cf 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 does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disbqxh z0da2+4,t3 x;nh azv f,fk pulley of mass 7.07 kg and r,2 3;hz qhf4btav0,xzxfad +nadius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs ojhoml/ 9q 6m55zl.(tt frkik6n a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mm5 ( il.fjltk k95hqo6/6rzt mass?

  A rotating flywheel can be used to store energy. If it is requi3gx3-v3dij;o pid- uzred 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 inert p(7-: jia 4lyfep0nghia 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 t)7xwmd*d.z4ollki+im0 y 2zh; q k9dradius 0.010 m starts from rest and rolls without slipping down a 1.0 +)* lzmyi x;h20o lmdd7qizw 49.kdtk-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 9i *xchi :y n-bpq/3tzand radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comingxhbiq9t/p3:z -yc* in to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from *p:xlm+ tn di;z73s:n xhs 9uwrest and allowed to roll down an inclined plhs7pu3ndx:nis : +; *z9txmwlane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rmnx73*ges wz8 olls without slipping down a 35e incline that is 7.0*m es ng73zxw8 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 by cxc(cl4iz9i1 $20 \; kgm^{2}/s$ 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 in,(vl ukf(k)6j x uj 14vb7irlaertia 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 exteekr:l1 e:xov6bvzv5 7lki9 5znded has a moment of inertia i xez:lb v96k5 vzer:ok1l5v7of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?