Angular displacement is usually express in .)2es (by zf67 hj5dwr3brftdunits of

  Angular velocity is expresserou j8in 55yr5d in units of

  Angular acceleration is expressed in units z7 . rmb (l)cfvdj+ b0+1zadgtof

  A boy and a girl are riding on a merry-g7 jdx5dgtrok q234n7do-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who ha3rd nk d2xt7oqj4d57gs the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a coadbt+b u:)f7u6ixff; wqne 3-nstant rate. The boy is near the outer edge, and the girl isae6 iu);uf+w-dx nt3b ff:7bq closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which 6i t0vx+/q3pnqd dbb*z:ot9 4u 9oj cris turning at a constant rate. The boy is near the outer edge, and the girl is closer tn4xptz90cv39q ri/ +*tjod6u o d: bqbo the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-roundcn/ 1d ojlr8bqzd--x; which is turning at a constant rate. The boy is near the outer edge -d od-qlznb;c8r1x /j, 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 a cons cb69e3 5zr mlp2q7y.hg)cdzktant rate. The boy is near the outer edge, while the girl 5)zbre zlcq7 m39g6p2khd. cyis closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an ajl,76um3 hnpu ccurate stathlumnj3p u, 67ement?

  Rolling without slipping depm0v ycy5 tw. rdcj-1),ohqa h4ends on

  Two equal forces are applied to a door. The first force is applied :zfa/q id caq5: u+5tix ,eet/at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpeniuq acziqf: 5:t+/edx/e t5,adicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to jbi(uix(4mo/.sx 1s/zf c-x va door at the doorknob. The first force is applied perpendic((s-/oiu4im/x bf v1xzsc. xjular 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, perpend; i38 2d(titzsoj b(qi28ggmjicular to the door. The first force is twice as large as the second force. The ratio of the idgg8oqzi( 3sb j2(jmt 82it;torque of the first to the torque of the second is

  What is the quantity used to measure ab+i- ggrlv+j;p,j1fx z k5 qa3j,a 6tfn object's resistance to changes in rotatioxb,p-al6q 1jg,gzi5;+k3tf j+fr jvan?

  Consider two uniform solid spheres wher 1tbh4fpw l)rg w8pr/.e both have the same diameter, but one has twice the mass of the other. The ratio of t4)r ppbh r/ l18wf.gwthe larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twimc-1rm y8qad9 s)n/apce the radius of the other. The ratio of the larger sphere's moment of inertim9ad)r8cs- 1n mpy/qaa to that of the smaller sphere is

  Consider two uniform soli5w p:s9somx(ax61ux j d spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that:ma1p u sw6ox(x5jx s9 of the smaller moment of inertia is

  A uniform solid sphere has mass M and kz(h8)p2m8m luy5jujyq-q r( o39fzsw k- sr *radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abj hmu*qs-)k lj298yzz(owm qfr(ysu 38 r-kp5out a central axis?

  If a constant net torque is applied to an objezxhi;w cpp +zo h:93r)ct, that object will

  The moment of inertia of a solid cylindst , /*auojl3mer about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kine* tl,ou3/asm jtic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mi;p okehq, +ezb:)0vi ass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the toqobz0h,;iivp kee ): +tal translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radiuslui 3ibrqkb( +c7 6-xz R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere lik q bz(xc-i7r3ub+6 at the bottom of the incline depends on

  Suppose a solid sphere ofc.8 txscbq.*/gwi:uh/ nz.jt mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends.c/h.zj bqtc. nug:w* 8tx /is on

  "The total angular momentum of a system of particles changes whe;+tm: + rtymg hg c44cle7d2iu so9ut7n a net external s9e 4 lgum7 hr7uci;td+ctom+t 2 g:4yforce acts on the system." This statement is

  In what circumstances can the angularw0l:micz*v x2 velocity of system of particles change without any :zcxvm*w 0li2 change in the system's angular momentum?

  The Earth orbits the Sun in an glu,jr/qd acqp h ;7f:s0l*8relliptical orbit. Ignore any friction which may be present. What happens over time to the qurfp;gald:c ,r70qhs/8j *lEarth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. h:7wq pfdnqyc2*z4 q6plh6+s As the Earth moves close to the Sun, then which of the following best describes the orbit4hp+6nq2zws dclq qpy* 7fh:6ing speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) b5p80a)bk-b t nfhfkz dh e.3m6y pulling in his outstretched arms close to his body. What happens to his an.bt amf85hp nk3)kf - eb60dzhgular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast 8fyoou8c),vpl * a1no spin) by pulling in his outstretched arms close to his body. Whap u* ,fon v1cyoa8lo)8t happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ( 2pn p260eq)jolseopin his outstretched arms close to his body. What happens to his moment of inertia about the axis22sonoel) jp06e pq( p of rotation?

State the law of conqxw3ghsov( ol; ; 6yza1s/uc3 servation of angular momentum.

  What arc length does the Earte;u5r e8pow oqpwo:r 4f**f8w let,p3h travel in a three month period in its nearly circular orbit about the Sun with a4*;w:8fpfqo3ppeeo8r ,u 5l wwort*e radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. k(ow8wj)r,,dc 7gyf jWhat distance does the tip of the second hand sweep through in 3 m7( wo,yr cjfgj8,kdw)inutes and 45 seconds?

  How many rad/s is 25 revolutions perygmvx7vo c46s+bm(8 h minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0u(p1 p( imtm6t revolutions in 4.0 s. What is the frequency of the wheel's rota (tpmt 1up(im6tion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHyec +rf 94rcjn ly:t:kivs 413z. The period of its rl4cci+n3y9rsv4ek1 f y:rtj : otation is

  A phonograph record rotates at 45 rpm. Through what angle doe2c.93 k(um nxd f1tbvss it turn in 0.20 ss3fn kut(m2 c. 9xbvd1?

  A wheel of diameter 26 cm turns at 1500 rp15cih//tlty uoj )saqa lod-1 sy,r: 7m. How far will a point on the outer rim move in 2.1ac /oa ,oissh jlt)1r: lt-d51yqu/7y s?

  A bicycle wheel rotates uniformbmw.jj*vocy:3c 9(ayb 1s 4ghly through 2.0 revolutions in 4.0 s. What is the avecg b14sc9w :y(3 .amyo bvjhj*rage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wc2sr 56n qm;wz:w:i j ;xpuao3hat is the lo::mi23c u5xrq6 z;ja wsn pw;inear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distaby2fbhc1 /b .k rsb ns,:dac+7nce 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 cs c.fd r,ahb/c: bn2sybb+ k71able car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.7/ o ws*)woi-w2 vjtsh0 rad/s. What is the linear speed of a point on the o 7ijovw wh*/-ws2s)t wheel's rim?

  The cutting cord on a gas-powered weed cutter iskp* j/5)95misip zu( )umvtio 0.16 m in length. If the motor rotates at the rate oviik (mp*os9j /u)uzp5m)i 5t f 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating wi.;unjwyyul1 f r1vz/5 th a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on thezfwy.v / 11un ;ujry5l wheel's rim?

  What is the centripetal acceler5hfg6du 2wlm -ation of a point on the perimeter of a bicycle wheel of diameter 70.0 cmuf5g-l62 dmhw when the bike is moving 8.00 m/s?

  How many revolutions permp98y7a. / i4pkbexyn minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to prod.kmb4p a/ixy8pen7y9 uce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50:ow+p on(yyi7g;mj r4 m with a speed of 20 m/s. wio mponrj(;y 7+:gy4 The maximum 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 speed ofz*vto mes35pz hc23d vjhs f;m)3vt6;+2gork 20 m/s. The maximum centripethf2hto2o zpr zv) t*;m5v;6jvsk dc+m33sge3al 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 around in846pdyr1i+ (dl ik0 :i edswte a smooth level table. If the maximum tension that t( i6l+e0 y1 d:etds4p8d iwrikhe 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 razte(roclwh t:) 9u/.ldius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/ lt9z uet.c/lhwr(o): 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 3dob7xp4 o+jq a constant 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 acceleratif j 9a 5wv4nrynir+6)von 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 rad: wj:r kti;j tn 8celmq.1(9txius automobile tire rotate after starting from rest and accelerating at a constant 8jxc:qet:n rilmk.j9t1(; twangular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angutc y0;7 zxwlimsff. 29lar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rx+hy+g av7f* rad/s decelerates with a constant angular acceleratig++ 7* arfvyxhon of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachia,ti :8ksmkf*l , f/ves an angular speed of 6.0 rad/s while turning through 2.0 ,v,sk8kf m/ia*li:f t revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slhylx76ujz */lows down uniformly from 8.40 m/s to rest over a disjhz6lxyl7 * /utance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniqe, l5 1jivguo;sx0*nformly from 8.40 m/s to rest over a distance of 115 0o ilnx;,equ*sv1 g5jm. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oxjs a7dm*(6jrdww(/p 2cz w pa8e:kt3ver a distance of 115 m. How long does it take for the wheelr /cx* j3aa8ezw 7wddw62 :t(pkmpsj( to come to the stop?

  A centrifuge in a medical laboratory rotates auwk:uh0m j5x*t a rotational speed of 3600 rev/min. Wuk*0j5 :x uhmwhen 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 wheel require tightening p aug9;hd8wsk3.w g*t6 s vuc,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 kg w3. ,psv;u u6awh gs98dtc*to the wrench?

  The bolts on a car w3pqjk yb511fz p( 2sntheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requijb2pq5 11n3f(pzy tksred when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i9i)n:d eru v7mnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: ghz 31ri ei+xl)w)0admass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Whatrz03 +i dx) hiealwg)1 is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted zz5y/r/ r6ddw 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 r6ddrrz/y /w5z adius 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 frictionlegea gp.7 .,u4w.nv/5 hln ogqess 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 wrapp5/uea gh w g.l.e.4nov,qgnp7 ed 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 from rest?

  A 4.00-m long rod is hinged a2yr. jmhgn8r .t one end. 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 momenrr..jhym2 8 gnt of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and4c/0w a+2mw+hvvse pt 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 rad a2vmcw +e/w+tp0vsh4ius 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 mass 1t0ad1vnp.1+x o+kbm jm (mfp 7.07 kg ano11xjn m kpt ma m(d+pv0b.+f1d radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless g. qn8s. n p4koh 0 qmw;l3(rzo+md k:9jkmq*tdisk pulley of mass 7.07 kg and radius 66.0 cmj0q k.o*(pn 4rh9okz;l 8mkdqmqsg3 t w +n.:m. What is the acceleration of the mass?

  A rotating flywheel c 2dfsg1fa v0dfgdj (;)an be used to 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 2nszf6e- m c,ainertia 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 aq3u 3 w4p; fm5 9lwwddfq.cha4nd radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere c3whp.qu34fd m;wfl45 da9wq when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kgp.mtw11 l; h+tdpfu .r3x 7vkq and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before 3x hrwv1tm.1fk tu. lp+p;7d qcoming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and 2qh(*usex d k4allowed to roll down an inclined plane. How fast is it moving after dropping a ver4( 2sk*h qxduetical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipbr mg,+qogv:ch 6ed94 ping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is givehr4em9g6v+ qocd b:,gn 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 momentu v)yk rg-q+u+gm 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 moment of ine.e,r*d qvbl 8y;qha*wrtia 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 rotat)xq (npo0 l0dv7ia bl.ing at 5.00 rad/s with arms extended has a moment of inertia ofv 0qda0i)l(blnpox. 7
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?