Angular displacement is +a;/u +d 2do/kpmmnec usually express in units of

  Angular velocity is a6s)h t;t8a2;,dt u( atmhnc zknxv,8expressed in units of

  Angular acceleration is expressed in units o */g skzo 9sh2a-pj w/blq:p,nf

  A boy and a girl are riding on a mer m rx(fjfukko65 ; -;pt)b0xchiyi 8j+ry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is +h;i fuxmpyxji kj5- ()8f6o0cb r;tkcloser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-g9oxqc(4t / cnqptf)z)o-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 speet9con)z/q( xc4q pf)t d?

  A boy and a girl are riding on a merry-;,j 0 e3e0w clj9uj /k+*7rdndywxviu go-round which is turning at a constant rate. Theu3 9r x d jujej0ew7wil0k+;c/y, d*vn boy 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 merry-go-round which is turning at a wreg9( h*--l;hqmbks:dce*n constant rate. Theq *es; gh*h c:nwk(lr-9b-dem boy is near the outer 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 turning at a cona-n;lg(k bbu 9stant rate. The boy is near the outer edge, while the girl is closer ; 9bgkanulb( -to the center. Who has the greater tangential acceleration?

  Consider a rigid bod 2 2p0jgdsgf6ry that is rotating. Which of the following is an accurate statr sgf6g0jp2 d2ement?

  Rolling without slipping depen btv 0 n/+y0vbzad:ff6:xjtc 4ds on

  Two equal forces are applied to a door. The first force is applied at the mip nk);l8kso.h dpoint of the door kkph8 sl.n)o;; the 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 a door at the doorknob. The (as v.opj ad/:first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the gr:sj oa ap.(d/veater torque?

  Two forces are applied to a doorknob, perpendijbz9kw i. 37qvgwpi71cular to the door. The first force is twice as17gk9i .bjp73wzi wv q large as the 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 object'st+s.c9a :(la ag rvr2j9o kmku) uhh+8 resistance to changes in rotatioam:ahalusu 2 + .ko 8g tj9k()9rc+hvrn?

  Consider two uniform solid spheres where both have the same diameter, bzoi8n.56g 5iw ro yxl-ut one has twice the mass of the other. The ratio of the larger moment of inertia to togw-5.5r 8 inoiz y6xlhat of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but l oh2)n.aaxkhl1b n*2one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the snh21ao n lh.abk2x l)*maller sphere is

  Consider two uniform solid spheres where one has twice the mass and twonh)g/uly 3-yu ,3if pice the diameter of the other. The ratio off)lp-33guy/ in hyou, the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has massr g:9sq(iaq.; n,*r b-bfi gz:g*qws y M and radius R. If these are increased to 2M and 3R, wha9-bifsqqyr z.(wi,gar*gn : g:s*q ;bt happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object m6 8r0o,+twn2nl jtktwill

  The moment of inertia of a solid cyy0hlb; :(x p,b wr.sfc d,-amvlinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, -f,0;vb ypcsrx m,l:d.ah(wb the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg,;3y) dg mb zcgvqle697 one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy 9)gc ld6e3g 7;zy vmqbof 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 without1t.o5mm +(dkz 6cjniu slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inck5m+.un 6d1 ojz(cm tiline depends on

  Suppose a solid sphere of (vu e9 4hvinokz*g .d2mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottk4u eoi 2 gnvzd.(v9*hom of the incline depends on

  "The total angular momentum of a system of particles c x+9 vbs1th0xohanges when a net external force acts on tho bx9 txvh1+s0e system." This statement is

  In what circumstances can the angular velocity of syste.-s-kb zupq (otpo67om of particles change without any change in the s 7 bo-toz6 ok.p-pu(sqystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any w(yhtu 3jxc-8 friction which may be present. What happens over tim( 3-w hjxctyu8e to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbi)i, w47nzhvcss by-5 qt. As the Earth moves close to the Sun, then which of the follov 5s yw)zqn7b 4s-h,icwing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulliw /o,i+amy e72riz 71 9silrkang in his outstretched arms close to his body. What happens to his angular momentumoe 7l9+ais r/i2yw, mrz71aki about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch .uq:;bpoc)bkph;l 8 red arms close to his o;p p :8kqbhrl)ub.c;body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling (fd l ;ao;at5/a1chk s(z 0fxnin his outstretched arms close to his body. What happens to his mome1s t (dzl5(c;fk; fh an0oxaa/nt of inertia about the axis of rotation?

State the law of conservation of angular momentp m(i w3. g7lsgts8rgsa 6g66ium.

  What arc length does the Earjrz4vz, 5e:oe th travel in a three month period in its nearly circular orb5e,vzz o:4 jreit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has at vj(zn0m*v-lzglm 8xc-x5s e9a s;s8 length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minux850t(mj- 8x svzsnz-cm*velgsa;l 9tes and 45 seconds?

  How many rad/s is 25 revolutions per majs) a) pcj iq/07c*leinute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions io ;9) -tzdnzurn 4.0 s. What is the frequency of the wheel's rotatuz- )od9rznt;ion?

  A pulsar (a rotating neutron star) emits pulses at a frequency o6i-i:nic9wu(tz q e- df 0.40 kHz. The period of its e:t 96z-nwqi cu( -iidrotation is

  A phonograph record rotates at 459.6vmz3jvn ynfx(g0d /yaby 3 rpm. Through what angle does it turn in 0.20 sm0df(3jv/y v.x3bann6 z y9yg?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will af kxq4/h)9+wbevqjq6uw. vc: :q n.gui2c z0q point on the outer rim move in 2.1:6g+bqhzf4cve)w/cq :u uq9 q2k0.i nxv wjq. s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sd3t. qhx+d(o86xes gg. What is the average angula (8xgg ho+6qddt.sx e3r speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. o/q8:y h ar5hbk4t;3ed qkl5u What is the linear speed of a pod :rkkbhoyt5/5lh4q qaue; 8 3int 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thel bu:df; eu2 .p6zggy/ cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast mu z6el pgfy u./:udb2g;st the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is u w:z5)ul0 (dm-fwuof,, q nx46wldikrotating with a constant angular speed of 2.0 rad/s. What is the liz6:,ouku x(ww fnd lmiw q54),luf0-dnear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the *e(s9kqfeqp.a *q ig: motor rotates at the rate eikp9 s (ga.eqqf* *:qof 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 (og0; bhb zup 2ube67ra constant angular speed of 2.0 rad/s. What is the centripetal accelerau;b0r6 bob(2upe7 hgztion of a point on the wheel's rim?

  What is the centripetal accelerationh,ma 2r6d2l sz of a point on the perimeter of a bicycle whm a6hlds2r z2,eel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spac :kil):0ui1( ulw hkhae station (r = 1000 m) rotate to produce an artificwhli :u( i0lau )k:k1hial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curv agx 3hfo /8yynkgp 7k5c45,wse of radius 50 m with a speed of 20 m/s. The maximum centripetasg cyw/y anf,pk34o5k 8xh5g7l 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 w5o;*1t6l vu,uuvx1h ncsv ( wcith a speed of 20 m/s. The maximum centripetal force (provided by static friccnh v,*vucuslo;(6w5txv1 1u tion) 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 whirra5pdj:(u x 6fled around in a smooth level table. If the maximum tension that the stringf:a xu6 5r(pdj 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 wit-x-b km ng5e/mhout slipping 10 m down a lek bg m5n/mx--ane 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 wl ).7f 2e b5g:xnuvzk0j 8ocqaith 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 wit,qa .eu/5mhr r t3anpmp/9blse6c00dh a constant 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 r/c d/yd 5u9i4h(tjoti adius automobile tire rotate after starting from rest andt5hc( tdu4 di/iyo j9/ accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has sb9 j aq6* 5ucaqduexv2/c:;e an 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 decelera/.cc4qaoau; fenf9/g. gxd :ztes with a constant angular acceleration of 4ecn ao:q .cd/;fg.9a /uzgxf$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an ah4y5oyei,*0c s . uaz-sf1la cngular speed of 6.0 rad/s while turning through 2.0 revolutions. What is tlu*.a-5fyzic y0ecs a4so1,hhe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unipd/ +kjr*agysxnh,u;z0l(r 1 formly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming nks(d0r ;,rzy+a jlh gx *1pu/to rest?

  A wheel of diameter of 68k d upax *li 6z3fz)3i-mx::nr.0 cm slows down uniformly from 8.40 m/s to rest over a dist*p6x):3ku:nri ia dxf zm- l3zance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s04/o3qkfci q0zex l; a to rest over a distance of 115 m. How long does iqal0 oe/ ;zk30qi4 cfxt take for the wheel to come to the stop?

  A centrifuge in a medi160jn0oqmmf)ui xl /e cal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 tufxie0)6 1mmo0 ln/ jqimes 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 req:;-;b qprhjpj uire 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 to the wrehp;jj;- bp:rq nch?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 c.smne3k . ldp7m long ws3e p7ndl.m .krench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in2o0j-qyl ::ure6 aky r*krcjy/vj90tertia $3.00 \; kgm^{2}$ 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, mf +a mj a;q/bcwev6e-)ass 2m is at x = a, ande/ we;c+j-vbfq)a ma 6, 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 f4hbb2vnncymf .h616 a ce.m8axis thought the center O. A rope wrapped around the outer radius 1bc4.a. 2yenfn mbhh8fc6v6m 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 kw -a+el*qu ;fdg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exwaf*d -+le;q uerts 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 from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in tzew 6)4fis0b1 r;sydnhe 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 end sb0) d;z4iny6s1f wreis ML2/3.)

  Consider a bicycle wheel to be iksac85dv7 3lx3lj;y 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 tk;xas5d8 vc7 y3lilj 3angentially 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 wy+poavs/ 0w,t )3*abieh.pudisk pulley of mass 7.07 kg and radius 66.0 wu,bw +eih*. 3/ o avt)s0paypcm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless di2wnz ) q( vu5pcqum:2ksk pulley of mass 7.07 kg and radius 66.0 cm. What is5 w q)mu n:zq2vp(2cku the acceleration of the mass?

  A rotating flywheel can/pzq;gx8 *z i9akwr 0q 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 hk -dxe dmip cdto251fyk+ (q* )r7lz8inertia 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 res5:bz/ u4nd4(pz6tf ti1ewd hjyt 88hht and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere wht8yi8z(nj5:hwh tdte h164/buzd pf4en it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kgy.cv z :u7kc*r and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming: kcru yczv7*. to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from jirj wmdq70b q..j9 g.8m qiu3rest and allowed to roll down an inclined plane. How fast is it moving after dropping a verti3qi.m.jwj qrb7 uj08.dqmg9ical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withoutsiazl*v x ahg+05m *m njt66)w slipping down a 35e incline that is 7xsa6t 6a m0vhiwl*jz )n5g+m* .0 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 chtncjm: r 9 y 10ul82zn07mdmnnanges 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 mow qeb741r7 h(glrhi-pment 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 wtn 77hleq/4 z5.00 rad/s with arms extended has a moment of inertia ofew47nt /z7 hql
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?