Angular displacement ). xqz./ r0 b9:kjjx9nbquavm yl0w-ois usually express in units of

  Angular velocity is expressed in afd 7l8hx/so- units of

  Angular acceleration is expressed in unp9h e gx9/e0003srkt h1dzco vdj:ct0its of

  A boy and a girl are riding on a merry-go-round which is ot i.)6idal: ikw04nqw. hbm *turning at a constant ratihn:*lq.ik) 6wao w0.m bt4di e. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding i*t55vws uyg :on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and 55*g t svu:yiwthe girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a coq8cf6n0b;4jf . a mytmnstant rate. Tjmbt 0.fq8m ;4a6fncyhe 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 turnin n dkrmigu6061pvv41pyomz 0,g at a constant rate. The boy is near the oui vyv1np1 ,ru0z6kom p6g4d 0mter 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 turninvs:uw 2xz:f)k g at a constant rate. The boy is near:2w skzvu:f)x the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that isuv. gy:) jib-c rotating. Which of the following is an accurate statyv- j).:ibgucement?

  Rolling without slippin8fl dzy)4dqvp) nqmg)vb :67p g depends on

  Two equal forces are applied to a door. The first force is applie/x,s .umcx pqeq8* n9qd at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?/ n.*sex,9u q xqpcmq8

  Two equal forces are app.wuv w v 6eu(4;lkul4ylied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exwu.y; l 4v6(uk4v weulerts the greater torque?

  Two forces are applied to a door;k txsyjlf )w0)k9ji /knob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the yjk) )ts;kxi 9/jlw0ftorque of the first to the torque of the second is

  What is the quantity used to measure an objectz wh 5ns*vw/mv8x*; +pq ;vxal's resistance to changes in rotationn h*mvsw+ ;xla/p;q8w5*xv vz?

  Consider two uniform solid spheres where both have the same diameter, 6g8s(6u g.uj wqc)edkbut one has twice the mass o 6eqcgks6 (u.jd) w8guf the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sphe*uf ./(5em7a jtfn ;ou7qyfxwres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to thmq 5atnjy x;wf7 f/u7e(*o. ufat of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice tha(hw.spsm6ns 5hc f,7e diameterh6sfscm s( hn.w7a5 ,p of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere shm2:zma1e;f(8 rix thas mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere (e 8isft;m x1mah:z2r's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object will8wgtb+e/e3ik7( k d12wci7jyiwh o ;n

  The moment of inertia of a solid cylinder auz;ay v6xg bo* u36nk5bout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its tr 5bgzonauyv u x3k6;*6anslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has jd+r,qly78.obbdl6 *e/ c 7v wl9yfeu a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy o7. jqcd87efdyby,*obe6rv9 + ll /lu wf 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 r4on7w95l rksjp ke1va3l s1kn :fcd(.zff)l7 olls without slipping down an inclined plane starting from rest. The linear velocity olf7w 7 z(lj1ro sdnf)kvae 4:c9l.s k np1kf53f the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass 8j8 )fvo;uxvjM 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 depends8vxvuj o); fj8 on

  "The total angular momentum of a system of particles changes when a net exter+, m; (xg 0lxto0ozapmnal force acts on the 0gp oo lxz;tamm+ 0,(xsystem." This statement is

  In what circumstances can the angular ve r.g/h37amg 1ucsg-f6rwj o (, ff2/qhgq3e frlocity of system of particles change without any change in t/hu3/e g7oq f gfrf.g a ,(3chmg6r12wrqf -jshe system's angular momentum?

  The Earth orbits the Sun in an ell3w/2.j,n+kfdrx o atriptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum /+ok,rdr.3fwanj 2t xabout the Sun?

  The Earth moves about the Sun in ant4pui9.ynil8 elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes thu.l p nt94yi8ie orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in him cimiq xino*3 u67m/0r/qlm4s outstretched arms close t 6/ul omii 30qxq*i mr/mcm47no his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outsxm )5 xsq z(sz1 puh73.b)wiujtretched arms close to his body. uuj7s xzs)iz1)hw5 q.p3( mbx What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fas b;3vg4,r cxp0mq )aget spin) by pulling in his outstretched arms closp3 4xqav , cr0mgbg;)ee to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation o(x3na* s(dk jxm/7uwwf angular momentum.

  What arc length does the Earth travel in a three month period in itsqib ) 9my4;gv+9mdd ftu(ae* v nearly circular ); fa49eq+ d ymm9uv bvig(*dtorbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a len.lm5 :8b/cv a6j3z 0klsrmvuagth of 0.30 m. What distance does the tip of the second hand sweep throsrauvj8 k0l6v3 .a /: mzb5lmcugh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute mt kawe 8: cpzj06,j6pequivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 7l za0u r)n;8ff)0f v hgc/1ig:ldp gaWhat is the frequency of the wheeg ;ah: llgdzaf/1 r0)cg7ifnv0pf) 8ul's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencyztzfq:*lbq iw9ab.1) of 0.40 kHz. The q:*t bw9zl z)bqi1 af.period of its rotation is

  A phonograph record rotates at 45 r5amo lo)hi7kwud;) zayp3,6 0 5q bwtmpm. Through what angle does it turn in 0.20 smpdk w ooq53;za, t)w7 ab6lu)05hmiy?

  A wheel of diameter 26 cm turns at 1500 rpm. How;d3j ,bm+/oswo0 yxgw c 8z*zy far will a point on the outer ricgo j;x +*s m8 oby/wdw3,zzy0m move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolqfx dmv(c,7 if-gq52outions in 4.0 s. What is the average angular spe gd5xf2 7,cqv-(imfoqed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 rg ljz 31(ezvj6evolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center jj6zglez 31 (vof the wheel?

  A cable car at a ski resort cargx52 *puo/e zm*,eqz jries skiers a distance 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 make 2zjo/g5uz ,pq e**exm the trip in 12 minutes?

  A wheel of radius 1.0 cslyu+hc(y*7 1iq0q2 uzk2;4p l hudqm is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on th+u u7hilpc2dh qs;yqc0uz q1k* 2(ly4e wheel's rim?

  The cutting cord on a gas-powered weed cutte-z yj 0g5zm4rnr is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cordzn5 yr4mzj g-0?

  A wheel of radius 1.0 m is rotating with a constant angular31 ak )ymm3xb+8jnjjf speed of 2.0 rad/s. What is the centmn 3j1+bya3) kf8jjmxripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poin7ot9p ik qre)+t on the perimeter of a bicycle wheel of p7k )oe+iq9tr diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statio/nsclok7g33pr6 c)ugn (rrgcn)c s6p 3l3ogu7k/ = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 uyoq;pa+,c0p 22 nsplm/s. The maximum centripetal force ( sy2l;o0 p,+pqnua p2cprovided 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 of 20 m/s ;:yi5n5mbb ub. The maximub 5;u:ymbn5i bm 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 u z3 cd*.wtc1nq-nzr. the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is n zn1d-utc.3q n c.*rzwot to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm n5ugc ep 9frixm4/-u*rolls without slipping 10 m down a lan necxu59r4*uf-/i mpge 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 9j ws3 d/zd xcy36a1sxwith 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 wpxg( i8,v e:jhith 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 doecb*cv vug 06q:s a 0.300-m radius automobile tire rotate after starting from rest and accelerati cc uqvg*b6:0vng 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 accehfr8; rjw/z(h46eo ylleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates wit)dsy 4 3-qocoph a constant angular acceleration oys)4p q-cdo3of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 ranmppu8a*h3 avl2s su-sxa h-9.1 pg;: rx wah:d/s while turning through 2.0 revolutions. What is the average angu*wp.: ;x mu-pau-v:apsnxhghlh 1 s82ar3 9salar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m vw*u d0*il oosx41v9q/s to rest over a distance of 115 m. What is the total number of revolutions 9w0xsi4lvv1oq**uo d the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifo a8) r2rhe)uza(o2 f/rb xbz+crmly from 8.40 m/s to rest over a distance of 115 m. What a )uber+r)f z8 x(b/hr 22ocazis the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforml)x:m0zrgs2: jlvfa 8yy from 8.40 m/s to rest over a distance of 115 m. How long does it take for the whzmay)0 xrjgl2:vs8f: eel to come to the stop?

  A centrifuge in a medical laborato :b,k ncy1kax-gy +;opry rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constanbngx 1 p-;+koyay,k:ct 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 to a ,1em*cjifho c7s 9qr9-gi .p ztorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendiculapogi ,riqzc. 9 fj9m7*s -1echr to the wrench?

  The bolts on a car wheel require tightening thena k7.lrq 40yi nzaw 3u79y;o a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forc nn9zau;7r4wyk.q i0ehy7a 3le applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 3- zi59vv2f+n mb ablj$3.00 \; kgm^{2}$ 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, m 5 salj m;myi.1egh05bass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origi1yimg lh5 .50;a sbjemn?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axion.ug7tam4we sm; x9-w/0yo es thought the center O. A rope wrapped around the outer radius R1 = 1.0s. e4-ugt/m wwmn 0xy7 o;eo9a 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 pivoted about a frictionless axis thought5mhi7 d/+kidmd n.sga9 a08v)mjyrb; 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 = 0b07rm5va y)a j 8 / mn+g.s9m;ikihddd.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 hel9 fpd j+9zbfr;r ;f5bod in the horizontal position, and then jfbpbofr5z9 9;+ ;rdfreleased 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 is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 c3l6(gssxo;8 zom:h b cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied g zmhso(c6o b :sx;l83tangentially 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 assfmu7** d0dv frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of them7dd0*fv*ssu pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulle,gnr n)z)52i xbu 3vudy of mass 7.07 kg and radius 66.0 cm. What is the ac)u dg2r)u vi ,5bnxzn3celeration of the mass?

  A rotating flywheel can be m k*pskh5j vnlo9bqhaq71 (* t(;+irp 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 inertial+ lt /,x-j kkmsh1r /9ujid9ou m1sz07d0rqp 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 ra/rm 8dhx v+0cest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the spv /r+8xdm0a hchere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. +9shq ae0 ful *kqru1; How hig+eu0;q1lfr qku 9 hsa*h up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and g v+;/v.k aejgh:*c oq2znt:za mass of 0.20 kg is released from rest and allowed to roll down an incle ;zk.g2/tc:vzovg+n q:aj*h ined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of masnji a w92(*kdjl.g ,srs 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assum(g2,anlw dji9.*rsk je 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 1k2 q o6vy:e 2 1,un)lpzvv3ipikrs;o$20 \; kgm^{2}/s$ 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 qlw7:k9vpnv1cq(r e4 i *0 pvu$5.0 \; kgm^{2}$ 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 w,e .qnu-km2 gs9gmp*extended has a moment of inertinq9*ue,pmwk gm -s .2ga 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?