Angular displacement is usually exkpz2hwg ug/+6 at( (tepress in units of

  Angular velocity is expressed in units v u l0 79oom4p;igqlfr0lj -3vof

  Angular acceleration is expifgva9+ x r 2f t8aak4t8;jx5kressed in units of

  A boy and a girl are riding on a merry-go-round which is ,fw3(,xlo qamxn j6r)turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. ,3mnxjoqwa,)x( 6r fl Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is tuohvt/:hio+d i9-rnf73l4 uao cu u :*lrning at a constant ro7/hond *- :9fahioit 4ul:+luc 3vurate. The boy is near the outer edge, and the 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 b8ha2jqp5a b 0at a constant rate. The boy is near the oua aqph058bjb2ter edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a mex/h thnqi+ -1krry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has t/ x1hi+k q-hnthe greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning atiseh 86y;:gw6w yf sl+ a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential accelerations6fhgyi e68lys w :w+;?

  Consider a rigid body roa h*w4h/qjcy 7a e6t+(5()qjroezv that is rotating. Which of the following is an accurate stateae r*rq(hhe5avj)(4+ t ow76o jyzc/qment?

  Rolling without slipping vbyf*ihq:d,a.po ny 618.w rpdpb 1z(depends on

  Two equal forces are applied to a door. The first force is applied ;nmf hc rwto-e/52v7z at the midpoint of the door; the second force is app;we v/zhnfc tm-27ro5 lied 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(urdkra(:mj asp:2 5 n. The first force is applied perru52d amkr(j:: (nsappendicular 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, perpendicular to the d3bh g vmr/iza-fq;q,lrr67u/bwq). ooor. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second iqbvq qrrrbhm 7-)iz/ ga6l3ufw; o,/.s

  What is the quantity used to measure an object's resistance to changes in gl2gbk3dy dh618a j4rcy ue/q*cyy(7 rotatih26/81 ea3 4bj g d7 yduclgyk*yy(crqon?

  Consider two uniform solid spheres where both have the same diameg 940zxv0jm*sgtqfkz9 b ) sp.ter, but one has twice the mass of the other. The ratio of the larger moment of tggkq z)04099j*.xsbfv m spzinertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has e 9z,v1/( vhhpcjq8 xltwice the radius of the other. The ratio of the larger s/9 qlepc8zvxjh( v1,h phere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice ta0 cho/pew0ip tkc.11he mass and twice the diameter of the other. The ratiow1. pkh/ cepa0io0c 1t of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increa4 q0gli *hdt0:bvc 8xc ,gu9wised to 2M and 3R, what iv d wu4c,lgt0qc*i h8:b0g9 xhappens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that oev9p(tfx3v9 object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 lyf*w3d6 jtth 7et (388acarrMR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic enejdy cwta8 6 arefh8t r*t33l7(rgy to its translational kinetic energy is

  Consider a motorcycle of mass 150 tybk1 7 xk:fh5kg, 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 of the wheels to the total translationa 7 y1kh5:kbxtfl kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M an6 yoi1t*5z3hpp r:yu id radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline5zt3o6pyh:1uy r*ii p depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an in5+gh7ws )h;d g prc:r+wanh+sn+tv,nclined plane starting from rest. The angular; s+ dv 7rhncnw +)tagn5wg++hp hs:,r velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of parti(dn yl(q0(i kqcles changes when a net external force acts on the system." Thisiq 0(l(qydn k( statement is

  In what circumstances can thegm)vs cx:)rcsc2 uufr.6-g5 j angular velocity of system of particles change without any change in the system's angularu2ccxm6rgg vf. 5uc-j))rs:s momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictioxpcdn 2y;1y12j .wnnlm( 2yr; rlcwu8 n which may be present. What happens over time to the Earth's ang(y;x2w;c1uclrnn. 2 j1l 8 pm2ndryyw ular momentum about the Sun?

  The Earth moves about the Sun in an elto(6ri :oqytw -vo8 ydj hdpv2b;5m ;8liptical orbit. As the Earth moves close to the Sun, then which of (5t;d byp i oomw8oj t6:d-vv2h8qy;rthe following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a faste-c mzny3dl)6c+k z8w spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about zd)8cnylc -6z + wmek3the axis of rotation?

  An ice skater performs a pirouette (a fas sfajo 02;qm:1 tmb*pkt spin) by pulling in his outstretched arms close to hjqsm:0*bp1 aotkf;m2 is body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) f/:( kbp kdx7 ;i-wjghby pulling in his outstretched arms close to his body. What happens to his moment of inertia about(kx:7fgw;p b- dk/ hij the axis of rotation?

State the law of conserv)mlts x jx+;r9ation of angular momentum.

  What arc length does the Earb(x*0 ka94t8gzlonxuth travel in a three month period in its nearly circular orbit about the Sun with a ra8gzx4kbx tu9*(onl0adius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distanxkx4xu -rzp4c .f;e8ace does the tip of the second hand sweep through in 3 minutes and 45 seconxe;fpc- 4 .x 8kruaxz4ds?

  How many rad/s is 25 jk4 q3wla-2+uop ftr: revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in zbr xt3 kq:y494.0 s. What is the fret ry4b z3q9kx:quency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenl e5v77 bgtv 18zmfcv1cy of 0.40 kHz. The period of v7clbzmt e758 gv11fvits rotation is

  A phonograph record s3.vqbl,e 6 q8nw1smo rotates at 45 rpm. Through what angle does it turn in 0.20 ssqblqe8 sw.o1nv6 ,m3?

  A wheel of diameter 26 cm tu0i 2mfvr1y. fm3 +ncn(ucgm 0rrns at 1500 rpm. How far will a point on the outer riv yf +.m 002n c1grucmfn3irm(m move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutiow,pl r*ukfs,8j). xnrns in 4.0 s. What is the average angular fsn)wu *r pjr,8k.,xl speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. q+1 o fixeq8p6opzt:4 yd1;qc What is theq do:4 1q6ytfeqzicop 81;p+x linear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6+ii(ebungtj 3 n;c,;1; hrfm g.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 the trip in 1ut; nb,(+;inhegjm 1;irc3fg2 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/mdw k1asu 5,dfu/ q6d9-b2moes. What is the linear speed dua6-wd9ke1,mdo bmf2s/qu 5of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length.vj:zep7v)3 hfnp/ m/x If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cox: / n/pep3mvfj vhz7)rd?

  A wheel of radius 1.0 m is rotating with a constant angular speed3f qb,xd u+cx3 of 2.0 rad/s. What is the centripetal accelera xfdu,xb33qc +tion of a point on the wheel's rim?

  What is the centripetal acceleration/* 8f(ltn//vgjp qwfoh 3/wed of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when theh*fwq ove3dwtfj(p///gl 8n/ bike is moving 8.00 m/s?

  How many revolutions per minute (m*d h.gxzv ius11/bjg6 05 gscrpm) must a circular, rotating space station (r = 1000 m) rotate to produce an a 50gcgs u 1ivs/6hx*bz1m.dgjrtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of af6asl1j wk5n h2b:b6-wh. qe20 m/s. The maximum centribw6b.an q w:j-h5se 1l 6fkah2petal 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 ex n622.qel; ..zdzno*+pmirr r z*du 50 m with a speed of 20 m/s. The maximum centzrnm2ido6 r2 qz.edz;unl+.r*x* .p eripetal 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 57 : i/-dqq,i ygihptjqsy t6xaq0 5;yto 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 stri iy-i ,y;q :07tysqta/pi q55xjhgqd6ng is not to break?

  A bowling ball of mass 7.5 kg 0 ctlhawnv:m)n)2udupi/.+p and radius 9.0 cm rolls without slipping 10 m down aut/lu p)m)w.+apnnivd : 0hc2 lane 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 w o9xet11-v/otyfal yke ;hx3 uxdi.x+8y, 0 tlith 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 acceleratioq1 /i/ptls6jz n 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 radius automobile tire rotate after )fhscq+i)zm6dxst)99 d o r9h starting from rest and accelerating at a di) 9xqhhcr 9zf9)os)t dm+s 6constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerati72)y6.1vlsgegmry-3k pca vx ry:ie; on 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 a con71*it twgo: iqstant angular acceleration i 1tgw*t:7o iqof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of /-npd.e syl*y 6.0 rad/s while turning through 2.0 rpd *sl/ny.ye-evolutions. 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 oq.d:l9/dx 4qgsd9vn,an u bx0ver a distance of 115 m. d:g0d9d q9 x l4sxbqv.nnu,a / What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down ukfnt+;(mr1n hy: : du3( lvlqwniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratioqhl w(n (+:my:dnuf31;trkv l n?

  A wheel of diameter of 68.0 cm slop3cnmi xb/ *3sws down uniformly from 8.40 m/s to rest over a disimnpx*s/c b 33tance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratorpx3rh+x gm )ofc0 w;t 40ierl,y rotates at a rotational speed of 3600 rev/min. w03 xp) txgohl;e4+rcr m0if, When 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 to a torque of 90 Nm. If a8;lvka /nqrs6i4a ub5 30 cm long wrench is used,as4a5 ;blrn/ i 8v6qku what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. Iqm7ug0b* 91k hty ius5f a 30 cm long wrench is used, wh7y*b 1k0ui thm5s9guqat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia(j tzpc0b .w,xl8b bn9 $3.00 \; kgm^{2}$ 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, mpu,4):/ j.c+vtbo eqwsqolpjnv 4d/(ass 2m is at x = ,4 po npje(c)vt//: 4 j+bq.qludsv owa, 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 axis thought t86(zz2c xirg9rf xl0v * 4tubehe 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 angular acceleration of the cylin*zxigz e(80blt2u xv r49r f6cder?

  A solid cylinder of mass a lgni ;8cg6pco)d.s/10 kg is pivoted 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 radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radg o/gpci)asd c6.8;l nians 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 robzuq , i+l:s;(izos3j d 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 end is :iu jz(sl+oiz;, 3sbq ML2/3.)

  Consider a bicycle wheel to be .exq3j9 64fl q gqf6n zlb fxp-x)j*x;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 tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slippin x)4-fjfq*zx;fxqll .p3xje6nqgb 9 6g?

  A 1.53-kg mass hangs on a rope wrapped jdji8*1ew.gi -r7ru n around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration1rwdgj.re* -ijiu8 n7 of the pulley?

  A 1.53-kg mass hangs on a rope wrappedg q/b6qdw0d38a.e)el x wavomc9i3 o : around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accel la8xo.q o3wimv )g/wdq: 90ec36e baderation of the mass?

  A rotating flywheel can be used to store energy. If it is required to store shezz,wh2 0 e*$1.00 \times 10^{6} \; J$ 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 ineomq04 x;ohcs qs3d)7ou/z9v o rtia 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. x0 0:nyz2w,;nzcbivf 0 kg and 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 when it reaches the bottom of thzw f,2z 0i;n:v0yxcnbe inclined plane?

  A solid sphere of mass 1 66a5au;t: x) h0 smxlf4vnxsd.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comu)66l: mn vh5fx;4ax tsadsx0ing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rel 09yn m84yoaazeased from rest and allowed to roll down an inclined plane. How fast is it movin ny m9za4oay08g after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippiti )h.ilwfr 5 4(7b naz)t6sosng down a 35e incline that is 7.0 m long. Assume i7ow z)htrs4(bnfsa 5i. 6l)tit 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 mom.y * lccve+c sw(gxe6.entum 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 inei.5 mkthxps7j03edp:e ; a3cfrtia 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 extended has a moment wc2 rdlg3y ( m9w/qswte.,zw/ blk -g4of inertia ol,t9 b2 wyrw//3eldz4w q g-kgm. (cswf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?