Angular displacement is usually express in units y;) 9whni *yp8ps qqy2of

  Angular velocity is expressed in 4ncm)0ugl .2b *;9tanwaxmv sna.pc(units of

  Angular accelerationot7hw 7/brq 8m is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turninge cu/9++ mgvwg at a constant rate. The boy is near the outer edge, and the girl iu/mcv ++wg e9gs closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a c,t vgzvm(q0jo/-i zr1 onstant rate. The-vvgt jzqoi (r1/z 0,m 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 at i4ul rvbpa3 ,wph6; 57qt wvl0a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wh7vr;w56vi pp34ulh,t0w qla bo has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant rcw7 bu8sklg37 ate. The boy is near the outer edge, while the girl is closer to the center. Who has the7bsgwc3 ku87 l greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round-(k8hp kewts;pm/ oku) b anr1/.5 ysw which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangento; mebu/k(r8s1stkp /w.5 y -nph )wakial acceleration?

  Consider a rigid body that h);tc;y ej)zr is rotating. Which of the following is an accurate statement?h ; zje;c)yr)t

  Rolling without slipping yl2 jxpp8q ad41gw 51udepends on

  Two equal forces are applied to a do*1k42 crduxxr or. The first force is applied at the midpoint of 21crxd4xr u*k the door; 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 doorknobsfyk yq7;i+6y:ch6ov. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts okif7;y :+hvc66 qsy ythe greater torque?

  Two forces are applied to a doorknob, perpendi cz 6 ;+xsvsp-w)0pk pt-hv vyd68x(rfcular to the door. The first force is twice as large as the second force. The rati)z(+k0ytv6sp cvv- x8 f 6wdphx;p-sro of the torque of the first to the torque of the second is

  What is the quantity used to measure ap+f*6w 9z4r dbxrb)zpn object's resistance to changes in rotation9wxdr+zrp* b6b4 z)fp?

  Consider two uniform sm-x()ovyxr:yv. nfbi ( x p4)holid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the hf)xn brx((y vm)xy-:ip v.4olarger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have vo b9(9 c)o;mp3espg2h yeo/o the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller v;y3oseg ( ophmc9 beopo2/9) sphere is

  Consider two uniform solid sph3;:tlelrw* t (c o5 rwxdmm (75xdjpy1eres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momenx7rr y(dcjot1: x;5l5ew3tm wld(*pm t of inertia is

  A uniform solid sphere has mass M and radius R.kdis) km(sq 8d rh91p+*ac. nz If these are increased to 2M and 3R, what happens to the sphere's moment of inertia hn9k)*zkd81d mcqr(a ps +.is about a central axis?

  If a constant net torque is applied to an object, that obx2hx l3 (g/fybkgy96gject will

  The moment of inertia of a solid cylinder about its axis c s(b;5po2x6i s.xmsgis given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel -w7-2wf 6z -avd imbhy)nxdzym/7jx/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 energy27w- x/wd-v/m yyz-x 6)ja bifnmh dz7 of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an iqb)5 wz:;r:cuquxjhxd oqu77,j *w3g nclined plane starting from rest. The linear velocity of the spcxhu *,w wdqbx:7o j3zjq :5)uur7qg;here at the bottom of the incline depends on

  Suppose a solid sphere ofyicj znf.y,)aa polj2d- 6.xul-q+v 1 mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom ofvx2p6au j1oc f y.izn la+qdyl,.-) j- the incline depends on

  "The total angular momentum of a sq-ov5dai ,k9t1q 0gfntz-a r:ystem of particles changes when a net external force acts on the system.itonzgvq afq 5- t9r,d :a-0k1" This statement is

  In what circumstances can the angular velocity ;c5wltjj/ lpoxz +oaogb6 ek8 z*7z5.of system of particles change wit5bg 5otjzp+j c zlowl/x6; 8 zok*ea7.hout any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptica43p bibq3sl6b0cr 3zlt+6 hu)froql 3l orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mo u z6p3)qc30 ro3fqibt bhll+6l4rbs3mentum about the Sun?

  The Earth moves about the Sun in an elliptical or l3 pud3 a,/9fg8y93 roitabuobit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earf3ub/y8 ug33i l9 a,rd9aooptth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre/umo*yiycr 7 f*i fzb1mu,:c:tched arms close to his body. What happens to his angular momentum about the axis of rotation?c:u *7 i:mo ziy bry,1muff/c*

  An ice skater performs a pirouette (. ovawhjyk b+ 6ueqd/sh -734sa fast spin) by pulling in his outstretched arms close to hihk4d+/av beq3soh-7uy 6jw s. s body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b2v )zq-cvyce .y pulling in his outstretched arms close to his body. What happens to his moment of ivy 2vqc z.e)c-nertia about the axis of rotation?

State the law of conservation of angu7axnen(+ d 6.z a s pdb( oh+knjyx1+yirm)-k;lar momentum.

  What arc length does the Earth travat:2yev2uq q 9el in a three month period in its nearly circularqvet9q2 :y2au orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a bytdlh85 .o) ulength of 0.30 m. What distance does the tip of the se t)bh8doyu5 l.cond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions perd7epc7*l ul h, minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolut,ohh osane09lx2w*3 eq 0 q3crions in 4.0 s. What is the frequency of the wheel's rotatisal e0*qe3o nh0cqo x392wh,ron?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Tsrz6zpr t2yjq3l j g9:5)ja8hhe period of its rj5hy2g s6az9t:r 3ljq rzp8j)otation is

  A phonograph record rotates at 45 rpm. Through what angle do)*p5 syyujm:r es it turn in 0.20 syr)y*p mu5: js?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wile;65j a0vaxo rl a point on the outer rim move in ev;o ajax506r2.1 s?

  A bicycle wheel rotates uniformly thro57hkakln: )krnpf )k, *i,lkmugh 2.0 revolutions in 4.0 s. What is the average angular spe7)arkkn:,*lkn)kl 5himkf ,p ed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolution/,gvg wy36bw lw/(*h hu r,qnas in 4.0 s. What is the linear w/ *g36y ,vqhnbwg,a rw/lh (uspeed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabl. 2+qoo7 fxm:dvm r/jve which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rota:jf o m7 2mvor/.x+vdqte for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m isz9k4bhy h8be1 rotating with a constant angular speed of 2.0 rad/s. What i194hb k zehb8ys the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengthh n)pqj,ik * v(5 d4nqixvk0x*. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of th 5)4ikn j0pkhxx*,i(n* dvq vqe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed ote4 2gd* f(kqeix.8defc*la5ume gfut 5, .o6 f 2.0 rad/s. What is the centripetal acce5 8mq(.f5kx, *.4dle * geu2uo6f egctfdietaleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycqmv m;zp.t2 dg uh v:u8hvf61/le wheel of diameter 70.0 cm when the bike imz/8 qhhd tvvv1u.2 fugm p6;:s moving 8.00 m/s?

  How many revolutions per minuteqdd*p:/gb2h+cs,1nww* b s do (rpm) must a circular, rotating space station (rbshdod1*:p+ d qwb c2,g/w*ns = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve ol nacvx;k 3hvhz:16b(x6 f p )a-u48n6wafgagf radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) isc :a ub6ax 6-(fhf)4;lva1xg3nk6g8ah pvnwz $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat aui0; jh;j ;trcircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by tu;;aj 0h;rjistatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end ol30dbp*t nz 8df a 0.750-m string, is whirled around in a smooth level tab n* 3dldzbpt08le. 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 not to break?

  A bowling ball of mass 7.5 kg and8+a cpx/qusantp6q 9gh;6w 2 a radius 9.0 cm rolls without slipping 10 m down a lane atp s tpw6qua9;xa 8g+ac qh26/n 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 acce /pxf;r w-r2+c vygwf9leration 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 acceluv + 5dvr*6jyzk4,x lheration 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 starting fro-bkf9v+hz b q f+j(kn 1aiq9l1m rest and accelerating at a constant angular accelerati9 1kqfik(a1+fbq+ zh-vnl j9b on of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and harp0 wvzqxk)c+,b-/rgw3l.ty s 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 decelerates wi.hpupj97 f ;xwth a constant angular acceleration o;h fwpj upx.97f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an a:l7yveooi )r 2;b.3bo db xepv*.ei2bngular speed of 6.0 rad/s while turning through 2.0 revolutions. What 7x.3:ropvbeo2lv*b 2e.; ib)ei obydis 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 obshm dao5-ag kl-2g8+l3h4ka distance of 11l+gbkmkl a s-d5o 2h4hgo-38a5 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 unifoblsd afcmi -+r-j:)d:knh m 82rmly from 8.40 m/s to rest over a distance of 115 m. What is the angu:f8sm-ma-ih+: kd jc2r )bdn llar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8dra u2,z qe9pl u2t/p1.40 m/s to rest over a distance of 115 m. How long does it takepdu/91 l qzre atu,p22 for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationa2fpml.x81fgd*t ei e -rde)i-l speed of 3600 rev/min. When switched off, it rotates 5m8ti *)xderf gp-ilf. e1d2e- 0.0 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 tighvi7r q6w 7 (lx)dzzer1tening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force zz7xq)e 6 r 1i7drl(wvrequired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90jkj 1 q-js pta14:xu8f xg,eeu31ax8x Nm. If a 30 cm long wrench is used, what is th-uxq ea:sf,xxx g1ja 43juk88p e jt11e magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ines2bns5t3 uqf0l;cy,y rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule +j3do dt 6qcr9 .iuvyr9ok*n3is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the 96 vndr*d+iu3ry joqk tco 39.origin?

  A solid cylinder of mass 10 kg 6 b1o4z,toy3y b3,q/s ncb ig.4xmmyois pivoted about a frictionless axis thought the center O. A rope wr.1 sqb4xy3my o3mbti, ,by 4g c/6zonoapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about 60,crtf ylo :id;b)yr a frictionless axis thought the center O. A rope wrapped aro0)o 6: ct yi,b;dyfrrlund the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 i -wmxx4eyc1 x+tf3e6 vn54 gqhnitially held in the horizontal positn1e x +yg4 q-3xfvhwtmc6e54 xion, 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 ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm andn8jl(q(h1i wd 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 4.0qlnw18(i (jhd 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 q usmyq5ech7*.6 ) y:i9jkxoi a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is theyq hokem59*)yijui 7q6s cx.: angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapu7 o 6lqg;ctml0;v ;dcped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. m cl;cvtdl;7g; 6u0q oWhat is the acceleration of the mass?

  A rotating flywheel can be used to store b -g6 yicl/p7n;mhrp e9;5tquenergy. 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 inertia of t i6t.gs0j5rl$5.00 \; kgm^{2}$ 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 axpnu-:j;t lj g(n2/y.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What i na;/pu gjnt2y(: lxj-s the speed of the sphere 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 156f mwu sz0w4kww2z8o0 m/s. How high up an inclined plane can it clim 64o 5uk08szzf2mww wwb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 )fjun d+hu z:lpv n-97kg is released from rest and allowed to roll dljdnh+ u u-z:)nvpf79 own an inclined plane. 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 rolls en;t)f3gnbr6 without slipping down a 35e incline that is 7.0 m l)egr36bfn; tnong. 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 momen nj7/mzxvba:aue - v -*alv0b6tum 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 inertia ofxu3 387 fpjb1xc2p qpm $5.0 \; kgm^{2}$ 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 extcaej3wtu(;8vn/n 0v +rrp b lp. 6mr*mended has a moment of inertiw*r(vpcne p+ b38/rlvnmmjt60u.ra;a 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?