Angular displacement 22 w7 7zs6dwh0oomj+ionw7lca q5zj1 is usually express in units of

  Angular velocity is expressed in uniz: xj/ n94zw7+t tcgcats of

  Angular acceleration is expressed in units oc x3.dz.j; yl1hh+wdof

  A boy and a girl are riding on a merry-go-round which is t;- q vu0nljy)dm:yn6vl *tg ;turning at a constant rate. The boy is near the outer edge, and thelu6jgvvd0y n; ty:q)l- ; *tmn girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridi g5hku pt0i5x z+n8s-ing on a merry-go-round which is turning at a constant rate. The n zi 5ug5pit+8k h-s0xboy 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 rf/ gblh0cpxu 7yw0f8r/,kj(n iding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. xwyf(70gbnlkr 0hjc/up 8 f,/ Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turniy3wyus7+kv2kvq,q)1 3.tqjm5 ts s vong at a constant rate. The boy is near the outer edgeq 2)7s,m53yqvy tvto .3uvqk jsw+k s1, 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 whi-p5 gqpbh6 2qxch 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 tangential ag5h q-bp2pxq6 cceleration?

  Consider a rigid body that is rota,wqx. p1lr 9 eq)hoq:bting. Which of the following is an accurate statement?q. 1,): l bpxqhqro9ew

  Rolling without slippp: jqnmr5-0 iu vnfzg+y.mbh 7047dhwing depends on

  Two equal forces are applied to a door. Th)t ,gib xh; rqsgt5q-c.r; g-ce first force is applied at the midpoint of the door; th; cibxt q,). g;ts--qrcg5rghe 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 first for13o,: w2xkj2repxqgs ce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exeo:1k exsg 2pwxr,q2j3rts the greater torque?

  Two forces are applif jogq /uoikn5 )t.3+;guy+oied to a doorknob, perpendicular to the door. The first force)3 kio+g+f.otu5n;/jyo uq ig is twice as 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's resistance to changes in rotatix/p 5,l-0ieuvk ob5 f*vgm*dq ox/5 ed,*50vg*-pq folvu bmkin?

  Consider two uniform solid spheres where both have the same diameter, but4s h 7h pi,+k:mdlf8 uei4v8pt one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller 7h4s:8h pmi+vu,le k t pfi48dmoment of inertia is

  Two uniform solid spheres have the same mass, but one has t j0o7c /m ktiss-*cz0cwice the radius of the other. The ratio of the larger sphere's moment of inertia tojcizkt-s 0m so*/c0c7 that of the smaller sphere is

  Consider two uniform solid spheu( 3; v n xitr,lw orof/2i)si/p+c7zo)2 jkmrres where one has twice the mass and twice the diameter of the other.osif(7rxo/23r c,vi w;nl)to )u/irj mzp 2+ k The ratio 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(9kc*j-tus i f tfwly r20y3-k increased to 2M and 3R, what happens to the sphere's moment of inertia about a centr -jr-wu9i2tky0*fl kt(yfs3cal axis?

  If a constant net torque is applied to an object, that io*r9 - ugz+o g7 5)xq4comae/qxc9xpobject will

  The moment of inertia of a so, )/q5z h:xeg9a lyq88efwjuj lid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of itsj,j/glu:fx 9eew8q y 85)azh q rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 2 0rs dg0lbb9a150 kg, 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 translatiog rl as029bdb0nal kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls witho,9 zzkw*jm;n 0sesmzix 0 8o.mdb.ba5ut slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline j kzs 05z.8 x d9ewbmz.msbi0,mno ;a*depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an invv8m1a6v kog5 clined1v vako 6gvm58 plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sy+,q pt 3bjja7tstem of particles changes when a net external force acts on the system." t 3jbt ,ja+p7qThis statement is

  In what circumstances can the angular velocity of syst p865-ypgqb0wz *m9 hcsgb *oaem of particles change without any change in the sys*mg0o*sc q59 8b6wzap pb hy-gtem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whicyd v(m6p*r- ka,,alnj-m dgv.h may be present. What- vg*amd ap,y d-kmr(.jl,v6n happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movesux i*pgz. ;g ofcurg/z 7-0vw+ close to the Sun, then whg- +ug if/0x zv.puw*z ;7orgcich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his omxr7oiv6vbm(53/ )wx;bke en utstretched arms clek(bx7o3vr;6w eb n mi/ mx)v5ose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performsr );len3 -sdsx a pirouette (a fast spin) by pulling in his outstretched arms closelsrs) -xd 3;en to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fasbncskad8 * -o/t spin) by pulling in his outstretched arob-kn/cd 8s*a ms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation o- xdspn:8++yvic gav6 f angular momentum.

  What arc length does the Earth travel in a three month period in its nearly:fyuhs js)+: vr b1:vnlvu 5d. circular orbit) :vjudsr:bn +f5shv. lu:y1v about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Wh .);mqvie gjgtes./s4ir 1y a3at distance does the tip of t4 m1 erjesvy/)gi.isqtg;a.3he second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equ(6jo im+z qnf9ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutiora.til t+p; 4) izu 6*fwpt)qjns in 4.0 s. What is the frequency of the wheel's rotatw ;4jrlpt*)tt f i) q.+ipau6zion?

  A pulsar (a rotating neutron st8+5akgygb iz 9ar) emits pulses at a frequency of 0.40 kHz. The peri5kzb g+g 9yia8od of its rotation is

  A phonograph record rot2m07lcfl sh1 cates at 45 rpm. Through what angle does it turn in 0.20 s?ml0f7scl21c h

  A wheel of diameter 26 cm turns at 1500 rpm. How fadh5 2rgni.mr 648ytlrr will a point on the outer rim move in 2g.58 drtnr2 4 iylm6rh.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. nj xi2sm27 cbrxh*ch;:-wi m0 What is the average angular speed*hswx0jcib :cihmr;7mxn2 -2 of the wheel?

  A bicycle wheel rotatesgb-2-jtdri v 1 uniformly through 2.0 revolutions in 4.0 s. What is the linv-- jrd2 t1bgiear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resor4ltkizslqw 6 +r27 f5ht carries 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 maw7k4h+ l2 l5ti6zrs fqke the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular s bia l9v/7tne,,j hw,bpeed of 2.0 rad/s. Whatb7j,baw ,i e vl9t/nh, is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed 1g ip27qdl1-9px pfn vcutter is 0.16 m in length. If the motor rotates at the rate of 20 repiv7 f n-g1ld 1ppq29xv/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is roeiqdxuv 5d3*w y7+kqz6t 9f k/tating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'st qyiqx f 59 wvdk6+*3k7ez/ud rim?

  What is the centripetal acceleration of a point on the perimeter of ax4l vf0qfd 4n/ bicycle wheel ofvn/fd x4ql0f 4 diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per myfu+a+ s30xq v. 7p:cg9 v/vgpfrx xsyf(1+zkinute (rpm) must a circular, rotating space station (r = 1000 m) rots p++ v1y(g f/r0uxqg+.v9a7z xk 3fxvcp:sfy ate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiukop zp79-jf qe un2ge. /k+zz2qxws-5s 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictionxqq9j/zk+zg -sp-5 pwofz2ku2. e 7en) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curveks;gu4von) h4jvl*td c,0y*y of radius 50 m with a speed of 20 m/s. The maximum centripetal forcel, gh y 40dj;u*tn4ykcv)sv* o (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached w97inf ao4e :xto 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 if:7oe9n ai4wxs 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 withouqp n jad7zjmm2 g,3e-5t slipping 10 m down a lane aj35,jg2qdapz m -emn7 t 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 a+ tw u5 m,9umo1 geyk5xckv8z0ngular 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 acceleg 9 9kk35gmzg e,sjwt,ration 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 radi*(ew v;i)quelus automobile tire rotate after starting from rest and accelerating at)w*ueiv ;le( q 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)u ;jrt88f aqkq+6vm h acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decele37wihvmyg 0 2mrates with a constant angular acceleration of m0vwmig 2h73 y$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angqqjwgc) ,b t l2,x-jg2ular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angularlj ,)txg,2qg2 qcb jw- acceleration of the wheel?

  A wheel of diameter of 68.0 cveo ./9hf+vyhhy7 hr;m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates i ;hy+7hvo9hf. rvyh/ en coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over ah .j c8x 2tr(ovhc rxwyt4 b1v1o72vq0 distance of 115 m. What is the angularw4b0jt vyho xrt78.o x1h(cc 2vvr2q1 acceleration?

  A wheel of diameter of 68.0 cm vz dnc+.m69/ctmm:e oxm29vm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wh /m9c v2mvdxmt9z:o+6. cmmneeel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational4oa m;ovg*9:: vn xkri speed of 3600 rev/min. When switched off, it rotates 50.0 times at a cov: *ar 49xi:nog; vokmnstant 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 torqdxp 18s6(2 u0juorpnahf5( iaue of 90 Nm. If a 30 cm long wrench is used, wp6pxsha a8 j2d5n0ui of(u(1rhat is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighmjb 7nul8n6hl8nzy (up32g6r tening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force n 6 l bn6murhj8u7p(n38gzl2 yrequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti)(i5fabzufltohmo;( j; gx6 1 a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follo0j;lc zjx sab.0xy.1ows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of i x;.acoj1bx lj0z.sy 0nertia about the origin?

  A solid cylinder of mass 10 kg 5y4, kv s7fphsv-k7ahis 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 Rs75vvpkk fs-7a h4hy, 2 = 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 piviuh*kx/ 9h bex*0jlu5 oted 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 r*0 uujixlhx* / hb5k9eadians 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 en2j;*zwb 1 zibgd. The rod is initially held in the horizontal position, and then released as the zjgb 2zi1*bw;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 radiuc1dl z ) b*sgngs 6ww/o(i)tx*s 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force * nbc)l*gs iwwts(xo16 /)dzgof 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless djzfsm 7 8b7uqf ;)oo.aisk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleras z 7ufb;of8jm o7)q.ation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frv -cca+ndyr/0d v(4aiictionless disk pulley of mass 7.07 kg and r/(4 n-0vdyac+ cravd iadius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is req*zn)avk/wr6 j uired 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 ofsz;fnzcl 10 pqbkw-mn: ;fu43 $5.00 \; kgm^{2}$ 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 fes2 xnqez (l1*a /+pu0.010 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 the inc+u(qp * l/esa1f2z enxlined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a spe8 gy4zir:, zbnmsm46led of 10 m/s. How high up an inclined plane can it climb before coming to resl :4m6,ribmsyzg4 zn8 t?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed ish cwo; ,a:)rto roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3c);i ohws ar:,.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without5vxmci vt*-5;zj w/ro slipping down a 35e incline that is 7.0 m long. Aw *moricz5v vx/j;5t -ssume 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 ch;dwlqne1 5gtod814 j(c5cz zbanges 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 ofaw g3jrs7h7b)p9f r3rmmmk8r 0, e/ )lijzk4r $5.0 \; kgm^{2}$ 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 extepumlj7nc0 (884(n;x:tpb efr b1np0hn pm8x nnded has a moment of inertia op40mjxnlh8 pnmf7rp0 (n(:u8en ptb8x;bc n 1f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?