Angular displacement is usually expressgj6;oz9a zz lrj)1 r2wj*3 lxz in units of

  Angular velocity is expressedmtn* d:)yrl:qln(7ylj3-m lu in units of

  Angular acceleration is expressed in units bomaush cmg883r31rp-8 i/ p eof

  A boy and a girl are ridingyff k3e6) w vr+ka*jamv3)66os8ogqw 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. Who has the greater ags)+avyjvkao3w6 ro fw)q8* 3fek6 m 6ngular displacement?

  A boy and a girl are riding on a oapj tppk*6 2y,om9 t5tu g-4fmerry-go-round which is turning at a constant rate. The boy is near the outer eatyt 2,p9p4omkogtu 6fp 5j*-dge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridnkvya (m2;0z9 u3,y( svrrb qping on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closerr(,03 zv vskmnp byqu2(;yra9 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 constant rate5-tyy/dq+ dllo o1qp6 . The boy is near the outer edge, while the girl is dlpy+qo1d l/-t6y5o qcloser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turningh u o7jxls940r-wyq 1x at a constant rate. The boy is near the outer edge, whi xq hy0s49- 7xr1luwjole the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate s2dz:fjmv4 p (ktatemedfkj4z2:m ( pvnt?

  Rolling without slippig3,2q n gvm5x*uo4dx,r8nryo ba2* lhng depends on

  Two equal forces are applied to a door. The first folcg9kn2mt 952er;mt c,wsj4lrce is applied at the midpoint of the door; the second fort54el2jl9c 9m2cmk;nr w ,sgt ce is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied xk +f7xt z6btp p0)p5vm9 2xxdto a door at the doorknob. The first force is applied perpendicular to the door; the secxt+km 2 pb0zdptpf6) 5xxxv97ond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiculo9h01 mv;tiimt7f t4kar to the door. The first force is twice as large as the second force. The ratio of th70h v9i ;4mfottimkt1e torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance toktboce j;y/lh/f3 h58 changes in rotati8hyjb;eo ck/5t /fh3lon?

  Consider two uniform solid spheres where both have the same diameter, but oovqm6 i8liac3 rp.n+ wtx4 -*mf)b)nane has twice the mass of 43)ftnrlmc bpqxiv.*n6+w oa8m-a)i the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the samerur( 9itcrk3 2z0pw05ohjy 9i mass, but one has twice the radius of the other. The ratio of the la5 w oc930ru(r2 jizhk9yprt0irger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sph:)2 fpfjtx bh290 *djbpw2ewteres 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 m 22wtdje:b*)2 0p9txfhj fbpwoment of inertia is

  A uniform solid sphere has mass M and radius -p-18j vo ea9hlb: dhcR. If these are increased to 2M andv ohcjbpl8a1e- -d:h 9 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net tord(b,rylg42tg soc8o3 que is applied to an object, that object will

  The moment of inertia of a solid cylinder about iqbjg;v.cd 0i2(3pj. 4:dsbb eigay7c ts axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kip 2c734s.cggie(j j;b q:0ybvbda. i dnetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one ;dw k)s/x8u27rb4du ho:qwbg wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the ro u7d 8b:r4)q/dx;hsgouwb 2wktational kinetic energy of 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 without slipping down anvehcrw5,h3d* a nd 3:b inclined plane starting from rest. The linear velocity of the spher vd*53cb ha3hed,n:rwe at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wi7d65wg 5xtm7n j 1hylm(bxwy8thout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the iylgxh5jw(6xbmw7751ym n8d tncline depends on

  "The total angular momentum of a systemsy ngsl*tv57bvs7pf3 gd(6 +t of particles changes when a net external force acts on the system." Tht6dntg7vb v3f+s gs7*5y ( pslis statement is

  In what circumstances c.bft6 hszmw m3z4ek(/an the angular velocity of system of particles change without any change in the systemhfb6t(k sw3m./ez m4z 's angular momentum?

  The Earth orbits the qa i l(i/a,uyplehd6xq6f:23 *gpnc( Sun in an elliptical orbit. Ignore any friction which may be pr6hgqda cyf6u(p:a/2xel n, ql( *iip3esent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliu53 dtsdplr:8 ;i2n fmptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earn i2d 5t8l: ;furs3mpdth about the Sun?

  An ice skater performs a pirouette (a fast spin) b7f b(0 cf 0o6kootv,ezy pulling in his outstretched arms close to his body. What happens to his angular momentum about the ax f(oc 07o0bf6v e,oztkis of rotation?

  An ice skater perfor2th b+hbln a l2cd7mkw)z-82ems a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the ahh)blct2 w2lnmz 2dak - eb78+xis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchede 3kwjog,w 9paf2x+iej0j1d - arms close to 0k,3 jaope- we+ig9dwjjxf12his body. What happens to his moment of inertia about the axis of rotation?

State the law of conqh dfrx,6xwlsp* /g3dxv 59a+servation of angular momentum.

  What arc length does the Earth travel innqdtif+- *i*7c nu 7in a three month period in its nearly circular orbit about the uii*n q*nf d77c i+nt-Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What diiri.bojw8/o+ txk0 8a stance does the tip of the second hand it8owr /k.+oi0ax jb8 sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions *wj6 pg( pg9irkr,4dmper minute equivalent to?

  A bicycle wheel rotates uniformly throug9q dg87e- i-co /cjgcns) jrxgr2(f3th 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatiiqsj(/cfdg3)trcr 9jgn c2--8o7ex gon?

  A pulsar (a rotating mci75n/al,lfoc) /a dneutron star) emits pulses at a frequency of 0.40 kHz. The period of io/ lil, 5cama7df)/ cnts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn i8m/jju /kv (ol0bbmc-n 0.20 obv0km/8 m-jl/(u jcbs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will aw.c0c y pdu06n)jv1 gh6t qg 0q.l3cmlys)eo ) point on the outer rim move in 2.1) p6y1cc3unedvt)sq)og0wy.m g. hq06c0l j l s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4vhdp-,kcu r5v wk(x1k gof*3lm ,f*:m .0 s. What is the average angular speed of the whoc1u kfvvp wfk m,:mkhg,rx(*5 d- l*3eel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What)k 1copp56ksm 7xxy+uf9mt 5-kl q3)hjz+ suf is the linear speed of a point 0.ym1pkx7+ p9h56os +-lsj5c)f)tumx q3f kkz u10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6v cx0q k an4m8 ,akw,hdn2.a/d.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 pullwx 0 a,nnmaad,84 kcv/dq.h2key rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angula)xqmq u8xta37wsw 3/g))sjbc r speed of 2.0 rad/s. What is the linear speed) sw w/xm)jtuq3g87sb3c)qx a of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. hg-i5f1gbg;i (w wu5fIf the motor (ii;f5- g5wwg1hg ub frotates at the rate of 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 a constant abi (xh5:nk r (g-9tvrkngular speed of 2.0 rad/s. What is the centripetal acceleration of r:v(9(hn -xkg bt5rika point on the wheel's rim?

  What is the centripetal acceleration of a point on the nfs6yxupbx q) z/h( .+perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8. )pfsh6/ n.(uxxb+zyq00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space-f2p cudpw83t8)pr/x3dtol 1hu q4qf station (r = 1000 m) rotate to produce an artificial3xqf-uplr 1842ot)dpdc3f8h q/ put w gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spe1v2 rc1lwximc (tv-d;r k3 ij-ed of 20 m/s. The maximum centripetal fo(3;i- j2mvrxr c-vdik clt1 1wrce (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 with a speed of 20 m/ )tilsssx (a:(s. The maximum centripetal force (provided by sssi (sa:t( x)ltatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the yi ,jcw-x7 clf 5hp;4yend 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 maxy4 7;iwh5,cxfy jcl -pimum 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 wi6 + snj(uoh()d uxeil7 76an(r9dv djvthout slipping 10 m down a lane on u jd9 iadv(l7ud7+(6re hn x(vs)j6at 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. mdf0oicgpzi ( e5r8y a5o8,abl3,fv 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 o(o2p,tb38 tusrlh;l 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 radius g;j:vn/*y* g l;gek+vcs0 vu nautomobile tire rotate after starting fro0 v+u :g*gyvnkn j*l;cs/;gevm rest and 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 an angular acceleration of n-*efs9s9h gy$4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates witwciqg i)6- qk4h a constant angular accelerationw -c)qk i4giq6 of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rexzfas7+c4g*w s8o:je st and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is thexezso7j+w:84 a g*cfs average angular acceleration of the wheel?

  A wheel of diameter of 68.0i1 ,8 + rqd3s)nj huor(cnzgnngb8;y0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. g s)nhr(yq0ro,n+g8b nj;dni 1c 3u8z What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to resvpq) l m.a/:jet over a distance of 115 m. What is the angula ) eqjlv.a:pm/r acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to dxaquw-pt2k3y ;c)* erest over a dy;2qe3ucwdat* kx-)pistance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a me*m z; +f9dbzqqdical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a coz dfb*q9+zq;mnstant 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 aat /u rw64:0j:e-fe uy/nyoce 30 cm long wrench is used, what is the magnitude of- :4unu/y:w6e0 eryc jafo/ et 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. Ifz-*frjpq22e a34 c*i/dh; jryx6n ibx a 30 cm long wrench is used, what is the magnitude of the force required whenqr-*peyix/ xhrz6j jdc2 if2; * b43an the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertianbb436,.tfa +tvj axc $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: 15(n tuiwls/plls-6umass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the m/un l l 6(sul5s1iwtp-oment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about mt(0k3hqnr 7bh-r6b. x6 i jyra 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. (See Fig. 8-1.) What is the angular accexby3 qhtikhj 7(m6rr6r bn0.-leration of the cylinder?

  A solid cylinder of mass 10 / hc*;x bpxw(b2-rwzb/b ii-e 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 thewer/;x wbpcxbzb*b( /i--i 2h 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 initiaw:hzfl a63z8+hfi:8e p7 absnlly 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? (8wb3fhap8+6: snhz:fz a lie7The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of rr iw n:ay1/(wqadius 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 ra :(awy1rw qni/dius 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 adr bx. r,z4y;wpqzc3 0 frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What p4cdzxr,.ywz 0r3bq; is the angular acceleration of the pulley?

  A 1.53-kg mass hangs onh9rydm) /g;mc a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mas)m ghd ;9m/rycs?

  A rotating flywheel can be used to store energy. Ifz 7 o+7zvia*znst. jq;u 3q,wc 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 ygm6 .)p* pyug ao46jp$5.00 \; kgm^{2}$ 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 03 rpp/ em3vz/u.010 m starts from rest and rolls without slippingr3mp3uv/ /zep down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of massrili:cfc.s69 hgpg* 9 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inc*.r ci9ghc 9s6pf:lgilined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass )z- x5 sak6phbof 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?za6 bxkh p-)s5

A solid sphere of mass 1.5 kg and radius 15 cm kl-d-t 1vgq1f7 vu bg3rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Th -lb7 3kg gvftu1v1-dqe 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 iej-97lelkjc84) yt/bph q (l$20 \; kgm^{2}/s$ 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 inertipr uy0drj 8f/0a 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 5renj7 a2c.hi k 7e)-,zjxmh5i.00 rad/s with arms extended has a moment of inertia-jeri5 j)h2eiknh .77cx, zma 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?