Angular displacement is usually expm 8 yi-ihven:fqveg4i /7x1 r6ress in units of

  Angular velocity is exprt seczg bnn,r7e6-) )xessed in units of

  Angular acceleration is expressed in unitsf). cc8:ttru7z(1aj hc.aa xs of

  A boy and a girl are riding on a merry-go-round which is turning at0*pynr /6zmiiecw nk 5zo+(; q a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?6z5 ennq+iy km 0r(ic* /oz;wp

  A boy and a girl are riding on a merry-go01 n/nz1 bk+eh sge(no-round which is turning at a constant rate. T1znn(ek/1neh0go b s+ he 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 uecv /4 xiz;hp)i7aq*at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater lva/7 )zqi4pxc;eh *u iinear speed?

  A boy and a girl are riding a c,hu10uhfy;sb5p w. zmerry-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 haub0s;hu,h1 f5 cy zwp.s the greater centripetal acceleration?

  A boy and a girl are riding a mer:s(u(* yyfmerswj fg3 ; z*ju3ry-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 the greater tangential accele; uj ufz:3jsyfw *e 3sm((ygr*ration?

  Consider a rigid body that is ro* .wrl, cnhhed -47 )0c as+lm;uzcikutating. Which of the following is an accurate statemenkc)i - h.wz;0m7rl ch s+nua ed4ulc,*t?

  Rolling without slipping zy.:xyvsm2 9bs rv0hn7i6qv5xgh(lnd/za9 : depends on

  Two equal forces are applied to a door. The firsrn 08 9eipr9ctpcw) /meg-u .ht force is applied at the midpoint of the door; the second force is applied at the doorknob -r9g).whtm nu9cpri0c/pe 8 e. 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 force is a)oi l,(0gfo hbpplied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts t( ob)gl0if,ohhe greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. c z 6c4+ *w6v,kv(zpt.e fnpay The first force is twice as large as the second force. The ratio of the torque +e*z( f6ayzw . knvc6,4pcvtp of the first to the torque of the second is

  What is the quantity used to measure an object's resista (pdbro( k sv(0.5cijance to changes in rotatipr(bvoad ( ik.(c 05sjon?

  Consider two uniform solid spheres where both have the same diameter, bug ew48wdf*flo9 9anz z 9 y,9mjrtb3u8t one has twice the mass of the other. The ratio of the larger moment of inertia to thatawz99efd*93omr8 ,wtu y4fb9z j 8nlg of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one h i wg4mf..cc-h bc-zaz90ib 9v;d 6niias twice the radius of the o- v4 ci b0;imn6zdfb-cig9 9cz.i.h awther. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twicec;oth7k,.vy6wf ffm5ege(0 l the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of wk5.,vl feg0 mtoef7 h6;c (yfthe smaller moment of inertia is

  A uniform solid sphere has mass M andv*v0azlgnx 97 radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis?x*g 7l0vavz9n

  If a constant net torque is applied to an objecwgx1kb r3f43gda z 5z;t, that object will

  The moment of inertia of a solid cylinder about its ax-u3h 0kb-8q.8g, cqfbg rv mrqis is given by 0.5 MR2. If this cylinder rolls without bgr,3g mu.qqkh-f8q- rvb8c0slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whic7tzvx ti4u6u:z2h4 /dzsn2d ph 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 kineticu:7 ztp4 /ui zsxd 2nt4vz6h2d energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M andsd 9+z9 2a7;vtoi 9r/rlrs den radius R rolls without slipping down an inclined plane starting from rest. The linear voird; a r9d9tsz/e+ 7rl9nsv2elocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an cj hm3x)1o .jq;lm; -pvwq/lginclined plane startin;3jc;-oqh jml/ 1vgqwlp x.)mg from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of partico a3 munefqgxu2t2e:l15 -7ggles changes when a net external force acts on the system." m1fnegu: o t2lu g75-gea2xq3This statement is

  In what circumstances can the angular velocity of system of particle w)(t,ql l2ahes change without any change in t(),2e llta qwhhe system's angular momentum?

  The Earth orbits the Sun in an ellipticl,+a cy;y+l 2hotm8mq hb-ds:al orbit. Ignore any friction which may be present. What happens over time to the Earthh lq,2bh+-s8c:ya tmymdl; o +'s angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical o lmz x06dhn++orbit. As the Earth moves close to the Sun, then which of the following best describes the omh+xl0+zd6 onrbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spilz coe)+1 lnz;tmh 4 *6pn,enxn) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotztx pln*l4 n+)emcnz,o e61;h ation?

  An ice skater performs a pirouette (a fast spin) by pullin znwz j*1-d9lfg in his outstretched arms close to his body. What happens to his rotational kinetic enezz1*jfd 9n- wlrgy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche ivs.wzu y79+qd arms close to his body. What happens to his moment of yz.svi7 q9+uw inertia about the axis of rotation?

State the law of conservation2sy(-ljsx0 ik85 txa n of angular momentum.

  What arc length does the Eareeiz/.*v6 t-rhi i 2frth travel in a three month period in its nearly circular orbit about the Sun with a rairev-tr6/i ie2 *hzf.dius of $1.5 \times 10^{11} \; m$?

  The second hand of a cloh(r n1uwwr 6o(ck has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes andn6h1wor(rw (u 45 seconds?

  How many rad/s is 25 revolutions djak1kl8 p 0 orm7w)e0 f7ezi)per minute equivalent to?

  A bicycle wheel rotates uniformly t wfs5pyomjxn8f ,4 3-5.fbh jihrough 2.0 revolutions in 4.0 s. What is the frequency of th53y x8 5mnipjws.of4-f bh jf,e wheel's rotation?

  A pulsar (a rotating neutron star) emswat xo er.;6k8+uj*bet qj1iz .(q /mits pulses at a frequency of 0.40 kHz. The peri1 kozeruijtw.s*(+/t6 . ; qqbj emx8aod of its rotation is

  A phonograph record rotates at 45 rpm. Throug4v 3)n jto i5*yhculh7h what angle does it turn in 0.20 n3v l jo5h7h tyui*4c)s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a w8ta3 bn8d+ty6vvg9 m:v74 a hl:eidl point on the outer rim move ina7g8wbla9tdy hdlt +v4 36m::v 8nvei 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sm6 zfaf7 ;xpxyt)(dfg0e, 5et. What is the average a5e )0gy 6pdt7fxxtz;a(f mfe,ngular speed of the wheel?

  A bicycle wheel rotates unifh(.jx. + f/)7tajxtbi ,imbfyormly through 2.0 revolutions in 4.0 s. What is the linear spej.fa m,x.b(fhbt y)i7 x/t+ji ed 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 r 2936z9 slfbous :q58rzf-emn s6ge acable 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 cao:b qs5u3e rf6s9z- r fs682zglm e9nable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is r h:e8, wv*oygzotating with a constant angular speed of 2.0 rad/s. What is the linear speed y:vg wo,*h8ezof a point on the wheel's rim?

  The cutting cord on a gas-pn jrx)*( obhb*7:eo wmowered weed cutter is 0.16 m in length. If the motor rotates at the rate we mx:**ho7(jbnb r)oof 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 angular speed of 2.0 rad/s. s ;cn+1, bytty What is c+ n1byt ;,ystthe centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acc ;gs-yg lvqbezcv b1-.-d:dego *4j*seleration of a point on the perimeter of a bicycle whlj-s:1. yvg4voqb g- dg* c-zsb*de;eeel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (;l es 0a1u-utm0)v ehgrpm) must a circular, rotating space station (r = 1000 m) rotu)hg01ea-v;meu sl0t ate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiusznk)vd vv8ki *jn6y 57b h0r:k 50 m with a speed of 20 m/s.8in: v*bk hvj7ry 6d0kknzv5) The maximum centripetal 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 50 m with a spee /wh6vg 8,v r adznfv)*)qsap5d of 20 m/s. The maxhq fz*a 5,)p nw/6avv 8g)srdvimum 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, attache/8 znay9d,vjzd to 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/a9d zzy8 n,jv 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 without slipping 10 m;r lvq p-9k7.8jxdzeap6bg +y down a lane at 4.3 m/x jg9p kyeq va7-b r+d;lzp86.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 accele mhz 49qlhqc i4p+22vxration 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 p0nt 7o.j vh vo-n-t ,cn6ue+da 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 automobile tire rotate after startin pa)chqv 73;zq )s z*,iuamurbn0u1w)g from rest and accelerating at a constant anb;aq qzu*)z um)nucs,v07aiw3 1rhp)gular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceler 1g:l )f( fmvuh 38bi9,iaotvfation 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 co 3qk((fra+ryr nstant angular acceleratfk+(r (a yrrq3ion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 radn8wq xxw5 w. pq9mcwcp4ep /go,64n; d/s while turning through 2.0 revolutions. ccw pg o/m68ed5pw q4xn;4x9qp ww.n,What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm1p/ r ph,rns /l+dxot*7nwv q1 slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revol1r/vnxorn/d q1p* s7+ p hltw,utions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to/dhl*cw (6b/e -fs2npq i6dyn rest over a distance of 115 m. What is the ang*nye2q(6p d/ dcs-bwih f 6nl/ular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovess 0i661iat0s kq.xqa xau;w4r a distance of 115 m. How long does it take for the wheel to come to theixa a1;us6aqx0.ssk 604wq it stop?

  A centrifuge in a medical laboratory rotates ,n. lwyv7*v* ,k8osgnbdm ig -at a rotational speed of 3600 rev/min. When switched off, it rotan,v*wkg 8ilg ,v-b*d msy.n 7otes 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 tighte;cb1b18jo :py8y( .dgxde g jmning to a torque of 90 Nm. If a 30 cm long wrench is used,y.mjb1d(g8 de c; yx:og1j b8p 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 torq/jlpq*ij zs iw2a+o0kxpq;;* ue of 90 Nm. If a 30 cm long wql k2*+pjqpi* ;s x;iawoj0/z rench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in)1x i5 hl(bzqjp +iu4wertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follhp9.ak gx 6q:dows: mass m is at the origin, mass 2m ish9 .adxgpkq:6 at x = a, 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 fri yjh+l(q)(kv ictionless 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 +l)yqiv(kh ( jof 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 thorpq: ey7 s0/aiught 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 ansy:7aipr e0/ qother 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 initially held in the hokm d+aql60 9n:bqywt) rizontal position, and then released as the free end is allowed to fall. What is the angular accelerat kb :n0y6+tamlw)dq9qion 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 o5f;uf (jn+hdmv7 lzz-f radius 30 cm and mass 1.5 kg. Neglect the mass of th zf7ld5n huj-vf+; (mze 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofv,o tw9)yd rp5 mass 7.07 kg and radius 66.0 cm. What y) ,95otpd rvwis the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pul/se:j nc prwzq/ 19 i+(7klkmno;r 4boley of mass 7.0join;q/l 47 wb mk(zn:1+rk9recs/po7 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can b) fz7zbk0uylnu)b i/0 e 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 inert/8bm vjjq9 6enia 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 3 u;yzq.qeq7w and radius 0.010 m starts from rest and rolls without slipping down a 1.0-mu. ;yeq73 wqzq high inclined plane. What is 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 8m;i)pk d83qlzhu7 ny) ym;fsspeed of 10 m/s. How high up an inclined plane ca3)yum nlm)7k88 ; hzfdy;pqisn it climb before coming to rest?

  A hoop of radius 0.50 m and a mat, kq gon/7ky)6hw*x nss of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast iqt,o n xh /7*yw)kkn6gs it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 k6q4gkurh b7hhs ,:d5fmv z9* xg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of 6q,7h d*s9vfbzxrk 5hu:m4h g 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 chg -g+7f dq ogtx4wzi /ec 603r-y-bcwpanges 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 iner.z 0 m26war;3un;sk ( lointkutia 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 t-l /friso6 dy s96:onq-o(yqat 5.00 rad/s with arms extended has a moment of inertia ofoft66:q(/ -niqyy sso-od rl9
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?