Angular displacement isrpo/,9wan zhip.r ner-0b - 0j ctq86s usually express in units of

  Angular velocity is expre*:sj1 nxoo;d* nfo6 kossed in units of

  Angular acceleration is expressed in unituc73:vhld8gi-s5vg - osi6 brs of

  A boy and a girl are ridin) foix(w;z+uw5j -8lssger z9 g 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 angular displacemex(5sow+jzr g wf l8z);e9i-sunt?

  A boy and a girl are riding on a merry-go-round which is turning at a constanvv up c6xee +*noz -45(ricp9it rate. The boy is near the outer edge, and thp-9 +4v5irpxeie nc cz6o(*uve girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are x5 o:n2ghv 2er 2nown9u5. gb4nqf: aoriding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is cbv ou n2:4nh9qga2:o55 fe g2. nnoxwrloser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-k (4q1lc.v5s rmzyqv0 round which is turning at a constant rate. The boy is near the outer edge, while theq.rv05m4zv1q (l ycs k girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-routimru-w e5j(7 nd which is turning at a constant rate. Them7rei tju( 5w- boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is ro4h+p +h woi+p qqok1 edv3gi:5tating. Which of the following is an accurate stateme+kgh1+w op iq4o: qiv53 pd+ehnt?

  Rolling without slipping dep1;r9rh aayvk fd :fc9ol*: g9wends on

  Two equal forces are applied to a door. The first forg9l :fuqwrs6us vt10o) k9q/dce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Whickt1069rvwg)dus/q9 f o u:qslh force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first for dke,t2e o)yk2r ax.d+yl41ylce is applied perpendicular to the door; tr41l,ydk.te ly22e xd) kya +ohe second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are appli-k6m dnd 7z4tjh.z9gw ed to a doorknob, perpendicular to the door. The first force is twice as large as the second force. tnj46d-hd 9.7 wzzgmk The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an objece8/d fnv bxc: nz.4x2xt's resistance to changes in rotation?enxcbz v fd/x24:x n8.

  Consider two uniform solid spheres where both have the same diameter,tgxw. ju jf6f6kxzzn74+( /b i but one has twice the mass of the other. The ratio of the larger moment of inertia to that(xk6 w jjxz7+g.t 4zbiun 6ff/ of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has 1(t+84ecz7fybqr y -ligru: bcss* ,s twice the radius of the other. The ratio of the ruiy7f8c,- ( lst:1gszcer qy+ 4* bbslarger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and h8 kbtovm bfwxr u4 b9 +49hx2/t+cl5atwice the diameter of the other. The ratio of the larger moment of inertia to that of the4ax9bolvt9mw /kc tx2rbb +h5uh8f4 + smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2g, kl ss6dvs7.t u b67.;qbgjtM and 3R, what happens to the sphere's moment of inertia about a central ab,s; .ts6j7bkvdsq67 t. lg guxis?

  If a constant net torque is applied to an cj(/iuqp;-t yvr8jgi1r t.rp)z2nh9j:fip) object, that object will

  The moment of inertia of a solid cylinder about its axis is 83kh ihcxwqh- 4zlgq4eng 95 ,given by 0.5 MR2. If this cylinder rolls without slipping, thihq 4hkcgn 5g98x,43wq-l ezhe ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a masso a0quhxsv2 -jn7 yy83 of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total tray- svhyqan7o032x ju8nslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withoutk5:j4,fh ksr d slipping down an inclined plane starting from rest. The linear vel fkhr k4:js5d,ocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rf;4pvipz*z7 a olls without slipping down an inclined plane starting from rest. The angular velocity of a v;4zfz7p *pithe sphere at the bottom of the incline depends on

  "The total angular momentum of a system of p0prsk9k/pe acd,lagq; /yo;5articles changes when a net external force acts on the system." Tpg/a;o9l;cr,ps eadyk5 qk / 0his statement is

  In what circumstances can the angular velocity of system of particles chan,:c8 j pn)vacdge without njd8ccva :)p,any change in the system's angular momentum?

  The Earth orbits the Sun in an elocecc 4q v7p-g,cqr.1 20wfzuliptical orbit. Ignore any friction which may be present. Whatqcq re21zp fo-c7vc,w4.u0 cg 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 moves closeof ovkwk:gl 51fgqe e-vp4 8): to the Sun, then which of the following best describes the orbiting speed of the Eartle)k4k:og: -p g18eqv5vowf fh about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulli*9 3x,mf 81td7 qajdz81s uhwtkbl,wrng in his outstretched arms close to his body. What hap fjdh18qt1, w ,ksb9lrtx 78ma*zdwu3pens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin :3bo0h wwfttcsx+o48 g in his outstretched arms close to his body. What happens to his rotx30obo +h c4tw8 tfs:wational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b ;9-vyfe2sg i+7qe roty pulling in his outstretched arms close to his body. What happens to his moment of inertia about t t-;ivo9+eeqr2y gfs7he axis of rotation?

State the law of conservation of angulap+6d uu6l- a6 78 w5rxhvvwuiir momentum.

  What arc length does the Earth travel in a thrr(/ d 0n4p:9rusg ncckee month period in its nearly circular orbit about the Sun k9sru r (/:pncn0d4cgwith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a p98p/ vaypuc);ysr9 cup 82huclock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 min ;ppy/uu8 cu2yvhspa 899)rcp utes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent t-l+v5a*3 vpb a, hrqpro?

  A bicycle wheel rotates uniformly through 2.0 rzz/ 2*fme, k2/j7gm cnadvn :zevolutions in 4.0 s. What is the freqma gedc mn:/z,2 /k*zv jnz72fuency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fr ,ilmi; .83*sfraw mrvitr y**equency of 0.40 kHz. The periyir,vi3**tmwaim;r rl f.s*8 od of its rotation is

  A phonograph record rotates at 45 rpm. Through whatp-1i4r/a;ymhl u q cl-7 dwns8 angle does it turn in 0.20 s c-ps m 14/-;uh nia8dqlrwyl7?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a ./veip2krtvt) x:5 pwpoint on the outer rim )x5/kerwivtp2t pv: . move in 2.1 s?

  A bicycle wheel rotates uniformly through2 ,(-cz2rebv ;faaik r 2.0 revolutions in 4.0 s. What is the average angular speezfa ( i r;-,22cabkrved of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4ar pze6o i(vq8n-;t1 m.0 s. What is the linear speed of a point 0.10 m from the centeqnrz v6o- (pmi18 eat;r of the wheel?

  A cable car at a ski resort carries skiers a distanceb(as 0gou fj)f-c5 rk4 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 musj(4fbfocs5-)r g 0 aukt the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed7;:w 7s2kfndgi d7z lll ))ftc of 2.0 rad/s. What is the linear speed of a poinsc l l 2):tdffl g7ik7wd;7zn)t on the wheel's rim?

  The cutting cord on a gas-powered weed cutxbicqcz,3 i*dl5,3-x w0ya tj c:wtw5ter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is thtc ,y z0wcqcd5 l- iai3xw5,:xb3*twje approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angularxcrrx72 9 w 4bx z9a:e;/jqd da(8grui speed of 2.0 rad/s. What gi49z:rjwrc92erd a (x87 xdq/;baxuis the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on mj9)1 *oxho blthe perimeter of a bicycle wheel of diameter 7 bojx9 ml*)oh10.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotxx j87yfa,m 1iating space station (r = 1000 m) ro, y781jfmx axitate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a sxs7rb ts0vq7+ peed of 20 m/s. The maximum centripetal force (provided byx+t07b7sq svr 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 radiu+.p :kbx6yfurv -vi-.m+rnkz s 50 m with a speed of 20 m/s. The maximum centripetal:rx6 z.bm++uypivfr nv- kk- . 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 to the end of a 0.750-m string, is whirled aronn: h7)r. eas)ioeue)und 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 string is not to7ei .o)hs ) n:nuraee) break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slippin(g89tl qhhp1iou/z t/ g 10 m down a laotuhlpg/z ( 8qti1/ h9ne 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 with a constant angular accelerationumv40k+n cs/ltg/ t5a 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 assal/2jw:c + n 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 ral bkd21+ojt1f,w3rq i i 364oskkdb 6kdius automobile tire rotate after starting from rest and acceler3wli1i23k4 ksr+o 6 tb1 q6fk dd,bjkoating 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 an*r), y+ v1sduaemj he)gular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s 6r , q:pmpdvpss.1zz))z9ign9wo:hbdecelerates with a constant angular acceleration owbpsri oz6vpm 9nd qhzs :.)9p):z1g,f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while wedyjbt7f- p )r2x* 0dturning through 2.0 revolutions. What is th7e2d)ryfx 0btp w-dj*e average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overv d-4,mbhne t.5 i god-xz62fz a distance of 115 b2oz h.mgd6 f-tx,e 5i ndv-z4m. 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 froml)i oyy6tk 27n+dk5xi 8.40 m/s to rest over a distance of 115 m. i2i l5t7yk +oydxk)6n What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforikm6wl xf9xb 9*rhi92 mly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to co 9xmkfxi 9hw29lir6b*me to the stop?

  A centrifuge in a medical labo1 ghb v:z9rr( jjy.qd)ratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times aty (jz:bg.h)rd 1vjr 9q 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 whef1deo 1 q30t05fflg srvne;4 qel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requiredf1f o tsqfde4 lnvre3 g10q5;0 when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90spifn r:85 h1g Nm. If a 30 cm long wrench is used, whapi8r: g1sf nh5t is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner l tbeakgp67m zy931)i:zltv- tia $3.00 \; kgm^{2}$ 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, ma aimn3h+ wcn /unlxzs61 *qds;sg+d 36ss 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the s x /dzq3w n61smi6ndh 3+cul; *+nsagorigin?

  A solid cylinder of mass 10 kgvy2n cat3+q54snr0)x.k s x zo 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 exeacn2 zsk+4 nx xrvtoqs503.y)rts 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 at (e*d coe74ofxis 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*t 4de7f o(eoc 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 hingedw sx97h2 h(heo q+tab/ at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as ibht h /7 (aw2e9+osxhqt is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radic)bw eo;xj8 8bpcy r :m;ghh02us 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of bmc;x:rjo88) wpb0 hhg ec;2y20 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 pullelwat7 2jr, pr+y of mass 7.07 kg and radius 66.0 cm. What wprj,+2ra7 tl is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a ro2/. wle 1npcnlpe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of nw/ll2n pce1. the mass?

  A rotating flywheel can be used to store energy. If it is rw w0tw-w7d wn(e8 zx)g-ssy tr; jxm/2equired 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 h;tvl7v9s6 sb $5.00 \; kgm^{2}$ 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 0.010 m starts jqlz (i5zs9x-cx: /v)3lzfrhfrom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottomqr-fszj vlzhx5 x (z)9 lic:/3 of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010/2qx(etx;w60iu0dw gyt /z sd m rolls with a speed of 10 m/s. How high u(s6ywd0z20t u;eqtwi/ d/g xxp an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m andt(hxcgk, b47 jwnzor4 mcv8se+ p6h.2ve+q f) a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How j 7+vshfcb o+4tmknezcx ,. q24v h(egrw6 8)pfast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kgnklk2;: pkf0 o and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume i0fp oln2k k:;kt 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 changes byy 07z zbv2vy;ljd; b.e $20 \; kgm^{2}/s$ 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 g 7vnp ;x+gyj)moment of inertia 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 of iner+-lh ak;o fcx (j+cx,x 6nl*.r +klsobtia of oj6kxnr(, ah*x+-lf.+ xsclb;+ ck lo
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?