Angular displacementout8()l cf ot5 is usually express in units of

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  Angular acceleration is expressed i*7be 4zamvi-km 1r. dxq +9o;+gjwbfpn units of

  A boy and a girl are riding on a merry-go-round whicmic1lq)uln/mm31c w( -*ybphh is turning at a constant rate. The boy is near the outer edge, and the girl /b) -3wmlyu i1ph( 1lcc*mqmnis closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding ogsytgv4fe :0fip14l* / *iklm; yzw l5n a merry-go-round which is turning at a constant rate.*s51:* /y;vm igfif 4lwt ly 4kzpe0gl The 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 nz/fm1 (wvg17 lwhrn*yex5z7which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to then*zyz7/ r( 7g mwnewhvx1fl 51 center. Who has the greater linear speed?

  A boy and a girl are ryz9e vn8ki x )evn4cq+rp t3:4iding a merry-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 centripetal n3k4yi tx erz:9+)ec8nvpqv 4acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a cols aw9,z)md. oeh/4wwuc / f7xx r+ul:nstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has toaswz x/9/e+wuw h u4 d.f7 xml)l:c,rhe greater tangential acceleration?

  Consider a rigid body that isr b .dzl.t7fr5wuh:*e* i ky5o rotating. Which of the following is an accurate sta yh *kuf.roi7ld: tzre*5b5. wtement?

  Rolling without slipping depends o2zi:nbtwgj4 . n

  Two equal forces are i:du redu(o7) gl*ci4 6bi5rt applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greatidig47duu* o:) r(irb ec tl56er torque?

  Two equal forces are*:fq)fc e e4ul /ylpf: applied to a door at the doorknob. The first force is applied perpendicular to the door; /e eu:4lc f:f fyqlp*)the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to tebnw x+9:9ds/2 hzcmlhe door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secondmcsehn :2lb9dz/ xw 9+ is

  What is the quantity used to measure an object's resistance to c7 3x:uf1r g bt-se1us; nxnz)ehanges in rotatig3nbnet sf xz) -:r ;u7uesx11on?

  Consider two uniform solid spheres where both have the samjij1x:su,wcy 1a :hv 6qbc(e :e diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of thebh::j ,i(c cjsaqew x1vy16u : smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the r:sj rnn54 vlanm2z +rz -:(fljadius of the other. The ratio of the larger sphere's moment of inertia to tr:r4n - + fnnl zaz(jvm52:jslhat of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the de,6mh tjp4 (j ns,qf (tml2ba;iameter of the other. 4qm b,6n je2 pls(httm; ,j(faThe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has masfeuk7gaut 8 i) (f26sws M and radius R. If these are increased to 2M and 3R, what 2i tu)kuf( 8e67 afgswhappens to the sphere's moment of inertia about a central axis?

  If a constant net torq l(v6 3 rjphi)zch4yr, 92vptmue is applied to an object, that object will

  The moment of inertia of a solid cyl4durfo8 v2tqgj47 )oyinder about its axis is given by 0.5 MR2. If this cyu yv 2f4ot8d gjq4)ro7linder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wk)(gid yip z1 0kq(o.5 5vcujbheel of which has a mass of 10 kg and a radius of ibvg.5 kd0)c(kuo5(qi pj yz130 cm. What is the ratio of the rotational 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 slippingc vzd d)5ih5 m0k:u6ag down an inclined plane starting from rest. The linear velocit0kcduh 65z5:mv) gd iay of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without skxz x)ju c w1/5+u.qeelipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of5.k)ee xxuzcj+ uw /1q the incline depends on

  "The total angular momentum of a system of particles changes when a net extern0jg3l)g h e(,uz vgpb,al force acts on the system." Thiehgulb0(z g,3pg)v, js statement is

  In what circumstances canqpl-s -a:nv8 2 trf:qr the angular velocity of system of particles change without any change in the system's angular momentus- qrn: tr-afl :pq28vm?

  The Earth orbits the S3 fuam23i;x3ua o gu:bun in an elliptical orbit. Ignore any friction which may be present. What3u3:ouu 2iam bxaf ;g3 happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipti1y av o,0.qocw j3i(wjcal orbit. As the Earth moves close to the Sun, then whca,3jo.wiywq j0v 1o( ich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pig/8ctdfosw+4xpvu+g4/vx+yf j- c x ,rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rj/, tv4+wg+c 4x+ 8gfvpu xy- fo/cxsdotation?

  An ice skater performs a pirouette (a f:kd lo2kfg--t3 9p 9 cbhv+nx,oh 1yygast spin) by pulling in his outstretched arms c hck,1d3g2:o99 yy-tv +g-ohpfl knx blose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedw8rn v u5c+k;qpw9,dp arms close cd,w urpv;n+qkp 95w8to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of anguled: +bny 5d*dxar momentum.

  What arc length does the Earth travel in a three month period in ita6rr7*ybye4gg li+i 7s nearly circular orbit about the Sun with a radius of r4e*7aigr gy+ 6i7lyb$1.5 \times 10^{11} \; m$?

  The second hand of a clock haba .wo*eq7c1o +p p8ogs a length of 0.30 m. What distance does the tip of the second hand sweep through+eb*go 7cop 1o8pqw.a in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per mi8y,3sv 1h(vd , jg8xs upanzfy j8*bw4nute equivalent to?

  A bicycle wheel rotates uniformlyd l7 rm75rcw6s through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatil7s6m5r wrc7 don?

  A pulsar (a rotating neutron star) emits phiwsbif 8,tz bgs duh-)q6n+* 97oh+w ulses at a frequency of 0.40 kHz. The period7uz w) q,++tis*sih-wfhd8bgoh nb69 of its rotation is

  A phonograph record rota y+sha8ad/1/,u di+idhfk ant5 1vy(ntes at 45 rpm. Through what angle does it turn in 0.20 sn distdhu+aah( v8 ky //n,ifd1a1y+ 5?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wmj2jhdsmfy 7xbwre9*5 0+ 4va ill a point on the outer rimx m*a07rj5vf49m+bedy sj 2wh move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thdv v;exyc22. 3kjs duym9 eg, ,rdd8-ue ave3 ;,re vdde d-9 d,y.k 2yuscuxvm28jgrage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions 8 euy4+ yscbp7vj03kxm ik m0f,vrz23 in 4.0 s. What is the linear speed of a point 0.10 m from the centerpy0yvmcks 40u7 xe j, 2f+rm3iv 3bkz8 of the wheel?

  A cable car at a ski resort carries skiers a distance ofpowj-l vb;1b5 6.8 km. The cable which moves the 1 wblob;- 5jvpcar is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is txv/sy 7m(bj) rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a poismx t/( )vy7bjnt on the wheel's rim?

  The cutting cord on a tz1** u9ahohe gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, wt**oh au 9hze1hat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant ang i.kl-o gg4bq5ular speed of 2.0 rad/s. What is the-k.g gliq4b5o centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point ymvs2 (p1:) n4mtufsnon the perimeter of a bicycle wheel of diameter 70.0 cm when yp1tsumfm:v() nn42 sthe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatinglyb)(4x+cwm lqt 6pe/c4 /af j space station (r = 1000 mmf+ /ewl/c ajqc bp(y4 xt6l)4) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a ff9+j km qs-shya+: 5xvlat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal foqjvs a :xy++-5mfskh9rce (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 cuhr+7vywy6thsx rdv8r5 w c3.d1: fz c(rve of radius 50 m with a speed of 20 m/s. Twftxzr7h hc r:v(6cd. s3r1yy+5v8dwhe maximum 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, attached to the end of a 0.750-m string, z.///gctewigi*g5 rm is whirled around in a smooth gc/iitw*z5m .e//grglevel 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 to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slippin mqoymki;s6x,j j;w*wh ;we 91g 10 m down a lawq ,jxh; i9mksm ej;y*6oww;1 ne 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 gm0v2l3c c-h 4x ovqn pneqgk )67:)whe fv70fconstant 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 a constant angulaq )c9ir5 lal24 zzn:l:8rswlh r 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 aua92 0ybr+lm/fb* quaetomobile tire rotate after starting from rest and accelerating at a constant angular acceleratmlrbq+uybaa* /92e0 fion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hal+iryik kpfj :j(,/q-:5 zd ucs 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 with a 5* upe fb.yn9vm93b 8zir7yxxey-t.pconstant angular accelerax9vt- re8.b7zxp*m 3iu.5y bepfn9yytion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an anc jw11s3wpu-zt,i6dpgular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accpw ,tjizds3 1pc -wu61eleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest khahf+wpl 9/(over a distance of 115 m. What is the total numberaw h9/(k+hlfp of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dosqd66,tr38te n *o xikwn uniformly from 8.40 m/s to rest over a distance of 115 m. What xrisd,e6no3t*8k q6tis the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to daie n0u 8*;; +pw*faal..lkbps qxh 0rest over a distance of 115 m. How long does it take for the wheel to come to the stolea08lu wbqk.x.;ipnh *; 0ad+afs p *p?

  A centrifuge in a medical laboratory rotates a9m phph/7faa(t a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a consam(h79 ahf/ pptant 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 torquw n zky4ue-1q:e of 90 Nm. If a 30 cm long wrench is used, what is the magni 1zu y:n4ke-qwtude of 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. Idk f*vyo 7:-kbd-zm oi5ktjuro; 3 4a-/( eibif a 30 cm long wrench i; 7kdbi5tkvob4rmo i: f(zkoe *d /y-jia3-- us used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 0ud/(;hpyh l n 6;aodcfh;iu7$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeledpux9 0ew5l2 me,fq0i u as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. lem up,x5 e 0w2iq0uf9 What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frq y asgumr m 07edr 697 0(gu9ghcct)phe9v42gictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a9rcm9 2 4gh77 e tghp6m0c0dyurgqg9ve)(s au 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoughtw:nj/mm i*5a u the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = mjau:i/w *n5m5.0 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 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 inbb:ks. fo i564brnw ;a the horizontal position, and then released as the free end is allowed to fall. What is the angular accel fnkba4.sbirb ; o65w:eration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle whee1qe-d 3zhj;( zt2k u9 w;hvttfl to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N ist9zftv eqj kt 231d -;uh(w;zh 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 ho.*pfmc0- lrf 3 al:ea rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 6e.h :mlapc0rolf*-f3 6.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p xn :60(amkjpx+5ltpf0em( rgulley of mass 7.07 kg and radius 66.0 cm. Whet0mn:06 pp(x gr(jk mxl5 f+aat is the acceleration of the mass?

  A rotating flywheel can be4v:z k8e3 xdix 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 inertia o5kaae r/a.jj8f $5.00 \; kgm^{2}$ 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 m1aj7 lm0pgrl ura979c starts from rest and rolls without slip79lpcgl1ram9u 7jra0 ping 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 mass 1.0 kg and radiuste8-: u( 6ye7q*rd-vata gqjw 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rewterqt* ad6 :7gqu a-8eyj-v(st?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released 6 4nms jsgz+1t * s)g4fd4elfdfrom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 mz41)ft s 4d+ d6lsm4gne*jsfg ?

A solid sphere of mass 1.5 kg and radius 15 cm rolls4)rivt.m:-)nt jjvv p without slipping down a 35e inclineprv :t )ti)mjv.v j4-n that is 7.0 m long. 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 m./.tloe,b 8 .7 tb bkovvse,xvsu+:p aomentum 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 inertizqtj+ iw 6h*j(opa:-ya 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 moe- id ocij (;n57)ni:9hpac zmment of inertiam7i cc ap5-:ni;ihje9 zn)o (d 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?