Angular displacement is usually exggwl z4nk:5sx4 wrb7 +press in units of

  Angular velocity is expressed in units of9f52pvizo, 7 twt:ynt

  Angular acceleration is expressed in units *igizk)2 , ,sk+irydkof

  A boy and a girl are rima10n2sy 0kdv ding 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 n a0ksv1mdy20 has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a 5m6rkm1tmj zl /3;14pnb z jngconstant rate. The boy is near the outb 6 mznn;jr1m4/ zlj1m kp3g5ter 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 is8u: e sdvf2ad 60 yc3gs8rm+kp turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the great8cs 8s2fk0u3 apdd+6e yvr: mger linear speed?

  A boy and a girl are riding a merry-go-rounczkaw kx)ol ykd,/ :c5brx528d 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 acceleraxwd ok,albrk:yx8)z5/c5k2 ction?

  A boy and a girl are riding a merry-go-am4a(.if 6x deround 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 acceledex.6am 4(fia ration?

  Consider a rigid body that is rotating. Which of the follo*v8r,n ,v+wocbsec6r wing is an accurate statemseo v,+ r8rv,b w*6nccent?

  Rolling without slipping depends o,gh8.cxb7g t 4m 4hj5)havpsmk uuf (1n

  Two equal forces are applied to a doo*f5t4i -zofg r 5x9qfxr. 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 theff- 5g4ztioq9 x5rxf * door. Which force exerts the greater torque?

  Two equal forces are applied ts , tv. 9uf5w1lc m(p1ge- do0zyqsm.japx4v0o a door at the doorknob. The first force is applied perpendicular to the door; the s,l1z1oc95 e d0.sux4-avf(q pt.gpjmyvw0m 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, acmzn)rg-g* -6 le 4efperpendicular to the door. The first force is twice as large as the second force. The ratio of the torque o 4-lgg-n ec f6z)rame*f the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ch,dx3a1 y60wjtis5 njganges in rotationaj3idx ,061n5 jwygt s?

  Consider two uniform solid spheres where both have tmfa9r7z)y / jnhe same diameter, but one has twice the ma9 /fyzrna jm7)ss of 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 same mass, but em n:/re09x1xcdbqy+qqzk 2 op.29 pz one has twice the radius of the other. The ratio of the larger sphere'q 092q9c em1q .zpox :xzk2p/eyd +rbns moment of inertia to that of the smaller sphere is

  Consider two uniform sj33r - 6+g buukk9suaeolid spheres 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 moment of inertir 9 u6ugab3-k+ju3kes a is

  A uniform solid sphere has mass M ,prjpe:; a4r0k p4e tgand radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axisk04:jpp e4gtr;eap ,r?

  If a constant net torque is applied to an object, that ob7glxd0; r+r*avn *qcp ject will

  The moment of inertia of a solid cylinder about its axis is given by 0.) d g qg3 :yvy991fernm:m;ceb5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energ;m1gqrdem 9cg::nfey )93 v byy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which ha wb2p:jn3:fez5 e*fk rs a mass of 10 kg and a radius of 30 cm. What is the ratio of the fke3n::b*z f j5ewr2 protational 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 slippi0t69b4* qdzv5afh rning down an inclined plane starting from rest. The linearrqa in9b05zht* 6dfv 4 velocity 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 in2 jimi ik cb;2gdf6zmav+), a.clined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depei idc 2+k) vai mg,z;aj.fm6b2nds on

  "The total angular momentuqn:lgqihgo) v8 ;p84fkv0;ht6dq i f7m of a system of particles changes when a net external force acts on the system." This sih8n8i0:q q 4;6k)d;qf pv v7gfg hotltatement is

  In what circumstances can the angulad3f bjeiu s681r velocity of system of particles change without any change in the system's ange i38 udf6bsj1ular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which 4c ,r)v l-,p8wsks kdbmay -bks,v) ,cs 8wk rdp4lbe present. What 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 x k7tz5;uqvrgrz7 7 )ahlfw)-moves close to the Sgfk7-w ulxv)h7)z ; tqrarz 75un, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a3 ncdvf5fwd(ss6. 5fi fast spin) by pulling in his outstretched arms closif6 w5fs5nv.3d(f cds e to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pir7bgix 6vwa.i/ g;lh i4ouette (a fast spin) by pulling in his outstretched arms close to his body. What happeia4 7/;6g.l wvhxiig bns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his o*th3;(narf8 p+ cqk a5 q jp f7sbe14i6.fybxdutstretched arms close to his body. What hape5.dfb3c 4n tjybq fk+i86ph p safq7(a;rx*1pens to his moment of inertia about the axis of rotation?

State the law of conserv6hlao/o98i es ation of angular momentum.

  What arc length does the Earth travel iwp 02.56kzo dxugtvv5sw;e+mn a three month period in its nearly circular orbit about the Sune 5 wou0t+sx 56 dvz2m.pgkwv; with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. W fui + vc283ktf kdx4-8z0amtxhat distance does the tip of the sc8kfukx i+ -f t 3x4vta02z8mdecond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 ry 7reue-y/xgeu+6q,a vee(z) evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sv682yu* bhdf0(xc fhkt w .sp-e*x 0yl. What is the freqb2 0fc-6hs x.ldv*kytufh ey px0*8w (uency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz 5hoa,eycgtir - 8vsp-p4b9 f1cq0nx 7. The period-0qarc-p xv87 4y gi ebsohnf5pct 9,1 of its rotation is

  A phonograph record rotates at 45 j(a q ryq1sboad;8r*-rpm. Through what angle does it turn in 0.20 syq-ro *aja;q sd b8r(1?

  A wheel of diameter 26 cm turns at 1500 rvj4ncqyw3c6qr +k * e*pm. How far will a point on the outer rim *6jc* rvqew +ckqyn34move in 2.1 s?

  A bicycle wheel rotates uniformly through 2. cc)yo/js 8(,e r*czzv0 revolutions in 4.0 s. What is the oezrz)8v ,*ccj/s( c yaverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whvd*xct)txew 2 8pjm ;/wf4u 4bat is the linear speed of a point 0.10 m from the centerx*u 4tewjbvtd 4)/w2mp;fxc 8 of the wheel?

  A cable car at a ski resort carries skbr.9s qu-fo e6v,j:w biers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slipp 9fous.br jw-,6eq:vbage, 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 roh)* 23bwk ew0ity ;ftftating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point onifw; )*ytkfhwe2t3 b 0 the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. k9 /oqvjd fc0-c-fo)n0sn/ecvi -gf(If the motor rotafqocn j(g--0 cis kc v)f//doven 90-ftes 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 angular speed of 2.0 rad/* ly,yggg- yct3s+*zxs. What is th*g-x+y l * szgc3yyg,te centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle w xm9apu:6 u)m00w2 ,esk firyvheel of diameter 70.0 cm whenx,r:0ammiwe v0s6p92yf )uuk the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rota1eo 3my /mf+msting space station (r = 1000 m) rotate to produce an artificial gravity of fm/ y1+msmo3e$9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2c )jj z(+7hv lw6.ci +iqdmer80 m/s. The maximum centripetal force (provided(w jzh +l)8r qmcjdv.7i 6ec+i by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circula1 2 i* d8rmgergzjgtop/l 5s(2r curve of radius 50 m with a speed of 20 m/s. The maximum centri o(5 1gplsgtzer2* 8 /gjmr2dipetal 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, itq 1ze2 ,pld5ms whirled around in a smooth level table. If the maximum tension that the strinqz1depml5 2t,g 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 withou x-f34 hedxk 748-;rjcd bzccdt slipping 10 m down a lane at 4.3 f d cb 3;-dcx4c478rjkhex-dzm/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 ae 3e o2 )v;iznv+9 +rtr ol5uzie4k9fongular 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 *c-+ ubt8,ei aj ubeu8angular 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 af)9e7mge cuv s5po6ma4ter starting from rest and accelerating at a constant angular accelerationa5meg7oms4c 6 e)p9uv of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has ay40u5v9z j+a vn9 ujw,xi,exrn 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 constant angular acp-mo,g n ;bj0hceleration om;0 gopn-h,j bf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reached0v-l: jpdqteut ijk 9+29rzv ejd516s an angular speed of 6.0 rad/s while turning through 2.0 revolutions. Whatvde-69+ u1rdvt0q 5tzjpj j9 ekl di2: is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mafy2fq va0,8 pyy (h,kh5ng7m/s to rest over a distance of 115 m. What is the total number of revolutions the5yaqv0h(m,yh2pf ny,a7kg8f wheel rotates in coming to rest?

  A wheel of diameter ofl.ssrvna-)h arj1 1 6nlgd i8nim+1.r 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is thejii61 l- n1n sv .l.rh+rr1a8s)gmna d angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s 93bbwukif1 1g to rest over a distance of 115 m. How lokb wgi1bfu 391ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/mgw+2* zevbos6in. When switched off, it rotates 50.0 times at a con vsz2o6+g*bwestant 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 a 0nys mf 9p2.;u4brvxq30 cm long wrench is used, what is the magnitude of the force required whx.u2sfq;y bn vr9p04 men the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90paugo8u 1l-s(00 sxtd Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applis su1lxp08 tag0d-o(ued at $53^{\circ}$ to the wrench?

  A wheel with moment of ineryxw4 bl +:z/9wx4lemetia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule i pw1lxgf o5-)3ol)u 78vljtb b7muff9s modeled as follows: mass m is at the origin, mass 2m is u)xw5mpf-fu3tbjl 91g )8obll o7v7f 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 fr;q23-w jdsydo8y nr(t/c/gy p c 4a)mvictionless 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 riqyoygap;/js48(d w vcnr3yt- md2/)cght. 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 aboutg (r )vj( q0vth.x,fcah8. yg*4ngmy l 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 rig,vx mcg ygh*v jn0yr8t(4f aglq..h) (ht. 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 inw-t3 gh*nj3zgitially 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? (The moment of inertia of a rod about one njg3-tz*g3w hend is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and 7qvvm5l5npn8c*y z:.0x; ml k6t ijnkmass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentx6i;5 mzkmpl8v5 vj*0 cnn:nt q7ykl.ially 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 diskx9 pwfp g0si26 pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelera fwxs62pi0pg9 tion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dabyg)gy,p h;/isk pulley of mass 7.07 kg and radiusbhap; g, ygy/) 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to s:o.irji*ayz 1 r. y)apc4bms (tore 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 6a1q vq *7 eifyii0mk-inertia 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 and radius 0.010u n8fbj2p b(fdto.ney t u lw68uu0,26 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.op fnuut b86l2y0 t2,feudn68 u(bjw the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010++m+ xrw ,fg q/3jvxbx m rolls with a speed of 10 m/s. Howgxfmw/x3,x bvjq+ +r+ high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from resbr9;wu:z5:sy id fm1 dt and allowed to roll down an inclined plane. How fasd9w:1f:; ms bui5ydz rt is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius u o(qm)( -rnfrf hg6 59ocohej+ru /1y15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is gi 9cug+oo6foj5hym/qn-u hf er(( r1)rven 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 bk0slcjfg o8) qkma uc) z9(924e arv.sy $20 \; kgm^{2}/s$ 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 pbf (; 73hcdl rcpr)v: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( hr*qq z4reap12zg:4 g .l;hwha pi7c arms extended has a moment of inertia :pqqrw ha 2hz7 lge hgc(i1p.z4 4;a*rof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?