Angular displacement is usual-p uxl(c/:lqk8b q vm2ly express in units of

  Angular velocity is express 8adl5 -cnuxr,ed in units of

  Angular acceleration is expressed in unith ,c7 p7ails)ls of

  A boy and a girl are riding on a merry-go-round which isov.m))n.ihraxl m4 ;o turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centerl)n om;ri4.hva o) x.m. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whi8wloqk4,u,6c lrum m.wg+f +ach 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 anguaqw o6 m,wcf+glul r,u.4km+8lar speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant wi4j0(v+ ;6rcgg xaggrate.40igx;(cgjg +v g a6rw The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridx+x7u0 (qcwvling a merry-go-round which is turning at a constant rate. The boy ( 7+ucv0xl xwqis near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is tupen.n/ dxax65g+ -. xmxv- :ojn 5buwjrning at a constant rate. The boy is near the outer edge, while the girl is closer to the- o-au/x.pn 5 jx5x6ndb +ejg:wnmv.x center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accuuiyag+3 tyk7m,l32p6w ,wg2gubqsc5rate statemeyu7yt6gpi+a w,3 5gsgw,lk 2uqc 3m2bnt?

  Rolling without slipping depends . ey6d 4dru+ y6p/bxqdon

  Two equal forces are appli6nbx* i fvtf-0t6 5ytjed 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 tht xv5*f0f6t6bt i-njye door. Which force exerts the greater torque?

  Two equal forces are appli15z: guj2 hcsh0dxqv; ed to a door at the doorknob. The first force is applied perpendicular to the door; the second for:s5zcq xv h12h;ujd g0ce 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 the door.+t 9 )hb q)3ge5w*s-pqq+l9eq ahnyoh The first force is twice as large as the second force. The ratio of tq ho3-)+*aqhewh q9e5ty lb+q9)spn g he torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance 6hk51a2fbvvq 88ny(puyi 7 zhto changes in rotation(hznvu6 ihyv 88pq21k f5y ba7?

  Consider two uniformpr)i2e *7fby8ew s k;h solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smalle ;ks pwe27e)8yfih*br r moment of inertia is

  Two uniform solid sp dbp;0z htq0o2heres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's0bh t;po2 z0qd moment of inertia to that of the smaller sphere is

  Consider two uniform v)t /w,crm,e jsolid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of iner/t, wve,)jrcm tia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radiusmfm 3i 2uasiembs( 3;;j2xmh . R. If these are increased to 2M and 3R, what happens to the s;ai;exsb3 .3ms mimfmh2j2 (u phere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that vw9 w)u2ql zm:object will

  The moment of inertia of a solid cylinder about its axo* :cx/ksm,sxis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mpuxn-d66y v*fg qy7)o ass 150 kg, one wheel of which 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 kinetic ene6y fu7v yn-)xg *p6doqrgy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping3 xyxogt/g iui5eww6w il,j7 3jkt,8da6 ca; , down an inclined plane starting from rest. The linear velocity of the s5,3,w376dj;/eci6 a yktt ljo gwi uxawg8ix,phere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius ynd1yoz8td1 3 g0z+ utR rolls without slipping down an inclined plane starting from rest. The angular velo 8g1o0y 13tzyzud+tndcity of the sphere at the bottom of the incline depends on

  "The total angular momen j g2mokdt+1c5s:4la+u zq4bp tum of a system of particles changes when a net external forc+b2 usz+:t la cj md14po4g5qke acts on the system." This statement is

  In what circumstances can the angular velocityvvfi yydb;: 02 of system of particles change without any change in the syst i;f 0dy2yvbv:em's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore apf)wzn 5 rj.4-b;e jywny friction which may be present. What happens over time to the Earth's angular momentzw-e. jw rnp 4)5yj;bfum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth m.-qr-*4 wiz yb yy0es82k jfzuoves close to the Sun, the fq-zuek.wz4 r-i8 y y0y*jbs2n which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater perform79qsyvhxwa:bv + ;y:gs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotati ha;bvy:g7 s +:qwvy9xon?

  An ice skater performs a pirouette (a fast spin) by pullinmif :9 y,xt0h9w* ; crite7eucg in his outstretched arccxei:9ty,0fwr;7 *9 i mehutms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a jmv(e,8x+ari4 mzm f7ur ex*7pirouette (a fast spin) by pulling in his outstretched arms close to 7 i rx4 8*7 (xevm,murzfe+mjahis body. What happens to his moment of inertia about the axis of rotation?

State the law of conservationip3cj rm5i9*:znz8fb of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cir.c- avx ydqd(map 5k9n6eng, 0cular orbit aqygp(-,va6c9 a. ex mdnn 50dkbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a. wi-) mdyaw;c,x.p wh clock has a length of 0.30 m. What distance does the tip of the second hanmi.wxw,c) ;w a-hdyp.d sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute i 1 )ms02ovtfsequivalent to?

  A bicycle wheel rotates unif7an3 :cehblzm rkp677 ormly through 2.0 revolutions in 4.0 s. What is the frequency oheb kpc3ln r67mz a77:f the wheel's rotation?

  A pulsar (a rotating neutron star) emits 3aj yl-g7cw2 rpulses at a frequency of 0.40 kHz. The period of its rotation is- gryaj3 c72lw

  A phonograph record rotatets4j3an8 / t/3tc jypqs at 45 rpm. Through what angle does it turn in 0.20 spns4 yj8j3/t tqc/ 3at?

  A wheel of diameter 26 cm turns at 1500 rpm. How f b/m1)q1/+d qek5jo7nk dz16r vijiiear will a point on the outer rim move in 2.riv1d5monq/jk+jb7 /i1e)kz6 1 d q ie1 s?

  A bicycle wheel rotates uniformly throug */u j.(kchwjbuizd l) 9b:w)jh 2.0 revolutions in 4.0 s. What is the average angck)u .uj bi()*jbl:/wwhj9z dular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is th3wlg o k4uk5d6ib j4lb;gz(/h e linear speed of a point 0.10 m from the center ok5gl3bz4o lg bw ij(dk6h;u/ 4f the wheel?

  A cable car at a skimxxfn.s yeh19aw5) .e resort carries skiers a distance 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 must the pulley rotate for the cable car to make the triea.yh n) f xx95w1.semp in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 t-bze otiaf.s3u8+6(y lkj0arad/s. What is th3 zs6 fy i+8.b katauej(-lt0oe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered wu3;t g2 (rfrj;5b5mrk go agj(eed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of t bkaj;g5rrgfg;m (u tjr53 o2(he cord?

  A wheel of radius 1.0 m is rotating with a constant angular speenj6v3i.o/pt+ip w m.kd of 2.0 rad/s. What is the centripetal accelerati 3mp itjn /w6..kp+ovion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicb: nijz31t/ *ls8;lsos6 muweycle wheel of diameter 70.0 cm when the bui*b3o8nzlm;1sw j/sslt e 6: ike is moving 8.00 m/s?

  How many revolutions per minute (x;l4e+ ak 5j6ber)ndqrpm) must a circular, rotating space station (r = 1000 m) rotate to produce an+;ak5e)j6 4 qdn rexlb artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed-c1 fay,5 e,wx.g4zov orj e3v of 20 m/s. The maximum centripetal force (provideefwo r.5ov41xcz 3,j e y,g-vad 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 kc75fjdo5- lewith a speed of 20 m/s. The maximum centek5co5f dj7 l-ripetal 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 around inftmbfv lyu/ h b,/c3k+h6q 7(g a smooth level table. If the maximum tension that the string can withstand is 250 N, then what mav(l,+3fyh/f bmuht bc/ 7 g6qkximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius v .w,-c5x5afde ii)g iudf* 2:7w)on +omexlz 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/sg:z-de.d)xuwi eo 2fl)c,m ia+i 57f5on* wxv.
(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 *t t8x bxe 3f:qi( kzef2z5;rdacceleration 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 angul*/y k7xnc 6tdvx kbyvrl-4j ;:ar 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. fhig44s9g ji1300-m radius automobile tire rotate after starting from rest and accelerat4ig9ghf41 jising 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 o-t4 u88gpn;fev ,mh.1vc vx inf $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angular ah3g(tr k;: f drn/zfwzz5 3zw:cceleratioz/ng w3:ztwzk(fr3 h f;z5:drn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular6 n1oy1x.gdtsk v s(f4 speed of 6.0 rad/s while turning through 2.0 revolutions. What is the ave 1(kg4yf1ov6xd st sn.rage angular acceleration of the wheel?

  A wheel of diameter of 682a(35u h-ymjdqoe/uvf 0:3y*skd j xx.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total numbe5m j0(xau: v/uxjsfq-y*2ky dd3oh3e r of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s2: hlcr l jn ky7z4e-w)d/rfb+ to rest over a distance of 115 m. What is the angc fh)r7l4 b rjz-2e:+wdk/y nlular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest e;dlx4+7tvw y*r4alrover a distance of 11da*;47 w rv4ely +rtlx5 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medicay:manojs045qiu mh e d*),,b2n rpyi6 l laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before co5yoj p hrd abs)yimn*62n em i,40,:uqming 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 309c8s6/ bjok4e rewho,y y+q 4a cm longk+ e9 6raqseo,oyjy8/w4 b4ch wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel req7tmmzb6uh++k37 6qei; lqnu g uire tightening to a torque of 90 Nm. If a 30 cm long wrench is us +z6mq;t6egl73humqi k+b n 7ued, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine27wld6rjkyz *8dl25 pwse sc3 rtia $3.00 \; kgm^{2}$ 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 tsg82ui+qdsp+ w5a;jl he origin, mass 2m is at x = a, and,uij ld g8qa+s;swp 2+5 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 frictionless ax6jfnb zekkq.bm t 6z.d w)/w-.is thought the center O. A rope wrapped around thqfk.wbenz z6k6wtb.. -/)d mj e outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionl4q5 ctaz*:(wzi. ttp cess axis thought the center O. A :4(tzt*q pta 5wcic.z rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 he/kx)olxr iuy;vip0 cti-i7 6*ld in the horizontal position, and then released as the free end is allowed to fall. What is *xt;vci yi)ui7 xpk/-loir60 the angular acceleration 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 of radius 30 cm and mass 1rn3 kguvl i,**.ox;/1psww s i.5 kg. Neglect the mass ofk; u lrp1x vi*w/sni .3s,gwo* the 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 f y khu2vi34/dnlji c.dg2(e*rrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratie .d3vd(cj /i2l2ugrknhy*4ion of the pulley?

  A 1.53-kg mass hangs c+n3jv u)xw-. kc(a-rlir6ri0gg*swon a rope wrapped around a frictionless disk pulley of mass c .*jrck (30 wgvrsw6g -x-) alniur+i7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be us dn/ fwfx9n5q9ed 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 sw6nfo7 / ,stlof $5.00 \; kgm^{2}$ 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 starzr09o- 8py9o-,t *mnelkqsy ;2dadkyts from rest and rolls without slipping down zdtes89rkld qpyo*;am-0 9o -y,2kyn 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 radius 0.010 m rolls with a speed ofzy *pg6ba6db9 10 m/s. How high up an incliyp gda6 6z*b9bned 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 rest andeuuhx e+f:usbkp0s73y 8 iu36 allowed to roll down as+ekeu6 p:7 3uh0iuy fu8bsx3n inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm)o3c, 1rle; r3jgvp4. o2abq lvg7ppn rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphpbp 7gv2c 1qov enlg3.4rlp a)o,r3;jere 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 b o5bsom 2-ro:)s1ktag y $20 \; kgm^{2}/s$ 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 momen5:w4ves ssz )/p0ybxft 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 hr- e giz;(,* 0guxwitpgxm13extended has a moment of inertiau1t ;, -hx0(ggg3xmi epzwi r* 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?