Angular displacement is usually express in uni(s.9pr*d3 4 grhzukfits of

  Angular velocity is expressed in 0,(tok x*m yhwunits of

  Angular acceleration is expressed in umpmz+s 8*d8bb nits of

  A boy and a girl are riding on a merry-go-round which i z+b-o/zcws 5/ ;ebj1ztmqew+s 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 displacee j+qc5+ wmzt/z;b1zb-w/ o esment?

  A boy and a girl are riding on a merry-go-round which is turning at a constanv; -z*yve9u+ klleub/t rate. The boy is near the outer edge, and the gireue lz+9y /vulbkv;*- l 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 e.ouijoeec0y78 v/, a at a constant rate. The boy is near the outer edge, a 0oi uvca/o. jee7,ey8nd the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-rk38 vfwkwwab rgew f1/; + .+sgol.:olound which is turning at a constant rate. The w:b.kefv +1w+;8 woa .s g lwgor3lk/fboy is 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 turning at a const frr*fa k0..fgant rate. frfrg.*0f.k a The 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 r9 ;p4,varw wvi yv1hw;otating. Which of the following is an accurate statement?,4pwv19 ya i;h;wvvrw

  Rolling without slipping depends on y2fv 1:7/ vujskp0 y4 iukya+ct6d1to

  Two equal forces are applied to a door. Tkzhjs3r:zzw/o1o . p/ he 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. Wh.:ko1 pzorz/sh j 3z/wich force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forcery0s*zk/vl +eza) zm kh51*az is applied perpendicular t*ah vr*k1l+kza 5s/myzz ze 0)o the door; 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, perpendicularhi g3)v r8ft*d to the door. The first force is twice as large as the second force. The radi*3t hfg)8 rvtio of the torque of the first to the torque of the second is

  What is the quantity usew.n)trz.f,wb1byp :z1h p gy 5d to measure an object's resistance to changes in rotation5w1 ,b f1zgzhyn rywp .t):pb.?

  Consider two uniform solid spheres where both have the sakrye(/kar,f:coe ha 8los; 6wo5 k-m3me diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment o e/ka o( o5r8,oflay k-e6wk;c:mh3rsf inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius or3 y7vccskr0e k xi2b.v xrd:.5 9;xrjf the other. The ratio of the larger sphere's momenk k5:9c0 x.r 2y3bjsdrx7.xiv e;cvrrt of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and50zlcte,vd p/.ip .ni twice the diameter of the other. The/ zn .0pd.,vic5ip let ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius 6j;d8jzbappul*p 8zo2 oa/15jqz 8tt R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia aboa tptz5lz8a6 dpjouo/z 1pqb2 ;8*j 8jut a central axis?

  If a constant net torque is applied to an object, thr la5u3qxen ti4pyj 91.e (h3gat object will

  The moment of inertia of a soli h5 m,r.vlvn,fd cylinder about its axis is given by 0.5 MR2. If this cylinder rollsnh,vrmfvl,.5 without slipping, the 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 maxeb:i eq 6 vl5xv+7gb79qek9nss of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total transx:5bleb67xvn7q kieegqv+99lational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rol- (cpsbn3d1m3 akh3 y,yvjn d7x4o2n els without slipping down an inclined plane starting from rest. The linear velocity of theden 3yk-32b(n4 hdya,3oc1s jv 7nmxp sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witho4j ewgegh3+n( 8n8s haut slipping down an inclined plane starting fro enej8w sh83 4ga(hng+m rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mom0x+o opl/zlhf.2p:mientum of a system of particles changes when a net external force actsoxl0/2hzop .m :fi+lp on the system." This statement is

  In what circumstances can the angular velocity of system of partic iu: * le3j;zo:vtzmd(les change without any change in the syste3 jz;utze: :dvl(mi *om's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. e ow6;aum 4s,n Ignore any friction which may be present. What haps4 n ;,meauw6opens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sunv 4z4n ib wzt)r-:k5cn in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed o :nk ntzvz- 4c4w5rib)f the Earth about the Sun?

  An ice skater performs a pirouette (a fast sczr*bx8;7w 1 3tb jw9fwfse: cpin) by pulling in his outstretched arms close to his body. What happw f xt3w:jfszeb rbw 719c;*8cens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hi. 4f,o grny(jr: o5shu )vij0ns outstretched arms close to his body.,j .f)orsnn5g v (ojr0hu4yi: What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullo 6pl;cm*r8.ba u0eiir/dbs(6t 3mcling in his outstretched arms close to his body. What happens to his mome *p6cuoa63lct br(m i 0edmr8sib/;.lnt of inertia about the axis of rotation?

State the law of conservatiziwy-z0 * aoi ix.v7/ryl( 3cron of angular momentum.

  What arc length does the Earth travel in a zt0 ozg) +;t jyuxf6aav;+yd:three month period in its nearly circular orbit about the Sun with azay )6ogzt du+fja ;+t 0:v;xy radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of r l)ld8 155s qpu-ygwr0.30 m. What distance does the tip of thel5)8pr d- s5 ylqr1wgu second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eq;pw 3qy ,tywn ni6enn2l03-fguivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutio,zjc ,gxtl 59zns in 4.0 s. What is the frequency of the wheel's rotatioxcz,j 9tgl,z5n?

  A pulsar (a rotating neutron star) emits pulses at a frequen3vrm4f/e ae9,u j lthy8n 82kycy of 0.40 kHz. The period of its rotauhtey el/42 9k8ny3,8fmr jv ation is

  A phonograph record rotates at 45 rpm. Through what angle does it (dphp9)p8 b qbturn in 0.20 ( 9dphb bp8p)qs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far0bul, nh a flvb8mt04/ will a point on the outer rim move in 2.0 4na0ullbt,fv/ h8mb 1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is 1t9ar5w-bv v87 kgrlfthe gt rb-wvf7ralk81v9 5average angular speed of the wheel?

  A bicycle wheel rotate 650 (ye7qyfsveniy8ks uniformly through 2.0 revolutions in 4.0 s. What is the lineav8s 7y0y ekyqi56 nf(er speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers z7l6 +lq5rc25 )q*joly zkfce 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 cabl)lo+ 2kq*e5yc5j6zl7q cr fzle car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotitn-.o )x: 6jrzj,xux ilo/j+ating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on thejr.-i xj +o6n,i:/xu)x tlzoj wheel's rim?

  The cutting cord on a gas-stuo5qa q :1(bu0kk,4q4jgxipowered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximat1uqk,(g5oqibusa4tj :4 kq x0e 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 raj2r1;2 aq1uscd8 p6 lgukqr*57xcd knd/s. What is the centripet*u2pul6sqdx11n7d 2rq5k gr k8ja;ccal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a pp- 9jer1y w6hu4ui1pl oint on the perimeter of a bicycle whee6ul -eri11p 4jw phuy9l of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions3u zd1z2b2t.m 2xpzyr per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to prodzzrt u.y23x2zbpdm2 1uce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 wbw4g d.8vze.cpg1:drl* j 8ium 4x.im/s. The maximum centrb48duw.1jld i*x 4 8pcmg :g. rewizv.ipetal 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 a8v,t7 ieel+)6.qxawtd/ik gu q.vt (s speed of 20 m/s. The d/g.xa,w l7tt )e6vi vkqes.(iq+ t 8umaximum 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 7wdcn5 ihs9xx70f( si0.750-m string, is whirled around in a smooth level table. w i(sh75nx d09xscf7i 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 w7rl) u i5a1+: djzsbvgru+rw, ithout slipping 10 m down a laj u)zrsa 5v+7+,birglu :wd1rne 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 a0hpy8+h lmxdk kh3-ye8u h4.dcceleration 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 angular acceleril,y 4s4sx cwo5jdmry0q:j, 8ation 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 radiq *c4kvh u;, t3ivouof7 3idw/us automobile tire rotate after starting from rest and accelerating at a constant angular h7 vt3u ,q/*uiwokidvoc f;34acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and ha: ls3jvm94i n u:xg;tq -wp pp))-ucnds 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 wif24f2b)axpaxho, u gup 0sb, lh (83y(p m0jntth a constant angular accelerationf3(uptx l4 f(h2j0s,)bhpmgpab n y8ua ox20, 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 q+huf z n)+gbs9f7a4 y6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheg9+uf a)qf74 hbn+zys el?

  A wheel of diameter of 68.0 zl:57fp *z unocm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to reszl:pou zf75*nt?

  A wheel of diameter of 68.0 cm slows down unifopxvsofaw .v2/1gzn rp) 1b y:;w .be(grmly from 8.40 m/s to rest over a distance of 115 m. What is the angula1( x n pgf/pwbsr1;by)e.2w v:gaovz .r acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8la/9ea8z1b rn zu*m)0o arg( w.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to th9zarga/8lb)r(m u0o1z wean* e stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 5rwstr1 q6, b21+te lwy7 klp60aiqjv3600 rev/min. When switched off, it rotates 50.067y21,0i5 6vqttwlbsrewk + jpar ql1 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 tightening to a toryoqa6(pn ,2xk que of 90 Nm. If a 30 cm long wrench is used, px2, nyo 6akq(what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require ealy7 42e1e-sqfqk6htightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forcefe1q h6s2 ek47ea-lqy required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inx,p(kpg,f1m x khmcen1akq m7vb52s:2h8;tmertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule9rw 4 1mgd.x/0 ahxjoz is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is theh .9z/d1m4 rawgo xxj0 moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis th d6 rk.n:h(/atx duwf(ought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 fa 6((/ dnxdtr.k w:huN 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 f n) (z(.3oa uy s,+jasmre0kpu2c.tshrictionless 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 exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, ia,s h(+ 2(ryuuap3mto)je.zsck.s0 nf it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially hs(iyx-b+ /s*srdap:j eld in the horizontal position, and then released as the free end is allowed s r+(xy/dibp- s:ajs*to fall. What is 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 1.5 kg. yops 0ig*-xy. bo/l8g Neglect the mass of 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, assum8piolx*y/ gg-yob .s0ing it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappe 8we )pl04bd4gsjpat5ovy a/8d around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What iedj4 o0vpt pb)aa5s8 y/8g lw4s the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wra1 ;ezhk:wmj6 ipped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratiz kh1jm6w:;eion of the mass?

  A rotating flywheel can be used to store enere p st2:,d+:fj0cqjtagy. 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 ofp1ls 2 pv;rv7: apr/rw 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 0.010 m starts from re0p sxy(mt 0wm5 rpk8t+vo2 :qwst and rolls without slipping down a 1.0-m(t0sxpt0wqy 5m8 2o+ r:kwpmv 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 wit 5y7gz zpd; d5,42pnsd4osi hih a speed of 10 m/s. How high up an4 ,54yznpgpsd di z;do2hs7 5i 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 rest and7 gd;zc/ .w6)ajtsxx n allowed to roll down an inclined plane. How fast is it moving after dropping a vertical7gntj)/x ax ds.wz6; c distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 64ne1qqh tbj+.+x: udna* nn l35e incline that is 7.0 6d:a el h*1qb.x jn+u+4nqntnm 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 momentum chx vb r-*)8ttneanges 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 inertia of h ua,wearg 3 9b(wa.y4$5.0 \; kgm^{2}$ 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 inxrmy)9 xfhr7 7ertia7 9xyxrmfh 7)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?