Angular displacement is usually expres eg bbip833g uquo-)t2s in units of

  Angular velocity is expressed in)grv fcb, hm1*p l*8k,psohzq+ ko 8c0 units of

  Angular acceleration is ex24xn3 dmkq9 dqpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning ap j+m(1f,yhs,ymy m-at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the gremp y-(y,aysh1j,m m+f ater angular displacement?

  A boy and a girl are riding on a meud,jh;v3 2ds crry-go-round which is turning at a constant rate. The boy is near the outer edge, and thej3dcs2h ;vdu, girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whiw)ndeud,s1y8s 0- ns xch is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has theu)80 sdx nsnew,ys1d- greater linear speed?

  A boy and a girl are riding a merry-wdp.yl t s)nr.idi5* ,wrtlx6au;h 3bqsy ;5-go-round which is turning at a constant rate. The boy is near th.bsr6;au s3x. iltwh,d5 ynldy* -p ;ti) 5rwqe 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 c b(09 gpphre0ionstant rate. The boy is near the outer edge, while the girl is closer t 0ep(bi 0grhp9o the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatsl ;/ kai +jkz,74sh.gsdbf2g ing. Which of the following is an accurate stk ksd;f/gs7si4g2bj .h+zl,aatement?

  Rolling without slipp,x,tcf++ m3xm w eob jx *5;+umralk1ding depends on

  Two equal forces are applied to a door. The firstp zwc.3w ae/wp2/mu7h force is applied at the midpoint of the door; the second force is applied at the dooru z.pe2mw /pw/7cwah3knob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at4 eibg5tc nl2. the doorknob. The first force is applied perpendicular to the door; the se4t5g2lcinbe . cond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perl9 1fi*rq xa7qct3cc9 pendicular to the door. The first force is twice as large as the second force. The ratio of the torquex rcc3i9q1 9a* lctqf7 of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rqfpz9 /wf9j-votatifp vwq99 /z-fjon?

  Consider two uniform soli0km61:j:,0ht 7gq x/ky+yth7eiit (nfawo cnd spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger mome,/ k6(ieh7njcxhtt g iy70t0qm+ wfk:o ny1:ant of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mpv1bmw yoo- 54l,s -tsass, but one has twice the radius of thp , wo5lso41m-bt ysv-e other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the z/xjxld2 os bw(k9+4yfte ( 6fdiamet2b6/tyxlw kf9d fz 4(sx +joe(er of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M a g3lp*w2s dm2hnd radius R. If these are increased to 2M and 3R, w glm*dw3 22hpshat happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an oob o7 kinwc++yc0r48mzp( (jsbject, that object will

  The moment of inertia of a solid cylinder about its axi 88*,vzmb3cfrrjr gi1g2l a4rs 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 motorcycl v c9)b,jbaa d:r2yg)ne of mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of thv2bcyd9gbajn :))ra,e 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 maz9r hd/x ,zp8rvcz-i,ss M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sp/zir9z rdp-c, 8zxh, vhere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down amjja l8p,9i3 lxwj; +kn inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depend3 j8;kxl+ m9aplji,wjs on

  "The total angular momentum of a system of particles 8e +3wkbzet/fchanges when a net external force acts on the systeb+83k we/eftzm." This statement is

  In what circumstances can the angular vel/q8y ;j/jw3b d( drjqlocity of system of particles change witho b;3/dd wqj( j/8qjlyrut any change in the system's angular momentum?

  The Earth orbits the S2zsrho gw+ici.g )/7l un in an elliptical orbit. Ignore any friction which may be present. What happens over time to the +c rhoz./g7gl 2i)swiEarth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves ceu mp05y*ee8 akaa(5r;apg r0lose to the Sun, then wk uy8 pgapr(eaa0; 0e55* mraehich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche(s/ fkd/xqig7 d arms close to his body. What happens to his angulag7 x/k/isdfq( r momentum about the axis of rotation?

  An ice skater performs a pirouette (a faste3nkw ta;9ogftb zzq;j48 (n; spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotk(wa q j; beo3;z9t8tn gn;fz4ation?

  An ice skater performs a pirouette (a fast spin) by pullinqxk97e u6mc qx-rd g0+g in his outstretched 7rx6dq9m+cu0x -gqe k arms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation ofudo12y- )py ig angular momentum.

  What arc length does the Eariey6q /(i+a ou)i,r mzth travel in a three month period in its nearly circular orbit about the Szuoaii(i )yrq, +/6meun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng0+f9fv*w l atyx/br)nth of 0.30 m. What distance does the tip of the second han)f*wt abvr /x+9y 0fnld sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolut*t7yt1 49gi.ls yo7ejfk 3 dwqions per minute equivalent to?

  A bicycle wheel rotates uniformly throughx zhx d ifo k(9(pl;f-6i*gwl+ 2.0 revolutions in 4.0 s. What is the frequency of the whilz+kp(h( x- ;l6 iwg *xo9ffdeel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Th9 1p4mdcx. rd.g)f wyre period of its rotation x )pd1r y .g.9wdrf4mcis

  A phonograph record rotates at 45 rpm. Through what angfs bx6.w,jq0m tyid zr42s( g4le does it turn in 0.20 sbs0 s (xywg.ditf6qj4zr2m 4, ?

  A wheel of diameter 26 cm turns at 1500 rpm. How fp gl18knht(ayk+ek4 2r/js/e ar will a point on the outer rim e/jkery 8 lk2t1s 4g+/kpanh( move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatm )2*g8fka4++u)xpe m fce rlqo e2)yr is the average angular speed of the wheel? +mu* g )efr2qc8plykema+ )feo)24rx

  A bicycle wheel rotates uniformly through 2.0 revolutions in /patb)) btrpkifswyqg/.,*; 4.0 s. What is the linear speed of a point 0.10 m from the center of/spq;f/ypktga b*)wi)t, r .b the wheel?

  A cable car at a skiq)4zn)tvmjr;/+f ( 92b9 avd5 gt.mymkkfhee 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 v.da (vjm kk)5zernf49g f;by+9qt)ht /m em2for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 ran-36auci e -r/8q *mm;n wupvyd/s. What is/evm;* qu u -p 3wnay-mi6rcn8 the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-power,k ip ou rg (:3r3h:agdtf/t,ned weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what g: h/udr 3,ikrtp a3gt(fno,: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 nn43e uig) b.nrad/s. What is the centripetal acc4ng.einnb3 u )eleration of a point on the wheel's rim?

  What is the centripetal acceler0g vl*hzj )x68k so3opmx3rr9ation of a point on the perimeter of a bicycle wheel of diam *vo lpg8 k0rmho)jxr9 33xzs6eter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) 394j m.fu dr,v)t nhpemust a circular, rotating space station (r = 1000 m) rotate to produce h,jefnu3m4.tr pd)v 9an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with c2 az-tp :e;8eo6ueeoa speed of 20 m/s. Thezeo2u8-tc e;e:ae6p o maximum centripetal 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 arsfldb+oe kc87-,h k1 speed of 20 m/s. The maximum centripetal force (provided by stakorfk,+bd8esch1 7 l- tic 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.xxgv.2)tds,pm1 py4 o750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speevs ty1,xm2 )xpd4pg.o d can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rollujnh pk7 ./*usb5chf;5no0wxs without slipping 10 m down 7bw5ph uj0o.hn/snx; uc5k*fa lane 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 aitbq+8cg7lxqr : 5iv ,/di. mx constant 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 angular acceleration ofw275313ded oop ecq /b pu1pht $4.5 rad/s^2$. 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 automobilhi*pye3rr27-hnr y2pb6uaf 6o n d/0p e tire rotate after starting from rest and accelerating at a constant angular acceleration oe6yppua i/ n2yfph 27ror 063d-nhrb*f $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angula nc8fkofo* u)l*/vz+1h /atnur acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s d;u+rk.+xkkm3zo 3p za ecelerates with a constant angular accelerationzk++ k.pukmxaz; 3r o3 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 55: f;unj3uycetc rrmkh2 z156.0 rad/s while turning through 2.0 revolutions. What is ykrntc31u5 25h; mf5e uz rc:jthe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down xs+; 5xl ksy*;* :ml*uswxesoao- q-w uniformly from 8.40 m/s to rest over a da* ukxs ;s :-o*;lwswle y-xqm o*s5x+istance of 115 m. 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 from 8.40 m/s t,zomf6oa 6/slf 40jw jdb69eeo rest over a f0/oe za69 ,m64jb w osdeflj6distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm ss f y2d98y8a7)jf s 3yop,mhlslows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take 8f9 yfysha )o7dysjm,pl8s 23for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rota nxo: xge h*r86jtni365ng y-gtional speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befory 3jt6gngx *gho exn6i:r5 8-ne 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.mugmywb.*c z / a/.v*t hbsr2: If a 30 cm long wrench is used, what is the magnitude gtb/m .m*ab. cwyv/su z: 2rh*of the force required when the force is perpendicular to the wrench?

  The bolts on a car whee k1:.uth icx, b:ilv,.* ujmjrl require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo.tc:k :m,j.h*l, 1 x rbjviuiurce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia2ui5m-h dh5s,w px: dm3qty-z $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeltvs;cu0q;)n j ow zze*6y6(ioed as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x =n6s o;; qe(zv0z wi)j6ytcu*o 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted abou3 at50*ajpi2 bauc;fe, c i.fmt a frictionless axis thought the center O. A rope wrapped around the outer radiu5ct;m f p eb.3,2cf*i0aiju aas $R_1$ = 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 frictionless axis thoujq7 ,q+mh.)b qpk(uir ght the center7jqqph, )u mq.( +kbri O. A 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 heln3xhpgq 2;1bbd 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 end is Mbx3bpg2 nq h1;L2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg)7ddlx, t ;o+8q-gesw dxps1 n. Neglect the mass of the axle and sprocket. If a force of 20 N is applied q;t d )g,dsxo1plswx+8n-7 ed 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 wrapp*x)kfs4lm x; red around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accele r *kf);lxm4sxration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlejvd2qx +j +bknc e,14mc6;gd dss disk pulley of mass 7.07 kg and radius 66.0 cm. What ;cg qvebm6j+j,4d cd k 1nxd+2is the acceleration of the mass?

  A rotating flywheel can be used to s+0wdzxy e:+6vqr bra 1tore 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 inertijq4t- 9u+odk3p n4 wopsi6 rvtg*n0k7 a 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 rest and ro* 5e.q jhgu ud7m owvzjay*4,:lls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined7w.vz4gu edmy5,o: a*u qjj*h plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a sh ;:typ u(dizs2ep)q1peed of 10 m/s. How high up an inclined plane can it climb before coming thd2:suz 1pyt pqe()i;o rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest 0 vnqk/s 1;beband allowed to roll down an inclinede 01;sb /bqknv 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 rollswo js r(00u1af:w 93keeva hyc q,eb22 without slipping down a 35e incline that is 7.0 m long. Assume it started from res e20r qufwow09vacya23s(h 1b,jkee: t. 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 by ./yo:d nzwr30 fosb8i (bjak5$20 \; kgm^{2}/s$ 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 momneuvy* 9u,*tb ls z5i1ent 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 a:.arer6il:ln t 5.00 rad/s with arms extended has a moment of inerti6r: elinla: .ra 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?