Angular displacement -dlr8h(u.8 odgs ht1z is usually express in units of

  Angular velocity is expres8ihtqi gao 53;sed in units of

  Angular acceleration is expressed in units o1fur;w83 damc* u 6vpof

  A boy and a girl are riding on a merry-go-round ))a9po f7gcx gwhich is turning at a constant rate. The boy is nc)go 9)fg x7paear the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constb 3jy8f, m/wwy cbi ,tbenz0.el nx5,-ant rate. The boy is near the outer edge, and th.z ,nwy tnxjilb, 53wcb80y,/m-fbeee 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 is turninl b4v .c7.nghwgv ww 6g,0cey+g at a constant rate. The boy is near the outer edge, and the girl is closer ty vgbwgnh+ ,eg w7v4l.0cw.c6o the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turnintu5guzizh/h* h0wuc i*75: a*z(r if4qcvbq 0 g at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who h c*z /0wba t*cfzih(5u*iq0ihvh:u zr75 u 4gqas the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning vx1 d x8qpp44sat a constant rate. The boy is near the outer edge, while the girl is closer to the censp48vqxp1 x 4dter. Who has the greater tangential acceleration?

  Consider a rigid body gw wwgi-n(4xh i./f /hm,7prqthat is rotating. Which of the following is an accurate stgxi h4,pr-/.(/fmnw w 7whgiqatement?

  Rolling without slipping dfiu58 :cb mo zv.v8p2pepends on

  Two equal forces are applied to a doorpmz o*:( y v:me:x-ovr2v:y qn. The first force is applied at the midpoint of the door; the second force is applied atp vq my(v:: zr:o2 *yxo-mevn: the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The9quyk xy68h zvx)/4at first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torqh xy v6xqt)y84kza/9uue?

  Two forces are applied to a doorknob, perpendicular tmpic 8ev: mny+j4)0rao the door. The first force is twice as large as thej8ma +) :y0er4inmvcp second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to change0:lhoq ob;3,ive/kccukzo 8,s in rotationik/oo kq vzc: , ,o;80ecub3hl?

  Consider two uniform solid spheres where both have the same diameter, but 3 c5+bbm)v icdone has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller momen5+ cc id)3vbbmt of inertia is

  Two uniform solid spheres have the s1eq *+d4p(7pfz e udz1q xy(ugame mass, but one has twice the radius of the other +*(pp xdzu41ydz gef7q(1equ . 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 f9xctcia 7 6wkyj*w)zc:j2) z)bw7tq twice the diameter of the other. 6)7z)9 :xfj y 2cw kc wzti*aqb)cjwt7The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radi:oq30vkh jk0vr:,ym *f sdhohcb .,y*us R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a cen qjcv *v:, :kbhs3yokh*00o fyhd,mr.tral axis?

  If a constant net torque is appli-ars6vlf(*,sze8r yyg x e.7qed to an object, that object will

  The moment of inertia of a sol+k+y3qjdu e zuo 0dc+ b,odi2c* */xsfid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetiu++sb,co0je*3kq *uy2dc/x df d iz+ oc energy is

  Consider a motorcycle of mass 150 2rt /:n;jrnoiniy0 1f6bp bm2kg, 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 tr2t b1nopj inrrf0nmy2/6:;i banslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping z h0:g3kq 6yuqdown an inclined plane starting from rest. The linear velocity of the:y 3q0uk hzqg6 sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls with -0ndqf.1t nj:q .xjykout slipping down an inclined plane starting. n:d -qqjjf.kn0t1xy from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentumerx at) jq 7swx2):bcb*p- m1f of a system of particles changes when a net external force acts on the system." This statem2t )*smeq r a1- xbxpwj:7bf)cent is

  In what circumstances can the angular velocity of system of parti9tss+1lc fyg: x9zak,cles change without any change in the system's angular mxkz t 9l9f:sgcs y1+,aomentum?

  The Earth orbits the Sun in an ellips k9r 85 uy+wman2sg7sbc1yy2tical orbit. Ignore any friction which may be present. What happensswb259amy28n1rygscu k s7+y over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticalig:x7bf .bd g9 orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about t 9b.g fx:gi7dbhe Sun?

  An ice skater performs a pirouette (a fastv*g msy(61:hktmolpg5m0zr n ( j9c (l spin) by pulling in his outstretched arms close to his body. rp:c5(t n6 m(0 g9 (s*gyllm1mk vjhzo What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spk bpt-q /kt9x,.au8cyd4 n8cpin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic q-k y4 p8tu bt8.dacxkp,c9n/ energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)e h2suz2 z((iy by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the as2e hzyi((z2uxis of rotation?

State the law of conservation of a q/ad0gk4ae*wngular momentum.

  What arc length does the Earth travel in a three month period ij,b fvm 5z-qrfy-nd52n its nearly circular orb,n z qd- yf-bm55vjrf2it about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a v wj jd+) g5n/jg/w;etclock has a length of 0.30 m. What distance does the tip of the second handjt)g/+g5ewj wvd ;nj/ sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivaknwv q )2ep9+h1vep i:lent to?

  A bicycle wheel rotates uniformly through 2.0 hzesh5btk m52e 1r:zna ;(2verevolutions in 4.0 s. What is the frequency of the wheel's rotation?2ez kth5era5z21e: (m;snbhv

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz5bgb8f7h: wu x. The period of its rotation h8fu b bgw5:7xis

  A phonograph record rotates at 45 rpm. Through what angle does it tns.xk+ne plfxc;kti :( v* u:7; y9bheurn in 0.20 s::ixhkn .97;xfcpv+ yeslkbn* et(u ;?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wdfu xb sddbnhbn 0:1s5*se0oxxnz+x(7* lm 95ill a point on the outer rim move in 2.1x 7lfdz1 *b+0 en bmsx 9(ou b0:55dshnxs*xnd s?

  A bicycle wheel rotatez8iose9agq5 ,6qrl o(s uniformly through 2.0 revolutions in 4.0 s. What is the average ang oois 5ez8lg 9(,q6raqular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0efuu,cf l .3zzrep,k3*b /0 kp-b(c kb s. What is the lin ue/b fcbke,(k uck*lzzfp3 -3.b,p0rear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries.pzlc 5)rrynlk3ji , 7zop9z3 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 rotatzzypn7pc9rl o.5il3,)jz rk3 e for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constayx,3*obb m 3ygnt angular speed of 2.0 rad/s. What is the line3xb*b yyo, mg3ar speed of a point on the wheel's rim?

  The cutting cord on a gas-powered we,90k r hvefbi7ed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate lh7e riv0kbf,9 inear 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/smiwrq8k(-*u5q we(x l . What is the centripetal acceleration of a poi5 (uww8rl kie(q-m *xqnt on the wheel's rim?

  What is the centripetal acceleration of a point on th 9trg85i+.vm h+rmm ble perimeter of a bicycle wheel of diameter 70.0 cm59h8bg++ .r imm trvlm when the bike is moving 8.00 m/s?

  How many revolutions per mxj pyff2,z sbq0 1ae1/inute (rpm) must a circular, rotating space station (r = 1000 m) rotate to proday seb1z,2f/01f q jpxuce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of r.eqc0n4p w)5i gmkcb.adius 50 m with a speed of 20 m/s. The maximum centripetal force.5 n kb.egwq 4p0ccim) (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 radt 6ktope)bb5 5ius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by spbt65te k5)botatic 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 st+5shoj pf3*rv ring, is whirled around in a smooth level table. If the maximum tension that the string can wjf53 pvhos* +rithstand 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.xbm/0l /i f( g7(zlimbdi4hn.5 kg and radius 9.0 cm rolls without slipping 10 m down a lani 7/ 0hzlbm/ g.4dibf(mnxi (le 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 ayruf9gn 0 hi;jqi1 ;2ecceleration 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 oa km 6ubkz ;mi/+dfg5ceaa a3m:j5 11wf $4.5 rad/s^2$. 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 afte48f6e.wdi hu9 d0 ouuor starting from resuu6eif9 o0do d84uhw. t and accelerating 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 of o5cq. 8ih143ijtyc w e$4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerl (hjh 7lc8zo+i jst+4ates with a constant angular acceleration o lh s7+4ij +(8tjloczhf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angulam hvx o n95yf-8q.c:*creg-mrr speed of 6.0 rad/s while turning through 2cge5v-*m -ny.rq9chmf x8r o: .0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 6)fe xh6lor sp .w:.isg:wf i498.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wp)h9 fs gr:f.:o4iw. wxls ie6heel rotates in coming to rest?

  A wheel of diameter of 68. :rki: 8rkj8ff0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is thekrf8frj8:i: k angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40tvqf8 2yp 5n,n m/s to rest over a distance of 115 m. How long doesyp2 qv5fnt8,n it take for the wheel to come to the stop?

  A centrifuge in a medical laborazx e34sr-* *er wt*bz*j1sc ct 8szq:atory rotates at a rotational speed of 3600 rev/min. When switched off, r*cse4j3a1e*trs * zw qxz8tbcs z- *:it rotates 50.0 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 ti+j:k4x9x mo ipghtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the f4x:k9+ioxj mp orce is perpendicular to the wrench?

  The bolts on a car wh0*7 ;gh *clrylxtd8.h mig31h/ rnnxzeel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requic7;mi30hrl*ghn tdhlrgx*81 xnz / y.red when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner ::s csl.xr sqtojb8,hps(/k4 tia $3.00 \; kgm^{2}$ 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 the ori +x4c/nwv q9x*: 0vtsp-tq0bpjdj/e qgin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia abjw0q+/4:vdqxj *9nbv c -tqt0xpse /pout the origin?

  A solid cylinder of mass 10 kg is pivoted about a g9b7va8 a y9lbfrictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, 97bb a9 gvyla8exerts 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. (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 rkeqj 4i,u6a; 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 4i;e qka,j6r uF2 = 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 enhkcsh6b5qa z4ng0ye9 .azr3;d. The rod is initially held in the horizontal position, and then release9scaa.yhh;6n 4zrg5ekqz b03d 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 ML2/3.)

  Consider a bicycle wheel to be a ring of /vuyg7( lfq0nradius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprockevn(0f u7y qgl/t. 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 l ooo3*tzm d ni,1j-c.rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerc.o jnolo* ,13t zi-mdation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fp7lil y fdg-xg syqh(a*n2.1 7rictionless disk pulley of mass 7.07 kg and radi1f pnhg-yi.lqx7*s(a 7gy ld2us 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is red;2l8*d rd3cu 4k)0 eloxdabkquired 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 in mi;y7/bn ka.buax-;mertia 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 radiu0dz3i1zvnwa0 (r 2 vrrs 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined pla rz rrv3d(2nwiv0a01 zne. 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+/vyv 9( ki r)ehva2b) psfz:fg5.cqc rolls with a speed of 10 m/s. How high up an inclined plane can it climb be/ v.bvrckya(z2hqvsp fg +)fc9:)5e ifore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg iv0sk +/yn p2vqfl82481rnx syb9ve fws released from rest and allowed to roll down an inclineeny l09pfqv 8sy22+vksv8w 4n/ rf1xbd 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 rolls w:vr visotk;+vjw*9 o*ithout slipping down a 35e incline that is 7.0 m long. Assume svj9 rv:owt v+*o;i*k 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 changes b l*2yzrf0wuueo)c + r/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 momenk8o tg/-j,ujbom4o jtgf c 3 ,q*+kgv9t 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 a4nj, lvvz2 etliqg :(h105 k+pm/oumdd3mrm8t 5.00 rad/s with arms extended has a moment of inertia vurq4+h0 ,ll 2mg8dd/ok1mvn ( m:jei3 pmtz5of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?