Angular displacement is usually 7s7/il5qwq 3owlti) :bm m2eq express in units of

  Angular velocity is expressed in kc i .04b h g7u4qqtqhrz4kt-*units of

  Angular acceleration is expressed in unik(y7u gu6yeu9 ts of

  A boy and a girl are riding ow *1jzbkpf6 h(n a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and t 1whfp*kj(b z6he girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-ro,h:4-0qure ,bnm1az tvh (uoo 8 0ibgvund which is turning at a constant rate. The boy is near the outer edge, and the girl is h a:tzb 4veiv,m8 ou10gbq -ro(n0u,hcloser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning afuaw .x(jz /h.,d izbr(x9g6 vt a constant rate.zrgv.(hb,.f/6(ixxau w9 jdz 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 riding a merry-go-round which is turning a0o -, 9mpzocu p /hw-e/mtsmw7t a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the great /hwpe zmmt-,0pcmu7osw9-o/ er centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turninam+/3cuuq- f:p- -knm y hitp8g at a constant rate. The boy is near the outer edge, while the girl is clfu uaph -/tkqpn -myc i8:-+3moser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of t-aulej /6rs1 nd atn 23wbf88x5tb)p9phwp p8he following is an accurate statemeu/n9ean 8-6w b 8j53l)s8whpfa1pt 2pdbr pxtnt?

  Rolling without slipp*5tkgrd6p) wr ing depends on

  Two equal forces are applied to a door.0ufeub xcyon5s)+9 t ( The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forcnt cbf)u9(yue 05s +xoes are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The firsujoxz(u5w +n6t force is applied perpendicular 6u wzox+ujn5(to 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, perpendicular to the door. The fir(m7yxzk:vsm4 st force is twice as large as the second force. :ykmv m z4x(7s The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measuro nh ceh*2zo*/e an object's resistance to changes in rotation neo/*2h*co zh?

  Consider two uniform solid spheres where bo8v5 faicb 2pn+ 6t:oswzpl*.nth 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 smaller oanb2n6f+v iz:c.s8 5pwt pl*moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of i7:gj)ea1z95whfnf a nh-d-0bmh a5 mthe other. The ratio of the larger shn-h1:zdm ) afhi5 nefa0gw 9jma7-5bphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres wheqjb3 l3+c tt;e6ejkyx s 0+g,jre one has twice the mass and twice the diameter of the other. The ratio of the larger moment o0jb gt qjtx le6cjs;y+k3,+3 ef inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass Mm )a 7jrr*jqm xq6ll (k:rif.+1fyu7o and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centrk o q6a+ f7(lqiurm7ylr:f*)j. jxmr1al axis?

  If a constant net torque is applied to an object, that objeif:vm6lcl1 yva*t )8hct will

  The moment of inertia of a solid cylinder about its axis is given bccz/-8c8r pyue,n rl+y $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of y(g2o hjw0 l6b10 kg and a radius o6 wgl2 0bhj(oyf 30 cm. What is the ratio of the 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 mass M and radius R rolls withou*h)nmo d*eg w6q7t5ght slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom g6 *wge )5nhthqod *m7of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an incj6 8)xmwy:g6c4awtx w lined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depent aw:) 664jxx8cmw ygwds on

  "The total angular mogn6 .*6h s3o ;naa+alfjadv r)mentum of a system of particles changes when a net external force acts on th*fahodl) +as6n3 aan ; v.rg6je system." This statement is

  In what circumstances can the angular velocity of system s:*hdhj .i4 77e hnljrof particles change without any change in the .7 eh:4jjdnhlr i *7hssystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbrcty8-ceunt psez ,4 c x2*4h8it. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Sun?c hn8uy 8tz te,4*cr -xspec24

  The Earth moves about c1 yq*xujtyzfm 32(c; the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describesqmcx (zfy3y1 t2 jc;*u the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou s+b4c2ldw3rxtstretched arms close to his body. What happens to his angular momentum about thx l3 +2s4wbcrde axis of rotation?

  An ice skater performs a pirouette (a fastb0k5bg+ ohua9rv;: c hr;r3pa spin) by pulling in his outstretched arms close to his body. Whar; + b3acrphv 5g9 kr0oha;u:bt happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) balk; h (tybuu,h+k7u-y pulling in his outstretched arms close to his body. What happens to his momkkul u h(-bh 7y+at;,uent of inertia about the axis of rotation?

State the law of conservation of angular momex5)6i *2)ym m zjmvltpntum.

  What arc length does the Earth travel in a three moi+- 2hkma:kog 13ya mvnth period in its nearly circula -a:m2kia y+m3g1kho vr orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tip oz+guk c; 13tvbf the second hand sweep through in 3 minutes and 45 s 1tbu +vkzg3c;econds?

  How many rad/s is 25 revolutions per minute eun gg0s 72 )r8vd n,j(yuit(ntquivalent to?

  A bicycle wheel rotatelyxiwi/-+l 5 ms uniformly through 2.0 revolutions in 4.0 s. What is the frequency of tm-5ix+ w /lylihe wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kH :2/3*cly .gbxqy fle f2liyv;z. The period of its rotation yyll*3 2b:;lvyfeqx 2 cgf.i/is

  A phonograph record rotates at 45 rpm. Through wha:-x hi7ht -kgu:2u1 gw2iorrdt angle does it turn in 0.20 uu:ikg21i2h 7-:x g-odr wrht s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the ouazq1ld f1,99 -ajm o2+ylzdwpter rim move in o1qaa9,zzmld w jyp1l9-2d+f 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatql. e0v-sx;z ny:pm6 e is the average angular spee-ys m;0n6 pz qevxl.e:d of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutionsw4oon;x0)zua tmw(x 2frxu9 ( in 4.0 s. What is the linear speed of a p(u94rx a2o) 0x;w(wxtumfo nzoint 0.10 m from the center of the wheel?

  A cable car at a ski rewz+2oml2n qwelr tzw 1zu 2/12sort 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 wn1l q tmzeo2rlw2 /21+ wz2uzfast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotat x u)w;cy-gp sbmse*8+ing with a constant angular speed of 2.0 rad/s. What is the linear speed of a poes*+p)sw ;uy8c g-xb mint on the wheel's rim?

  The cutting cord on a g mm)qu g ut8yd6h 2n+ja3euq56as-powered weed cutter is 0.16 m in length. If the motorhu3m68d ) enm u6gyqujq+a2t5 rotates 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/s.q wxto;obsvo57.;d +f qbtsw;o+7.f d 5;v ooxWhat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyclc:6yy fp2pb 8ne wheel of diamyb f8: c6ypnp2eter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions p(o qrckw0 v4-fer minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an arwo4cr0-(fqk v tificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of ra0/, a 3u6ksfwhlj6f.yhgb janh/ 1ok7onro0/dius 50 m with a speed of 20 m/s. The maximum cent66oj gak1olkjo/n0u,h afh30/ .7bfhw r /syn ripetal 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 circulatvp3/t* 7 ( an+ftigyar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictg v7t f/+pay*an 3itt(ion) 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 strg. e upblf-edb9*n9( ning, is whirled around in a smooth level table. If the maximum tension that the string can withstand is *(gnub9n e -deb 9p.lf250 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 wimis6n 7hfh)m.-qy5,(ljb lzythout slipping 10 m down alm 5fn7ms6yyb-,hil (h).qj z 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 a constant angular accelera:rdj3 bj wm.y:tq*k a1m5 zyx ,o;8xgmtion 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 of r)bk *glx9xr )$4.5 rad/s^2$. 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 after starting f)p mp8yzr4 8n-xq0th srom rest a)0xyp-8pn zt4srh mq 8nd 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 a ( rfe;t3p+vp kvj/0gzc(0ho rxn4k (3mx2qfqn 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 constant4dzv/szz qax 7 :l1w*r angular accelerationsl 7qd/*r:4zzxva 1wz 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 spn /zdqt1i)-- u:e cvhjeed of 6.0 rad/s while turning through 2.0 revolutions. What is the av1q:/ jcn-e idz -h)utverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slomn jo, , zcqskim.;iv+q -8kf1ws down uniformly from 8.40 m/s to rest over a distakmqv qjm 8-s1. k+coif,,n iz;nce 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 sr:l v bct5;jysxw /5r ks)(pb4lows down uniformly from 8.40 m/s to rest over a distance of 115 m. c5skxpjs)45b(blt /v r y;r:w What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dow09gjbu3y-60nhqfk-p2;v ut2pl tdk an uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take 2vbkq0tkj p9;ydft02-h6uu3 alg-pn for the wheel to come to the stop?

  A centrifuge in a medical laboraz-1ax7 gmse-mpef.jq )1 *ol ctory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 tiepg c1ma zemf*xqs-)l7-.o j1mes 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 torque of 90 Nm. 49,ke5b * kwtu:u59idc hoxj j If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to th,5j*bu4j 59k9wx k:eu ihtcode wrench?

  The bolts on a car wheel require tighteninyn y0z8vdr6hal8 1nc3 h j9x arj3p.+sg to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force3ly8 +ry azns9x6a8j0hjndhvr13 .pc required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia px7rwfre*52 bnidop n*m9 0c)$3.00 \; kgm^{2}$ 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 origi +vi8 jrfox/5fn, mass 2m is at x = a, and, mass 3m is at x = 2a. Whatx+5if fo/v 8jr is the moment of inertia about the origin?

  A solid cylinder of k0now7cw1;2b4q x5cbv8o b jc mass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped arou qbcx1o7v w j52; ck8b4co0bwnnd 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axycq( whs (wfc /:s/co:is thought the center O. A rope wrapped around :(cssyfc o(wchw/q /: 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 ej t a-6d*kh)kste m0j1nd. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it isd-jeh kka6m*t1s j0t) released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ringiz0ko,)jo ea*n8 ys4i of radius 30 cm and mass 1.5 kg. 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 line oza,0 o4k) j8i*eysinar speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a r(e :/fm j1ekzdope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of(/ekjfez:m1 d the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pull g+wh fb9gg0c*9nx (syey of mass 7.07 kg and radius 66.0 cm. What is the accelerbg90wxy ch nggs f9*+(ation of the mass?

  A rotating flywheel can be used to store energy. If it is requintyfp( i,2)oo )g3gzrred 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 ofeld8vq-cc60lvne/yb j 5*q 0di5 bwx; 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 stk(atz48zfy:w ;d2xsk4kxum* arts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of thdw 2;sxf tykm 4kukxaz :(4*8ze inclined plane?

  A solid sphere of mass 1.0 kg and ra,ilyxa5u9 a x(dius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comi9a( yxa,i5lxu ng to rest?

  A hoop of radius 0.500d6 h ky6ro 5lmlw8jq6 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it ml5 kdr6j m8l6qy6wo0hoving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippi74tkc 1ylod 4yqe o/p/ng down a 35e incline that is y dyq 4k o741ct/pl/oe7.0 m 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-om m+u.1ow.lvjfcah4u htyc4 / +bl . changes 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 mome7lxa e2+)- dwlpx 1okqw7r mkvv:(f;int 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 wj9bs dj,d.sx;ith arms extended has a moment of inertix dsbj;sj,9.d a 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?