Angular displacement ag)a8 6c-jnk cis usually express in units of

  Angular velocity is expresseda-u 4)*trhtp pe;j+if in units of

  Angular acceleration is expresssej k(mm/o+6a-h3ia aed in units of

  A boy and a girl are riding on a merry-go-rouxk os 8hue88ml1yzc4 1nd which is turning at a constant rate. The boy is near the outer edge, a4x kco ym8es1lz 1hu88nd the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merrgqxn m)c3h6/ u8gtp y;y-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has t3y8gmngp; 6utqxh) c /he greater angular speed?

  A boy and a girl are riding on0;w pd cvvaw*;bwrq :l1-ett) o4pva 1 a merry-go-round which 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 lin * c:4v lwapawt) t1b-oqvpe v1r0w;;dear speed?

  A boy and a girl are riding 2t x ast+36 /fqtoevjj 3 /zrs4ytfj,(a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who h ej +6ss/4t jf/ozvqa t32rxyt, f3j(tas the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turn, 4vok 3vl8kxoy2ol r8ing at a constant rate. The boy is near the outer edge, while the girlo ovv,rk3l 2y884ol kx is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is a6rg4d5- yh huna.eaxw 97m( mdn accurate staa hg(ddyuwn54xm97 -6ar. m hetement?

  Rolling without slipping de7* c,o9+lpdc lqxt2dbpends on

  Two equal forces are applied to a drwfzs mx8f5( :oor. 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 the door. Which force exerts the greater torqus: 5 wm8x(fzfre?

  Two equal forces are applied to a door at the doorknob. jdqh,6/3e0 wmiu3 lg oThe first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door.de/6o33 w0mh ulgi ,jq Which force exerts the greater torque?

  Two forces are applied to a dottpsel46 u+lu9v s )8oorknob, perpendicular to the door. The first force is twice as large as the second fo s4t uep)6oslluv8+9trce. The ratio of the torque of the first to the torque of the second is

  What is the quantitygo(: h,q8t3 u+abfnyv used to measure an object's resistance to changes in rotation?f:go ( hy,q8b va+un3t

  Consider two uniform solid spheres where both have the same diameter, 5hin.ux:js 28g t9 + 5.iixnaiahwg9ibut one has twice the mass of the other. The ratio of the lah5t82 .+x:angsiix 5ng9i9aj .hiuwirger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sphereso+elcuf ,.q x. have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the suce,f+lq .. xomaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice *pa 25 cnjittq5aq 7*bs3+2 :wqvdmvqthe diameter of the other. qn bw v*s t5 5+dmv3qc2:7 j2aqt*qpaiThe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphereqllo;:j nc 41--vjxu s has mass M and radius R. If these are increased to 2M and -u4;sjljox c1n: -l vq3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object ks)/x+tq 0rfup6: n6q)s i hqz7eo co26 eu2pxwill

  The moment of inertia oi w:dd;no g-yq t,mn+*;vxd f3f a solid 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 kine*yqnit:g,3ov;+dn- ; d xfw mdtic energy is

  Consider a motorcycle of mass 150 kg, one whee qga)g nb+hn8(oh)1y(j3y tkkl of which has a mass of 10 kg and 1ng o)8j3g qyn+yh khb(a()tka radius of 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 3u 4ms; zumrc/ my03lnR rolls without slipping down an inclined plane starting from rest. The linears;u43 n3mlmmy0rz/ cu velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rollsz6 lwtry2g .;z 8da5t tfthw63 without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depent td glr6w3az8 fhz.wt5;6 2ytds on

  "The total angular momentum of a system of particles changes when a srh/pvdr3;,, l 1xwjmnet external force acts on the system." This statemehj/ rwrm dv,,;3xs1p lnt is

  In what circumstances can th988o 3/o c5qrvsxyexxe angular velocity of system of particles change without any chseor qc/ y95o x83vx8xange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mayl)u1 5iu:t:e l xh/8pydbkd-y be present. What happens over time to b: elh85u:1)ddk putlx- y yi/the Earth's angular momentum about the Sun?

  The Earth moves abouutx hx1y 3:hfzhe j(sgpp 39*9t the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which p :p3yuh ehh31t zxsj9(x*gf9 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 ixf we,g/6l 6den his outstretched arms ,x 6eleg/ w6dfclose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullincm u:iue xh.n,,at ,oa:nio9(g in his outstretched arms close to his body. What happens to his rotationa xo:n iium.9aotcae:,,nu,h(l kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fj7 ,udk.mrg8,nj6 aeuast spin) by pulling in his outstretched arms close tjkjnur67, d .mega,u8 o his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angulcw9t3)iby 8wpar momentum.

  What arc length does the Earth travel in a three month per4k2za/r.g tjt iod in its nearly circular orbit about the Sun with a t/ tg4kjz2a.rradius of $1.5 \times 10^{11} \; m$?

  The second hand of a cloc qtgns;hd g7z,iubj d(0ju b5pc,o::* k has a length of 0.30 m. What distance does the tip of the second hand sweep through in ,tousndb;70gd:*( i,jq phcu5: z jgb3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivjk)m5ic0h s+r*d;utobhnzo8 0o 3j -t alent to?

  A bicycle wheel rotates uniformly thr;coo 2cg-y :haough 2.0 revolutions in 4.0 s. What is the frequency of o2 -yhc g:c;oathe wheel's rotation?

  A pulsar (a rotating neutron star) emits pul;1c9 dz f6)ldwvwqyo -ses at a frequency of 0.40 kHz. The period of its rolf9 - o6zwcw;yd1 dq)vtation is

  A phonograph record rotates af 7h tt8al6.gnt 45 rpm. Through what angle does it turn in 0.20 s?68f lt.7tg anh

  A wheel of diameter 26of0i7 sixd3k*b x4r g+*od, qkwgsc 3: cm turns at 1500 rpm. How far will a point on the outer rimb 34id* i:gosxfcds0 k3qxkr+o*g w,7 move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W;* ou ahpffv:-hat is the average angu : f-*p;fahovular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolun:o+9 3xcllqf.p8/rjy49s :sgq6lm plulkd8 tions in 4.0 s. What is the linear speed of a pointgn p 6c9x sl84 d:ys r8:/oll93kquq+m.plflj 0.10 m from the center of the wheel?

  A cable car at a ski res*agf-9yr n;+tt9 bbzj ort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuzt abb;9t gy+jn9-* rfming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with h0/t *l/1ljx ca g,klya constant angular speed of 2.0 rad/s. What is the linear s chjg*lk,1t0 //ayl xlpeed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the0 ;vfcxwq+lhsz* 30l hzaay :5 motor rotates at the rate of 20 rev/s, what il+;q:*l vyas35z hxf ah zcw00s the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a /i,xahc 1dca5 constant angular speed of 2.0 rad/s. What is ha5c c1d/i, xathe centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a v2/(rhqbyzb ; point on the perimeter of a bicycle wh rb z2;(vqybh/eel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating*iy skh6b5mds-73zqg space station (r = 1000 m) rotate to pmi* 7yk56 b ds3ghqz-sroduce 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 mbep;2gj vh6z (/s. The maximum centripetal force (provided by stabp ghv6z (e;j2tic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cirq)jy,*m- +r0mrt 9ea)b ch zgocular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictibr-a,) q *9jthe+mmgo)zyr0 c on) 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 0e sqk2l2 c-i:k.750-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 speed can the m2ek2q:-l c ksiass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls withoz1c3n ubahg; rg9 7yc0ut slipping 10 m down a lane agh ; 17z c0yr9ab3uncgt 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 accelex5 a7xp9+egvn.v0i x fsj*w9pration 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 angulas l6iy orb) 9ssis/+46j/h pwjr 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 0.300-m radius automobile tire rotata)2;*vu2qm af h8nwk 54d+ bue utsye.e after starting from rest and accelerating at a constant angular accelerati5bu; aw+qdt.ke*sva 2ufm h)82e4 yu non of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration h*6qa4em( *bojl/tuxr9m2 u owp79y e 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 cons-hbgq(pw5j s 9tant angular acceleratsgbpj59 q(w- hion 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 6.0 rad/s while/ nlm7s 4tm7qe turning through 2.0 revolutions. What is the average angular a7 s4nlm/ e7mqtcceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unifot(wuo,a 7cj s5rmly from 8.40 m/s to rest over a 7t oc 5w,(jasudistance 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 to rest oo-g9nq86f1) ip r vosjr .n*hbver a distance of 115 m. What is the angulqj.nfn8roo)p - rh9s*1b gv6iar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to j4xg4k0j zf mj rzqyr*vd 34/:rest over a distance of 115 m. How long does it take for the wheel to come to the vr jdzy0xg*jzf/j 44rq:34mk stop?

  A centrifuge in a medical laboratory rotates at a rota n6 35gwyoit+ztional speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration beforeiwn 35yg +z6ot 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 requirq2-w : pk83(m1i oi0ep ctzpkte tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicuzt3tkmwp 02q-pkc 8 (1i:ep oilar to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 3bya6bo1e4;b 1 wrez f,0 cm long wrench is used, what is the magnitude of the force required when the force applied at 4zrb b, byo16eaf;we1$53^{\circ}$ to the wrench?

  A wheel with moment of z+c 4z6u6 1x ttij.kvzinertia $3.00 \; kgm^{2}$ 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 t56vz vl1u2ie2htuh :ihe origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of 6v5uiuht21 h vzi:e l2inertia about the origin?

  A solid cylinder of mass 10 kg is pivoteyqg1gh t; b,eg.g-t)v d about a frictionless axis thought the center O. A rope wrapped around the outg) b;tyv1etqhg- g,.ger 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted aboupja7(gak . os)t a frictionless 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, if it starts from resto)k7 .jagpa( s?

  A 4.00-m long rod is hinged at one end.(za ;bqnc-5ho+x jje( The rod is initially held in the horizontal position, and then released as the free end is allowed to falxj+c-e(h b(;aj5nozql. 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 radt fs3r 7hb1 29nm*xmbaius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force 72tsrbbf*ah9nm 13 mxof 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 a6d6 z7hckwmwk:se g7d- op eng 3pg.p /4:-ovi rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pw-pp- e 67egk:kzv d3/ 6cigm go:on4dw7s.hpulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dis.u lu,quetlf9vy 548)f, 9yhs lbc a2hk pulley of mass 7.07 kg and radius 66.0 cm. What is the a8cluuy9 4 hqaf )lu 9vlh,.y5,bes f2tcceleration of the mass?

  A rotating flywheel can be used to store ener 1qu0w nkdm:e.1mvr,,l:x z fdgy. 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 t d*v3 pxxgd57of $5.00 \; kgm^{2}$ 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 masv d 18c5kp8vmgs 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. Wha v5gd81cmk8vp t is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.fgr7w:8r-baduz ,3k jz9j oa3 0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it clirz 3 9j8j3owku-d ,aafbzrg:7mb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest a qx1 wznl:iv7ulq m.-dw,w/9hnd allowed to roll down an inclined plane. How fast is it moving after d,zhw7 lwl.qux id9/w:vn1 mq-ropping a vertical distance of 3.0 m?

A solid sphere of maqb8l;j )n)o eqz1,kqrss 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mome18 n oqr))lkjqq;b,zent 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 change7i65 ao bp(nohq6)(ij aj oo.zava hh e)3/ih8s 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;(tje7*naylsu/ v6 vl yw +fv* 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 extend6cb,gt* aq7vxt n (n6bed has a moment of inertiaavg 6tx ntcqn* b7b,6( 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?