Angular displacement is unwjh t+aqe.a 0 x(v8)rsually express in units of

  Angular velocity is expressed in unusr oap(x gl,xh l (/qlh4/d71its of

  Angular acceleration is expresvq6 x0xxc)y 3cys .4bqsed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a consca8r -h.zfqs (w- jkq-k r;r+htant rate. The boy is near the outer .ac-ksjq;rr (+fhz kr-q-wh 8edge, 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 turningi5 xjr d8c)a3w at a constant rate. The boy is near the outer edgcwrd3) ij8 ax5e, and the 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 turning be30)yst; pwb at a constant rate. The boy is near the outer e0p wyset)3;bb dge, 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 at a constant ratllw14 yw5kcr 4e. The boy w5k 4llc w4y1ris 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 a-x, gey5pwx;lt a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleratiowxxge-l;y p,5n?

  Consider a rigid body that is rotating. Which of the following is an acstw dq,ka s:70curate stdq, s ks0a:tw7atement?

  Rolling without slipping14c0c:*jox.nhyk jkq depends on

  Two equal forces are applied to 8srzw /vhd4qxd20kf*d hz 7k -a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular dkq 87/h4v* sfz xz 0-hddrwk2to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the d/w (qd4cgrqgp*t f )1uoorknob. The first force is applied perpendicular to the door; the second force isq gcr(p u*fw1gt/4 dq) applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to 6mk ,(t ;zsv9l.tq dafthe door. The first force is twice as large as the second force. The ratio of the torque of the first kfqzt 9;. l6(matsdv,to the torque of the second is

  What is the quantity used to measure an object's respx; h9byvmvso8:6el /istance to changes in rotatibvo6she;y8l9p :/vx m on?

  Consider two uniform solid spheres w.8 n.ub axau.hhere both have the same diameter, but one has twice the mass of the other. The r u.xab..anh8u atio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but9+fc n m l;3 emrf:7ryj9wjn(y one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smfre +w jjry39 n lm:7;f9mnyc(aller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the /qhv7n z/ j2w ckr,5d1uc dobi7xtl92 diameter of the other. Ti29nq7lccrv/bk ,o dzwj71 tx/ 52uhdhe 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 R. h-l1cltygsj*9)a ;fz15l irc If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centra1-ct5l c9zijsr f )*l lh1;ygal axis?

  If a constant net tor1z (h / vremyr vlr6+5te/b.5rglh 4glque is applied to an object, that object will

  The moment of inertia of a solid cylh hol+ 12ms*jw;vmdj.cj ) mw:inder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its1+jvclwjs d ) jh;ohm2mm.w*: translational kinetic energy is

  Consider a motorcycllyu a;+js*h4 ze 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 thaj;zhus l+4*y 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 mass M and radiusaoior4ge3h 0hi:a /iqc * x)/s R rolls without slipping down an inclined plane starting from rest/ac0i:4*rohsoexq/ igih a3 ). The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoutl/8hkiy0 hs +(g*dt lv8z: pdw slipping down an inclined plane h 8kg(p*0s :dd+yhizvlw/8ltstarting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momey (zaq57ydqjcb81a :(mj h 4xyntum of a system of particles changes when a net external j7yb1 58xcy4yzj (qh aaq(:mdforce acts on the system." This statement is

  In what circumstances can the angular velocity of s tasm5x1iybt k/ )*b0zmt37rh ystem of particles change without any change in the system's ang) tk5y3ms h17 rb/0t*imtax zbular momentum?

  The Earth orbits the Sun in +2nuznu/ j1tkds+ 5cx an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Sun?1cn2 dux+tk js/nuz+5

  The Earth moves about t( 7n2 h1tyxtyri0: myyhe Sun in an elliptical orbit. As the Earth moves close to the 2:rmtyyh7 tny (x10iy Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fs p-9qp10jouu ,wwi 65*h dqeaast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the a-5ueu9pqp, 6 a0*jis wd 1qhwoxis of rotation?

  An ice skater performs a pirouette n4wj1jy vdak9-q4 z*zxzy 6+z (a fast spin) by pulling in his outstretched arms clos -d9 zzvaxjj4+kwynyz1 q*64ze to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstu f6; uat b6irsl/e:, gor.ll/retched arms close to his body. /ra;66tll u,log.:r/ufs b eiWhat happens to his moment of inertia about the axis of rotation?

State the law of conservation of aa 1d1ehks(b )x hbv6t0ngular momentum.

  What arc length does the Earth travel in a three month period in its nearly )mm7:n hi*a0i)yrj5.e 0ju m v3u xhjpcircular orbit about the Sun with a rad uh 0rpuj*xevyma0i.) nhm:7)j 3ji5mius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of pw 8)( fr8oxlr c+r/au0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 secondx r(rc +f8w)ua /lr8pos?

  How many rad/s is 25 revolhax a) fyhub2ux-.u7 ;utions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wla mex*mfq:7.hat is the frequen7l:*mm a fx.eqcy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at ck5rxnx3r0 m0 a frequency of 0.40 kHz. The period of its rotation i 5rmknxcx 00r3s

  A phonograph record rotates at 45 rp; b3*zpr(jlh lm. Through what angle does it turn in 0.20 lphr;z*l( b3 js?

  A wheel of diameter 26 cm tur v11plqj5v wralg)( 9vns at 1500 rpm. How far will a point on the outer r (v) l1vva1g5rpqw9 jlim move in 2.1 s?

  A bicycle wheel rotates uniformly throuoob 2*us) ol*lgh 2.0 revolutions in 4.0 s. What is the ave)o* slblo* o2urage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.j4 nn;6,ig +wphca9sj 0 s. What is the linea c6nh j,;+9j4sai wgnpr speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a dist c9xcun u cn/6r8pb6k.ance of 6.8 km. The cable which moves the car is driven by a pulley wi /8kc6cbr upx .cn69unth diameter 3.0 m. Assuming 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 a constant angular speed o ..tgtbjwfi49zo ro:mro 9n5,a 9wsl0f 2.0 rad/s. What is th.ob :tonzwtl09m g49 wor .,irs59 jafe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-pow/ moex yesl6*sm+a61m ered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end oams61/s *xmle +e6o ymf the cord?

  A wheel of radius 1.0qde x,nn;gu7vv*. 0kf m is rotating with a constant angular speed of 2.0 rad/s. What is tk 7qev. nvx,0gu*n df;he centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle w:hxd ac j mn, 4*lxyh8..o8kiwheex:mj* h.x,i d 8 w.84kyhoalncl of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, row+ptvy h/x92 ztating space station (r = 1000w2x hv9zy+tp / m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circularopxuta2)4s3 a curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force4s 3axu2a )tpo (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating(,jssjij6s oii74r b )a(no2 o a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictionri64 ) i(2an sjo,b si(sooj7j) 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-mj,xpxx;e ao *6 string, is whirled around in a smooth level table. If the maximum tension tox *xjex a6p;,hat 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 without slippinupb;., -fdnha g 10 m down a lane at 4.bpun- ahd.;f ,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 acceleratb 3k *,lwb9no7vw/ bx4iaex*1dn6 nsoion 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 acv5:nfrpq)3voef1 2ub8ox/ ys celeration 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 ti skmif;t q)y tgkj.-42re rotate after starting from rest and accelerating at a constant angular acceleration of2k)jgtf.;k m-4 istyq $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, an9yql0igd)9 yhz.2 69 fbitspyd has 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 djok nn5w x5+1vecelerates with a constant angular acceleratinvj xo 15kn+5won of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest a*r 2.0k giwq 6z;nmazhnd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. k 2i0hzw;qn*a .6mzrg What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly j d.9xi)r0mz rfrom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in com)xd0i9jz. mrr ing to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overq-wi6co s, oarm(:)kw2t wrz0 a distance of 115 m. What is the angwmo2t z( k:c0-is6qw,owr r )aular acceleration?

  A wheel of diameter of 68.0 cm slows down ucf;ufnd h/ 1s3niformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the st; f3df1nc/suhop?

  A centrifuge in a medical labo. 1s- t:aquizyratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befor-1.szuqyti: ae 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 tighteningyc5wk k8b8 3 f t;5ia94fsbkdl4 nzb5m 5hjl:g to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when th5;b83m li5k b5 dgylkj4:bfhk8 ancwsf95zt4e force is perpendicular to the wrench?

  The bolts on a car wheel require tigbcwvlcb69:n , htening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force require9bn:v wb,lcc6 d when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i lm3zh(r7fy 0fnertia $3.00 \; kgm^{2}$ 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 o ;8.pwae5uyhc) ynif z6oe l(2rigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about (; 6a.5fyno8i)yez2 ewpc hulthe origin?

  A solid cylinder of mass 10 kg is pivoted about a oo nui4u 2uk1.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 seco4 u.o1k2inuution 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 ab33 y rhcf* sqd,pq*u1zout a frictionless axis thought the center O. A rope wrapped around the outer radiusy f13qd,** pszru q3hc 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 rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in the 6yv9jgx i16sthorizontal positiont j6yv9 6igsx1, 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 ML2/3.)

  Consider a bicycle wheel to be a ring of radrug,9 b9rlbh b*)yt6f:a eb+wius 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 linear speed does the wheel achieve, assu a lh) bg9twfyr ebbb9,*ur6+:ming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionles;uw)bek 2(: 0b4 -lii(q iqlyc 4sbcous disk pulley of mass 7.07 kg and radius 66.0 cmqs-li4 ye ;k0 :wcuq(cuoi2b )bl(b4i . What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped v;*k 9tuernq6 around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the anqe;rv9t 6 u*kcceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required tubz dng,j dlyf; 1i66c* af*u)jbh44n o 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 ofer n.+0oa3lc u 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 star phke)uwnr;;3+mmgr+d,/ hjw ts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed ;,+k/ghmwwumh )n3dp+e ;r rjof the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rollss*c1))fqn (w ql/ swju with a speed of 10 m/s. How high up ansc/* w1 jqluf ()nq)sw 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 and allowedbgtz:k o6- mfst/c53t to roll down an inclinc:t35 - s/mk6t otbfgzed 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 rz533 kz:ld ncjgpx,l- olls without slipping down a 35e x-pzlg:35 jlc3 kd,znincline that is 7.0 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 mome.wq0dsimdv 9fv (0 ia/ntum 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 mome w;. uw3qzimc0nt 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 with arms extended has a moment of inertir1 bpcvrlvk7 a9+qlve- .aet(c9-c 5 ma v-+7 19m vctl c-vre9rea b(c5qplk.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?