Angular displacement is usually expri(*m 0 brf08eywh:dhr0 p-2cdc(t sdzess in units of

  Angular velocity is expressed in unwl5ao-/i(de4/h2y qv 4 mc xg2ahah * jol7dg0its of

  Angular acceleration is expressed in units oz /sd(oeajmjf+4z 60 u2*e gnwf

  A boy and a girl are riding on a me0 yh;nyyvg s/e+f; )elrry-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 tyf0e;g+)e s/yv lh;ny he greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constanfhzghdu(g:lp09 4j( g t rate. The boy is near the outer edge, and the girl is clozuhg4 j0lfp9gd( :h( gser to the center. Who has the greater angular speed?

  A boy and a girl are riding on aa7 zk0md((zne merry-go-round which is turning at a constant rate. The z0(k7z mad (neboy 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 ridinky.(qlig ij 97g a merry-go-round which is turning at a constant rate. The boy is niigqy l9. (7jkear 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 issn:mhf m4tfv + h1-mp5;e ilj2 turning at a constant rate. The boy is near the outer edge, while the 2 mlihsjh+nm :pftv 1m-4 e5;fgirl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that p jxws-;g( u-mis rotating. Which of the following is an accurate statementx- ;m(s-pug wj?

  Rolling without slipzcm awq,,92kg ping depends on

  Two equal forces are applied to a doords-0 xbixza *+. The first force is applied at the midpo *bxzxi0-sa +dint of the door; the second force is applied at 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 by/fd -z-e0mv. The first force is applied perpendicular to the door; the second force is applied at bdzfyv--e/ 0m 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendinoyncko +t*o9 o -q58qcular to the door. The first force is twice as larnk*o5- q9on qco8ot+y ge as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to,k.g m bim2z i4ihd:w, measure an object's resistance to changes in rotation?d4z .k h:b,imm2i ,igw

  Consider two uniform solid spheres where both have the same d nddhl3g b.j7i 7e27phie5j/xiameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment g7be 7.ji3j hh 2xpddnil75e/of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius ) o;j9 zmzv;qgof the other. The ratio of the larger sphere's moment of inertia to that of the smaller smgvoj9;z )z ;qphere is

  Consider two uniform solid spheres where ozu j:-sb87vxni7dtw+kxcv 7i ol6*2one has twice the mass and twice the diameter of the other. The ratio of the larger mo 77x-2wd:nvszt b* l78o kovxuji6c i+ment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass e1i eu6va 9aorw7(-v,choy7v M and radius R. If these are increased to 2M and 3R, vh7 ae,yvr6( 9aouw71c evoi-what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is ey.e1hbyn : /papplied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is givenkn 8+l93up l nvwsk1*d by 0.5 MR2. If this cylinder rolls without sl3l +pk1 8wnnkvs* d9ulipping, 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 1kpxz 9jblw*i a014x;w0 kg and a rk bj;w*lz4xpx 09i a1wadius 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 mas/ bt*3z 9(w nwlgyn8fjs M and radius R rolls without slipping down an inclined plane starting from rest. The linear velo8 n3 njb/y(tlfgwz9w *city of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wwrs pp x7j(mtm*;09 trithout slipping down an inclined plane starting from rest. Th9sr px pjw7 rt(;*tmm0e angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles cxn efk 9uoej/7* ega;9hanges when a net external force acts on the system." This statexo;ue7e fnge ja*9/k9ment is

  In what circumstances can the angul -hx r s 4w*bqz;n,7scvdiw.3zar velocity of system of particles change without any change in thei3r ch d.z,z4sb;n ww*x7q-sv system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore an86- n llsof24fekvqr eon-4p/ rg- *ody friction which may be present. What happp-qeff*lorvogr6ne/o- 2k 8-nl4 4 dsens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in a )tu;kk/q4//ler qdk sn elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of theld/ u4r/sqt/;kek) q k Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch+kxxi g780z3r 1yy nrtju6*z cgz7zu 6ed arms close to hiszzz*k6 i +3g0nuj1x8g7y7 cr6z txryu body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouettjlmv,px061 fve (a fast spin) by pulling in his outstretched arms clo,jxmvf0 pl 61vse 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)rvktku: 0( oz outstretched arms close to his body. What happens to his moment of inertia: oktrk)( vzu0 about the axis of rotation?

State the law of conservation of angular morfn:+ch0w mt5/y3m nmmentum.

  What arc length does thdy/77;zfy iy :slj 6ime Earth travel in a three month period in its nearly circular orbit about the Sun with a radiusy f:zyij7s6i; / dy7lm of $1.5 \times 10^{11} \; m$?

  The second hand of a cloc 94fov8zn8n ya84lsfk k has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 min8sy4ff a98v ok8 nzl4nutes and 45 seconds?

  How many rad/s is 25 revolu6,ty9cmi5t i btions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.iu5xr; 9ff0d wg8(5tr(d f tjg What is the f5wtrt5 dxfufg (rd ij(80f; g9requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thlqzkkh , + ag2+rxz;);ue)bm we period of its ru;2k,rxba+mh lg + )zzke)q; wotation is

  A phonograph record rotates at 45 rpm. Through wh +2mp8u9/ dkma xgqr6cat angle does it turn in 0.20 umkd/acgr 2x9+q 6pm 8s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on th0ur7+ mccj75hy 7klzje outer rim move in 2.1 s?j+zl m7j5y cchr 707ku

  A bicycle wheel rotates uniformly through 2.0 revolutions reo/ack.e 5f1 ,.msay in 4.0 s. What is the average angular speed m,arkf. 1y.as5ece /o of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions it+telw 0 ,diz6 7yah0zn 4.0 s. What is the li 6i+7dz ,z0wl0t teyhanear speed of a point 0.10 m from the center of the wheel?

  A cable car at a skis +g.x/ o) g4ns9vyjta 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 for the cable car to make the trip in 12 minutesg 4tyoaj/9snx)gv+ . s?

  A wheel of radius 1.0 m is rotating with a constane/ /h 6v3gt8nk v9walk*e 0 ,mejhodl,t angular speed of 2.0 rad/s. What is the lied,30omv/v,ah *k/9ejewn gk8 6l htlnear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lo6ris7o p)4njftm.:o ength. If the motor rotates at the rate of 20 rev/s, what iroio6:o f)m 74n s.tpjs 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.ve7tnv ea;)+ muzg(*g What is the centripetal acceleration of a point on the wva) +g7(*;m te evgnzuheel's rim?

  What is the centripetal v rn0lx in/v*x,9 4vglq i0g6facceleration of a point on the perimeter of a bicycle wheel of diamet4*vrx0 ilfnqg/0ln6gv , v xi9er 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotati 1nik/ w(kv vbgdj5qeq*4p1 3 onf-df*ng space station (r = 1000 m) rotate 1f/ dbfe 315 -gqjqinv wo4p(kvdk *n*to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ofksd)vkl zg6 1 0i r1f5/q-cjpn 20 m/s. The maximum ce 1gpj01kvkqz-d)n i5/6rcslf ntripetal 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;2zgp dy rw+x-e 5w :s)gu3rtp flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) it wps-:z yrpe5d;+x23wu ggr)s $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whi:;pugn-gxe2uty)b q0kg(f- n :efmom*z5o,v rled 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 mass have if t-gp50 g)bm*q;zyfkunxt:(o-geu f 2ov nm , e:he string is not to break?

  A bowling ball of mass 7.5 kg antdo rq/vddg,- .mm3u1d radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s3udmd.q /om ,1vdrt-g.
(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 withb lm7dsd5cqp hc1e20 : a 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 oq/k-rv a+ 9lgff $4.5 rad/s^2$. 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 rh ux) ty)md3.uadius automobile tire rotate after starting from rest and accelerati.t d)3hy) uxumng 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 accelerrsp:vi/ygj9a 23j +z/ 9pydmtation 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 constant angular *spvu0ou5*fwo8v-vr h)1ib a acceleration of vo50** i uu)s rb1ohpfvav-w 8$-5.0 \; rad/s^2$. 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 wh7)zpogcss79ose . h+c iq*p)pile turning throughhsg7p icc9.psops7 )+qzeo * ) 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.d gvdo 36hnbh95l);oj0 cm slows down uniformly from 8.40 m/s to rest over a disdh5 3 hobjg9ov ;n)dl6tance 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 sl p 8if4msqtd a6/cyyz 7w;85 tevoh3la:o81wbows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accele3 y;w t818amf cz476o:pbyhds8 lie oa5vw/tqration?

  A wheel of diameter of 68.0 cm slows down uniform8 i2aofy4fw3q ly from 8.40 m/s to rest over a distance of 115 m. How lq4yof f83iwa2 ong does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at i*qkpktg5)rzat +b i5ghp ,rm s5*79ja rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acizp9ki)rp, 55 * hgrtaq57 tbksg+mj* celeration 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 wh a-h9i8g6l p0q xn /e4u/fjdoveel require 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 perpendicular to thepvq l8j/ ix/-h0n4af69udo eg wrench?

  The bolts on a car wheel require tightening to a torq.keqou dg) qm .,jyq -45kkfj9ue of 90 Nm. If a 30 cm long wrench is used, qe 5jumjk.)4o,qkgy d.9fq- k what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine4b; w f7hvpwvb..e- oartia $3.00 \; kgm^{2}$ 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 origin, mass 2pe 6b0q ev1s42wfyd7dm is at x = a, and, mass 3m is at x =wfsdpq v b16720edye4 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thou sfq6ydnix2:5 sq4v0aght 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. (See Fig. 8-1.) What is0 :42ndsfi 5sx avqyq6 the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionleakl,ar db 8rqy*;n6 3xss 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 seco dxknl; *b83 ya,6rrqand 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 iso 6jt;n g80t qq,z*cth initially held in the horizontal position, and tjnt 6h* 0qottqg c;8z,hen 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 rikt4dvj t.d1u0b 5lo 9vng 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 linear speed does the wheel achieve, assuming it rolls without0oku59.1jtd dvv 4bt l slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p9 gb)um2 qx b d4lr),ogmhrm2c gk-a:9ulley of mass 7 )-uld marco:)qgg9,r g92kx24bmbmh .07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless di9 nl w:8e ohzbqhza0)bar0q.5sk pulley of mass 7.07 kg and radiusa8)h r a ezo0nhq9wbqbz5.:l 0 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. Ir-9nk)yd 3fxg f 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 ineei8)a k.vg fp3rtia 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 kxir 4 7l:rihmhep -6a(0pdj+ig and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined phx pld7jim4(:i0+irpa6 rh-e lane. 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 rolls with a speed of 10 m/m6mrv5fz9; s nk f,4wwsfx ;0js. How high upww4vzf;fr 0jk 56m,x ssm;9nf an 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 jvlv6 :x8unf2f vs,j )from rest and allowed to roll down an inclined plane. How fast is it moving after dropping6f u jsvnf:jl )2vv,x8 a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 8rr bp 1slz+o:gw5w wn5k1j4g15 cm rolls without slipping down a 35e incline that is rbgsw85njgwpwr41k+1:z l5 o7.0 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 chj ol/qj(y+ q/vanges 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 mftnkt0t6zsg9*p 6h q)oment 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)c- 6d*,f4-euk4etu s8fu6 fgggsppd has a moment of inertia of8p6dg4us *,ugt)-dufk 6 4cfgesf- pe
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?