Angular displacement is usuall (f h-946gs,opj sn vfdplt ;ep25s8(txykg;a y express in units of

  Angular velocity is expressey u .r)04fq,vu+ 9deq ajao+qid in units of

  Angular acceleration is expressed in /ep -8xe harfupi48cpygppigy5d j)1.ae ;. :units of

  A boy and a girl are riding on a merry-go-round ikr487bf*a trwhich 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 ang b47ti fk*rar8ular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rzk1ulvv,6v2e ate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater an6v2v z eu1kvl,gular speed?

  A boy and a girl are ridin4eij4,82jjv3c n4u0 vd dtvpsg on 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 linear speed?44jvvc 0 48ndu, t32vi pjjdes

  A boy and a girl are b8zps,yols 1ee:hz9*riding a merry-go-round which is turning at a constant rate. The boy is near the outer l,sy pz91h* zeb e:8osedge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding nisvo d*-3k 2 2hkn5gqa 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 has the greater tngq2di k*-kv s 3h2n5oangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accur3lff,o9cte4 +;di nh4.ubq klate state elf.94,qu+cto;4ik l nbf3 dhment?

  Rolling without slipping depends o dznu15ik2wt58gu 6 pbgfa5u)n

  Two equal forces are applied to a door. The r:g,*;w *oa6soc7ofmazud uob; d +t+ 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 ;d*a;otd* o76o: b,z+afor mc wuu+gs force exerts the greater torque?

  Two equal forces are applied to a door at the doork7b;log-rp t(o nob. The 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 tor-b(7lp ; gotorque?

  Two forces are applied to a doorknob, perpendicula ocl1.ks/t yn1c7ni -jr to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the s1jc/n .ylti-k17sc n oecond is

  What is the quantity used to measure an object's resistanfb *u73b*zhrgj5l5 s-gf x+z hce to changes in rotati5r*buhszz-f h x+g 7 glf*3j5bon?

  Consider two uniform solid spheres where both have the +au a);4stiak (3jnpo same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that(43j apkon ts)u aa;i+ of the smaller moment of inertia is

  Two uniform solid spheres have the same mass 0)b iv-bz4bjs, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of zi0-bb)4 vbj sthe smaller sphere is

  Consider two uniform solid spheres where one has twice *wk3+nmx mkyl od5*tfr*(, ntthe mass and twice the diameter of the other. The rat3xn 5odrtlw* mmfknk*(yt, *+io of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and ,qud4zvpw 5) cradius R. If these are increased to 2M and 3w5c4 dzv)u pq,R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thy ddi3kbu:4o )5dvy;dat object will

  The moment of inertia of a ilck vwqd*6 gy i(b3)*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()bqw* yv ikd6l* gc3itic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass ofw( aqt soe((c1 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the csw qa(o1(e(t total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipa 7 i-o*47 +zv2a*hw9oopb axkux;/pdmgz/a uping down an inclined plane starting from rest. The linear velocity of thed7uu9 aa *m7a4 /w2i- p + xa*/hxzobkov;ogpz sphere at the bottom of the incline depends on

  Suppose a solid sphere of massgnzshk ;u.j23o,euo h68o1c m M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of tjkhoh ,e83cuno 1mu62;zs.oghe incline depends on

  "The total angular momentum of a system of particles chdw83e0 zk1a uz i0bhdya0s7(j anges when a net external force act a1ue7 ijywz0(bkdz0s803dahs on the system." This statement is

  In what circumstances can the angular velocity of system of particles change wbqil8 dy( k.c2f9ud,mithout any change ,im(kdy89 . b 2uldcqfin the system's angular momentum?

  The Earth orbits the Sugr9ya88o8:hpe oscj;t5 q2ul n in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum92e8 ghl;rjc 8oty :quas 8po5 about the Sun?

  The Earth moves about the Sun in an elliptical 5s z* c0as5 nem)1*q.pmvadly orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speezsqd*mp)n s vy01a5*em a.l5cd of the Earth about the Sun?

  An ice skater performs a pirou*lpsoc3/ ij) jette (a fast spin) by pulling in his outstretched arms close to) l si*/jjpco3 his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs v+lna0) f-x1n jzy b9ba pirouette (a fast spin) by pulling in his outstretched arms close x vln0bn+j-9 z1a b)fyto 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 hisjt9 j6w b,9shq outstretched arms close to his body. What happens to his moment of ine,t qwjb9j sh96rtia about the axis of rotation?

State the law of conservation of angular momentum.)pbj8 3xbjkrk. * yj v:7bqvhnk54kr8

  What arc length does the Earth travezs urw8xh*m,:l in a three month period in its nearly circulaw z8m*us:hxr, r orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of -lvnriuk3+r bbtu4ys d (+n: 60.30 m. What distance does the tip of the second hand sweep t+it 6+k4r:3nnby urdsb(u- vlhrough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolut8dj u wg(t)tqq3*u4mmp mmf(6ions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sxr2cs w7;f8 tu. What is the frequen8rcxw u7tf; s2cy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a 3q js hux4**;dx09doykw znh38mo2zm frequency of 0.40 kHz. The period od m;*hou* 3 0z4hx o8knsmwjyqx9zd32f its rotation is

  A phonograph record rotates at 45 rpclkr-kw4 (x/ fm. Through what angle does it turn in 0.20 kk(lx4 cf/-rws?

  A wheel of diameter 26 cm turns at 1500 rpm. How far willn)u; us.i.eyz8 gc uwo, 7t*axzpqv .; a point on the outer rim move in 2.1,o;tzu ap cv.;g7u8.e s*zw)i nuxy.q s?

  A bicycle wheel rotates uniformly thro)ni9e yxy3 (zfib qp0x k1z0g+ugh 2.0 revolutions in 4.0 s. What is the average angular spey9xepgi+3()00bz xnykfi 1zq ed of the wheel?

  A bicycle wheel rotates uniforwyv gdfd+gif*xb7o: h+l1 )h+ mly through 2.0 revolutions in 4.0 s. What is the linear speed of a point )f+ fv1*woyddgl7bhg+ :xhi+0.10 m from the center of the wheel?

  A cable car at a ski resort caoi 6hbbg)h)lhzn33 0 srries 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 fb0 hoiz)h gn3shl6)b3or the cable car to make the trip in 12 minutes?

  A wheel of radius 1.-azm clmv:8/inpr2i8bx) ;+8uu h nd r0 m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speedl uav:bx;h2cm)zri8p- r 8 /+diu8mnn of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.163gyx4w0 3k:q5 6:cpddhgg-itl*o u vk m in length. If the motor rotates at the ra khi 4pgxg3oq3c6 k l0u*g-ddy:v:wt5 te of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatingy1r 7ap q/ncu2r8uxj8)uk2v 6yfm j/jz nr-5j with a constant angular speed of 2.0 rad/s. What is the centripetal ac5r yz868ny/xva /1mufrnqpj )j rcuj7 -2j2ukceleration of a point on the wheel's rim?

  What is the centripetal accele ie;:.as* yhy 5s:itsgration of a point on the perimeter of a bicycle wheet:: e.sgasi; *yh yis5l of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cirp d0)uak0ayz5cular, rotating space station (r = 1000 m) rotate to producuad )pay k5z00e an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating7wvieb f),(dr 26ehqekt gnr+2t/l t; a flat circular curve of radius 50 m with a speed of 20 m/s.g,v q6/drk2 )7iw l(r+ hfe2 ;nettteb The maximum centripetal 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 circular curve of radius 50 m with a speed (471x2ulz4 o,o aal kd9dupve of 20 m/s. The maximum centripetal force (provided by s k 12(oze4d,vla7u 4o9p xualdtatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachcngmx9sc4(*)f;kim l8qka )xed to the end of a 0.750-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 them4aikqk f 8; nx*m)9x(cglcs) mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.09hkb l3,x bj+fyzs,/ v cm rolls without slipping 10 m down a xjlbbv,sh3+, yz9k/flane 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 auwzo 8yi a3r /cwr43/kndf :i a1s3rc+ngular 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 ofze-vtc7)7vp i *ng:alaa6t ynq+5 b 3x $4.5 rad/s^2$. 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 star 5/nn.lwn85ryf 6xpelting from resn6r y.5/lxpfn 5lew 8nt 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 acb;7nc2. +gm rfo7rrs aceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates 0;,qhr .obyl.f gk)p lwith a constant angular acceleratiopgf,.;ylh)l0 koq. rbn 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.eet-p5wr:w rdsg f32 rad/s while turning through 2.0 revolutions. What is the average anw5p2-er.e fd :3rgtswgular acceleration of the wheel?

  A wheel of diameter of (- zw)lwxt 2ewa6 f7qf68.0 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 wheel rotates in coming to restewf (7aqw 2fzl t)6-xw?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overorje 3,ay .y2h a distance of 115 m. What is the angular acceleratiah.y2,o3 jrey on?

  A wheel of diameter of 68.0 cm slows down uniformly from 8. z fl4-pre.m.p40 m/s to rest over a distance of 115 m. How long doeszf l..epmr4 p- it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotar *uqgu9 2isvka8+q9 otes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration bugsi*9vk 9 qoua8q2r+efore 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 trbr5w(p6uk wg9f: h eh0m9rmmb6 r *;gightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude ur hpwmkr e;509fmr wbhg*bm9(6 gr:6of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If aqzto/bm4y)ez2:, gl k 30 cm long wrench is used, what is the magnitude of the force required when the foz,z:g 4y2molebk / )qtrce applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofy9 p4 v9,v2qvpn+fbaj inertia $3.00 \; kgm^{2}$ 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 c-- *f pzxwi/b c:ws7cthe origin, mass 2m is at x = a, *-:cccwfxi 7bwsp /-zand, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kwjhhh+9 *xea3 g is pivoted about 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 =w9ax h3eh*jh + 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 thought tpxjdk6 3z:ng lh**m w3he centd:wnkgm p3x zjhl*6*3 er 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 rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held;y ehyh iqc.rtc r)1kc:23x5l in the horizontal position, and then released as the free end is allowed toyl ;kcxhr3c: 5r)y.tch ei2q1 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 radius 30 cm and massuu 48awp u+f e3;y:gfu 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 linea :u u+3f a;wu4fpy8uegr speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped hpxrp mj:-,+7i3fkgc )m x g+haround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerationxc+fxgh+j iph)g, : 37mm pk-r of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless d(bf qypz 4h:n m24.eesisk pulley of mass 7.07 kg and radius 66.0 phmq4 .:f(b n4ez2sy ecm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requir.;1f,:h0kn hvgjt g hoed 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 ine3ntt-t c9pvdrt zv,)0 rtia 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 0.01 *d3wygy( *vy/byvne u:t(h-eg 3a )py0 m starts from rest and rolls without 3nw g* evyy y/y-yb*ah3ue(:t(p)d gv slipping down a 1.0-m high inclined plane. 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;r0frx++s skos 8esb :;g kj1z 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb b:e0 s8jf+z;srbx+s o k1r;gskefore coming to rest?

  A hoop of radius 0.50 m amqv kmur 2n04ha78cyi(8it k8nd a mass of 0.20 kg is released from rest and allowed to roll d r8v82q umyicki0t478h(makn own an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of maz b(2xex1 84(ezl)z,tvhv tkm ss 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 moment of ikm( 4z(2vbhx lz)vex1 ztt8e ,nertia 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 momente/1t ymwuh96zn.,ougp m 8cca hba1() um 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 moment of i q0cl8z yepd y*ydd83.nertia 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 inerti(4uu1 w,hc/gmvl l aq-au4( w/ ,l1chmvg -luqa 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?