Angular displacement is usually tdi36zku/um890s agm m )lfq /express in units of

  Angular velocity is ex d7zjfhg1ci : nw,.b(wpressed in units of

  Angular acceleration is expres -1uvc;ozn m,vf/6iq.a qjft* sed in units of

  A boy and a girl are riding on a mev qp r;(aakgd a(0m*h2 )jcbcyp/0 i4drry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whoppq/ c0kg 0a bmj;dr a*)4av(cy(ih2d has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a coa kk*)ry ;qvkd5rtn (az o44:gnstant rate. The boy is n :q(rk);kvy kgo4* a5d tzr4anear the outer edge, 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 at a c qheyjo*zi/m 6.bn u2;: b/pedonstant rate. The boy is near the outer edge, and the girl is closer tyhjop zn .q/b/im:2 ue 6b;de*o the center. Who has the greater linear speed?

  A boy and a girl are riding a w35 zu( (jr5l)wp lleimerry-go-round which is turning at a constant rate. The 5rp(ej(zlil w5)3ulw boy is 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-rounrz fg64ia7 8los1*-k pbdpk7 zd which is turning at a constant rate. The boy is ne-li 4pk fpr1bka z7dg6o*zs87ar the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body rtzyhq8m+ mcy vz:z3fu2y 1 4+that is rotating. Which of the following is an accurate statement?z2u1 zcrym+m8hvy z+34yt:f q

  Rolling without slipping vp fbf:la0 c ib qw;)v8;l26*4lf fwcpg 2w)ladepends on

  Two equal forces are applied to a door. The first force is applie2.kh 5xf91 s 7ddsjfaod at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the 1dah o sfd.57j2x 9kfsdoor. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. Tz6btd ny*;p e6he first force is applied perpytpe6z ;6bn *dendicular 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 doorknop6r5ojlr4 :h4pwnv a2 b, perpendicular 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 therp4o2a5l j6hw nr: pv4 second is

  What is the quantity used to measure fhb3k)e(tt-mf j hw9 .unyg31b;p9fn an object's resistance to changes in rotatio pwj1-f ye9h;ntbhb39t)g ( f3umnkf .n?

  Consider two uniform solid spheres where both have the same diameter, . ue:sc.;jlc:n rhbfan/dur73 f s.f) but one has twice the mass of the otrfa.f .h/lurds c.fcbnne 3 ::;j7su)her. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, b ijw xwj718vn*6oa k/xut one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphi kx/68w xvwoj*na7j1ere is

  Consider two uniform solid spheres where one has twice the mass and twice the dd lx9blc .4j;wiameter of the other. The ratio of the larger moment of il b.xw;j d94clnertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are vh4 -d 8t8v5wchy)5c3 woqd ly79 ztmeincreased to 2M and 3R, whe m- vvd38wh7czt)w5qoy lh 4y5 cd89tat happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objecr ,uw ewlym 704/n vf58cjsaf7t, that object will

  The moment of inertia of a solid cylinder abobd:mj./o1jtzc 3yh1 hut its axis is given by $\frac{1}{2} MR^2$. 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 ma1/t:s pn ptej.ss of 10 kg and a radius of 30 cm. W/pjptts ne1.: hat 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 without slipping dowhe am2vrxd7z t5pt9c6q(l t*pj ;5df 4n an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the 692etrp vct 5azh * jftd(pm;5dql4x7 incline depends on

  Suppose a solid sphere of mass M and radius R rollskrciab 4x2s1 v:7l 6wc (hxbp. without slipping down an inclined plane starting from rest. The angular velocity of 6hva.bp i cc1r 7wlx x(sb:24kthe sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externa n 3hgwcet47a6l force acts on the systemewn 3a76thc4g ." This statement is

  In what circumstances can l/..bd 1(1sg ,)9izluzbiqtqtpdf p +the angular velocity of system of particles change without any ch+b,9pi.tptz. )d1 (b/dglilq zusq f1ange in the system's angular momentum?

  The Earth orbits the Sv *kaw1.0wun.*7qks ng 1rvzw un in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mok*n7wvwv* 1s qznrg.u kw10. amentum about the Sun?

  The Earth moves about the Sun in anxx e7 6/rzmbotz. s3/a elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes rx.7em z / ox6t3asz/bthe orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (sdvbc/ z(wnu7*g98p p a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotati zsc(u/p7gpvnwb98 * don?

  An ice skater performs a pirouette (a fast sp3 h(ysvhmw(kzgj59tr :bs 5(ein) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic enygj (rehm:9vssz(hw t35k (5bergy about the axis of rotation?

  An ice skater performs a pirouette (a09*c lj1cg7 oitgqu ste qb.5-.b8hzr fast spin) by pulling in his outstretched arms close to his body. What happens to his moment u tisb0*g18-tjqb7o. r9z.g qchcl5eof inertia about the axis of rotation?

State the law of conservation of angular momentum.*wj8;ykkdwj z/b.xr4

  What arc length does the Earth travel in a three month period in itsan.pzk /tp1h8 nearly circular orbit about the Sun withtp h/k.pa1 nz8 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 2b zm); lbo*-ibmyfezjx 3 r18tip of the second hand sweep through in8oe*lm 2m )i 3bz1r bf;-jzbyx 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute wbz;b f* nseeakekn8a) .65 n-equivalent to?

  A bicycle wheel rotates uniformly iqvw4lx p;gvzj)45ams ;pu0y, 8 8 goqthrough 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotation? q j 8ol8 5givm4a,;upyq0pwxv z)sg4;

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thhk ahlh0h mh577wus 6-lq0 ex+e period 7qhahhmlk u 5-0w e7hsl 6+xh0of its rotation is

  A phonograph record rotates at 4chl)m *d)le gj 57fdu+5 rpm. Through what angle does it turn in 0.20 m l 7*g5uhjf dedc)+l)s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point os*l q.v8lwrf os84(gqt )0 gbbn the outer rim move in 2wt fb b(lgqro g.8q)4ssl8v *0.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh3.fnk+ b7stjy at is the average a .nbstj 37yf+kngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0cg7nf kcuhg,gg 5).z/a(z-v0b2ivng s. What is the linear.ug5zgvciv n c(zn g7g/g-)h,0b 2ka f speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers aw (8e2axuap:f 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 minutes?8 2wpe: a(faux

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 ray9: )vshpjouhpw /m,7 d/s. h,:o/s9pvy 7jhwp )m uWhat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered we* llzuh:i*x9xke+- zsed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speeh- l**eix u9x:+zslkz d of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constaq m:1cgyd-qc3vn k*y9nt angular speed of 2.0 rad/s. What is the centripetal acceleration of a poiyngk1c 3c m:v q-*9yqdnt on the wheel's rim?

  What is the centripetal acceleration of a point on the perimmy0do)dvpt2 2eter of a bicycle wheel of diameter 70.0 cm when the bike is movingmp t20 dyvo2d) 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotati (w+q) dlu7lpl*lsv 5wng space station (r = 1000 m) rotatedl(7u * l+vl)5qsplw w to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 mt *6 *6rqdmx *oopu7to with a speed of 20 m/s. The maximum centt*x76*o q d omput6r*oripetal 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 cvl0y x* 8jis-f pwlj9 oi 2c2x**i+lxnurve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by statijxo*w9f 2ji- * vp2x*l+yxcl8 n0sliic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end q *s5znchh,qet1v)( a0wb8awof 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 the mass have if the string is not to sqww*c( h hetn5,)avza 108qbbreak?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10n1b(wknd0rty n s1l)2 m down a lane at 4tbr21 1kl w d0)yns(nn.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 angula4 awt u0;x,8gpbbo4ahr 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 constag lg j5r.xj 0zcgxu- i439xsn4nt angular 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 tiw+1)uqweerka7d-iqdlgn2; w .r z (+nre rotate after starting from rest and accek7 dg+qrwd2eaw.el(n) wi -un+;qz1rlerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at re.vzpg;9. *-syyh tt pust, and 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 decelerates with a constant angular accee+b8 iccu)c;od2m nt.leratio)u8cmitc2n+. eb cd ;on 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 spetrul n8u-s 8 xa-v6.pzed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of thpz--8n 6 luvarx8tu. se wheel?

  A wheel of diameter of 68.0 cm slows down uniformlaav,l65jn gq-1z7 kn .fov2nky from 8.40 m/s to rest over a distance of 115 m. What is tg q1, nov6nkjfl vaza75-2.nk he 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 over a md r1zoe 4vhuafu51*4 distance of 115 54r*fu odmv1ea z4h1um. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows rv/f4 fmc aa;odplq873u-; hydown uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel tofd c;78 v ya4f/o; aqhpru3m-l come to the stop?

  A centrifuge in a medical laboratory rotates atpx+ 5e1nsx 3bl a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angularl1ex x5n+3sb p 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 tighoc3pr x az) g kl47 tq:newwva.k(ddh*+t7(p9 tening to a torque of 90 Nm. If a 30 cm long wrench is used, what .p+np9w47 xad(dkgtlq :(3zo car )tk7whev*is the magnitude of 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 li7o9:o 0uexzk8pso56h7h ru a 30 cm long wrench is used, what is the magnitude of the force required when the force ap 0hh6:7uoo9rp75sz u eoi8lxk plied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerff- )bh dsxm6,tia $3.00 \; kgm^{2}$ 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, m,vj c(hl-o(z e0m7e trid fs,0ass 2m is at x ov, e7l drzc0f(-tshj i0(, em= a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pi33thb3 ,a i;aa(3inb4tn fkzuvoted about a frictionless axis thought the center O. A rope wrapnainb( f3;ahb ,at z3i43ukt3ped around 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 ax2,rj+ b2jfuao :wz+c( mbz6wa is thought the center O. A rope wrappedz2, c jbj6+ u(aomazr wb:w+f2 around 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 *ni*0kzhe1e) o-6j gt --ip briryf5 rat one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fa ob)r6z*pn1kg eh-r-tijy* e0f i-ir5ll. 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 9o,dvl. y49r8xqqma5b5xunk to be a ring 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 without slipp ad qxnvo85,xrb.4y ku5m9q9ling?

  A 1.53-kg mass hangs on a rope wrapped around a z2:c, a fnrx5ufrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration, f2ncur z:xa5 of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around+ 0gqobj4t f6d4/wa9 :jrse rl a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratij6f+:t0gsq44wob 9 el r j/ardon of the mass?

  A rotating flywheel can be used to store energy. If it is required to sq7h b2b5kij;f/ bsvq,: vftq )tore $1.00 \times 10^{6} \; J$ 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 0il-yumn :gav;e:2j;fckx1zwxyk ; 7 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 starts from rest and nz 9xb2.h ndmd6dib0+-b7bo;ng 1ada rolls without slipping down a 1.0-m high inclined plane. What nd01m-9a +n72 b 6bdhongxb.bza dd;iis the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radiubl5 1ihyjz gp7gokk 53a:c,67zpv4 vbs 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before co7v4l y5j5iag vzg6p3,oh z7b : 1kbpckming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowe)+i:j 2cf)eagpmk8 xcd to roll down an inclined plane. How fast is it m pei: c))kmjc2f gxa8+oving after dropping a vertical distance of 3.0 m?

A solid sphere of mascu7an) 9ulvw3 4kzxr3 s 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 momentu3zanu c47rx3lvk9)w 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 c6i/w2nfk jx (5ie g2zbhanges 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 inud ku)+ v7flw7(- f ;:sy+lsqegwla 1vertia 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 xhgwbo) /:b),a(7 a1r zzdyrprad/s with arms extended has a moment of inertiwh1z)o: /byrzdrg,p(bx 7 aa)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?