Angular displacement is usually e 8wuj/3dl8xjgw.1 ol5dprc:f xpress in units of

  Angular velocity is expressed in uni4zxw - 9/wswt t3hxav3 gq)2mfts of

  Angular acceleration is expressedv,jt )5yri4xdpl8c 22pr5n og in units of

  A boy and a girl are riding on a me6 ly hxjv ujj;,t) dv8kzx q/)47xng*mrry-go-round which is turning at a constant rate. The bo juxz;vkq8lx ,h) g467j *vymj/ndx)ty is near the outer edge, 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 turnin uudwy8b+f+9x p(xe5fg at a constant rate. The boy is near the outer edge, and the ufw(e x85f y xu+p9d+bgirl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roun8,;wc(9 bhooh: godgy d 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 linegd8 (b o;,y wcoohg9h:ar speed?

  A boy and a girl are riding a merry-gaf9,,:om82 gdiz l xmco-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 centripetal acceleration?z,mm9x2ilafcdo ,8: g

  A boy and a girl are riding a merry-go-round which i yedr66c1f xr(s turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center1cfr(6y e6 dxr. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an ag otss(72qg va:r bt1iyx1:3u ccurate statemvbra2 t1ggiy: sx13 u(:o 7sqtent?

  Rolling without slipf x,ga//(+ l/khdbsbnping depends on

  Two equal forces are applied to a door. The first force is a7uvlex y hz ;zel280 3gwu c;+5x3wchlpplied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicxhw l28 v3 c0;;elwexczz 3gu+y7lu5hular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at kq+y9dh*b7vp;s(v,kl -m mn qthe doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exert( y-nq vv;p k+ks7*mdh9lb,mq s the greater torque?

  Two forces are applied to a doorknob, perpendicular to thgc i3zm)56g :qyi3 hguqbd /y,e door. The first force is twice as large as the second force ib gqd3g5/ ,iyqgym3 6:uc)zh. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's l f4w3vgz.3 fru. ovni-2 a)oqresistance to changes in rotation? u)rgn .z3f2laqfo4io3.v-wv

  Consider two uniform .l9cy4 r,b ck b.y-w ngzxq01usolid spheres where both have the same diameter, but one has twice the mass of the other.w-.n09qrczb4.y,guy x bl1 kc The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spherunanm) 3v bbggqiw36w -bi fq -x3/z12es have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia tb bu3g)g312ni xv3-qbw 6 z-im awnqf/o that of the smaller sphere is

  Consider two uniform so1-mxpm2 g 4d oz5fw.jnlid spheres where one has twice the mass and twice the diameter15 j4mmn2-zw .podf gx of the other. The 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. If these are incats 0pbzb*a08. f lbqb-v7u x2reased to 2M and 3R, what happens to the sphere's moment .b bbu*aax0b2l-tz f8 vqp0 7sof inertia about a central axis?

  If a constant net torque is applied to an object, that object will;*y ssv;-r 1ry8fvlus

  The moment of inertia of a solid cylq* (3uu( nyztrinder about 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 bp naful-.7 k;s 88yw)lv zpn9u9ym5ca mass of 10 kg and a radiusl8 -.9nmv pz sp7 5alyuf wk)u9c8b;yn 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 ekv6c3 ur w(i+and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the u(c k +rwi6e3vsphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R /m3t7 behj2wyrolls without slipping down an inclined plane starting from rest. Theh7ey2/ bw3 mtj angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whenmtsse8+e j1 4ei(jt0 e a net external force acts on the system." This ss0e j8t +je(t41emei statement is

  In what circumstances can the angular velocity offckkt7 t87p ww69tc40yi,ho p system of particles change without any change in the system's awto6wpk hc9c4770 i8ytk f tp,ngular momentum?

  The Earth orbits the Sun in an ell.0/z7tf ol,i6 rbfwbe*bsy) diptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mot0 .)ybld6 ,fb/7ieo bwz* frsmentum about the Sun?

  The Earth moves about the Sun in ab 4mlw5wab- c-n elliptical orbit. As the Earth moves close to the Sun, then which of the f w-mw5-bl4ac bollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched9 ietrzmg04wwb f37 -k ,cf4ox arms close to his body. What-fg wi7 f04xmtkbrc,z9w34 o e happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fanl95lu6 f 3wc3z +;lrgif/imfp 27 ikvst spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic i i 6i3 +fzg;lw/cfku923m 5nfllp7 vrenergy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin+:aqrsh+b09u/sjva qd3 cog0 6vx v+i) by pulling in his outstretched arms closr0+/ xsav cj9sq+bq+0o63vu:hvi ga de to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mojx1zo ;z64z4 0kha jeize ,1uqmentum.

  What arc length does tieps *lwtd75h91xv c/cu/oo(2ef : n the Earth travel in a three month period in its nearly circular orbit abt1x/ 7ne tuwpi: cv*dlo9/fe(hc52o s out the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance doel0p3 7 o(h yn6hul2kyes the tip of the second hand sweep throug0 3 yy(l6huhk p72lnoeh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutionsw(pf *(zvdi, q per minute equivalent to?

  A bicycle wheel rotates uniformly through/m 8lui8s kd bjzx(:t6 2.0 revolutions in 4.0 s. What is the fre uj(i/kztdm x :lbs688quency of the wheel's rotation?

  A pulsar (a rotating neutron star) e/-(iqlnv)le+ x;ygfxmits pulses at a frequency of 0.40 kHz. The );e- /in qylx(lxg fv+period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doiqr7m2q.o hrwcpyfy4m j,d rd-cn;v .3vv ,,*es it turn in 0.20 2n-qo7p cq,dyj*h,yr4rfwvv i mmc.;,3 vr.d s?

  A wheel of diameter 26 cm tx bagn zjzv96*4yb ,l0urns at 1500 rpm. How far will a point on the outer r bazzgv 6,0b ljy*49xnim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t47u :4bvbkllq ,/ rulvhe average angular speed of the whe qv/v,ulubrlbk 44l: 7el?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.cd ;eib633v 4 d5/r3ije zeqir*jyb(n0 s. What is the linear speed of3ey4iqn*5 3rj6jr3i zb;cv d/ ie(deb a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cab2xks i; 8b--vtl(tliele which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotats(l v8;tik el bix-2-te for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular s4emjv*lt *b.z peed of 2.0 rad/s. What is the linear sebz mvj*4lt. *peed of a point on the wheel's rim?

  The cutting cord on a gas-powe4n tt-v(+tk st uw89bbred 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 ekt8 u-tb49wn t+ts b(vnd of the cord?

  A wheel of radius 1.0 m is rotating with av 83bitvdv z .jrih+ wea0 )onnv3a+;6 constant angular speed of 2.0 rad/s. What is the centripetal acceleration of3ivo;)nwa vj+.ive06nrd8z b at+h 3v a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bic8g*di9w h6i7iv 4 nfhcycle wheel of diamev7i*wg 948fdicin6h hter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating sprbot6rk2 im; 7b 8puw1ace station (r = 1000 m) rwbti o126rkrm7p8 ; buotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cirds:av/sgry ueh q :,c1hd0a(0cular curve of radius 50 m with a speed of 20 m/s. The maximum centripeqasdgcdr0as,v0y u:h (e/ 1:htal 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 wi5wp)cf gsvxj.;c8p y2th a speed of 20 m/s. The maximum centripetal force (provided byf py8 ccv .)s2w;pjx5g static friction) 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-m string, is whirlg5 .2ptkp 6yze9ftav5bo q,;d* tq 5nled around in a smooth level table. If the maximum tension that the string can withstand is 250 6 tqky .bf qz5ta5vpge5;, d op92*nltN, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5(gk +p l.z/mn:t-l bfsmyukw 8l7 1kt5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/. 5mk l(7s8 klbmt/n pkutw -:gzf+y1ls.
(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 acceleration -f 9mvpn1k1yt1dzxt-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 cons le +2. cbsfkt*nke85ntant 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 0.3: iejzu512yw nt-qdjef t9+1 v00-m radius automobile tire rotate after starting from rest and accelerating at a constant angular 921u5nj-+td : yw vftiez1jeqacceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accey u2; s6jr- ec,a(:;ibajvb xsleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatingq)l(2e z6rrfxixu4 j76 *c etv at 20 rad/s decelerates with a constant angular acceleraex rtfj c7qvlzu( 4r)e i6*x62tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and re nc,z 0 ghdgh4p2z(2l hzv(/ufaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of t( uzl, pfgz h(/hcz vh422dng0he wheel?

  A wheel of diameter of 68.0 xmx1)frxk/u * lw 9*:wxyo82v p+dqu thg2 h+scm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revdup hwxsoyfrx*lxw2/)+9q * 2k8 t m1h:uxv+golutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 1ayxa 0snm.m.cm slows down uniformly from 8.40 m/s to rest over a distancsaxa.1 0mynm.e of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 gio4jd j 9/ n0yd5sgf+m/s to rest over a distance of 115 m. How long does it ty/djisdo5n g jg904+fake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed01qq tne 36lpf,augnmwi 3o ;: of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratqinw:a3l3u;n0 1t qom ge,f6pion 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 tighte7wq3pga ; jmzbv6 3g9fning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnit vg mpgjzwa9f7;36 qb3ude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 9;(e;si 0hbdyc tt g2e50 Nm. If a 30 cm long wrench is used, what is the magnitude of 2 y(sb;;ht eg5cedi0t the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner+j*);hm nnus e16pyvt1:n+nk3b uega 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: masglvx;a . j6c0aua/. ucs m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is thuuj..aa/ ;0laxvc c g6e moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pijwb9h+:l fcpzzl gj 5no7- a3kl (t5:lvoted about a frictionless axis thought the center O. A ropljzg7l-5(bz t+9kjnh llf3: wp: 5ca oe wrapped 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 pivdw8.4vckzr)dt; 9g-ouu e +yloted about a frictionless axis thought the center O. A uk)dolr ewg8 -ztu;v4 dcy9+.rope wrapped 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 at one end. The rod is initially held in the horpg.r 29nsgf7kqo1 bp;izontal position, and then rqk2r g7;p g no9spb1.feleased 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 radius 30 cm and mass 1.5 kgv g gt. x:7b+.cd4zaby. 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 ach 4gx.db vagt+c7y:.zb ieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley cx0 p)e(kc 5jbu k;mo4of mass 7.07 kg a 4kek5 ;(0pco)jcxb umnd 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 disk pulley of ;3cp p f1f9mgry0g bu8epx( l7mass 7.07 kg and radius 66.0 cm. What is the acceler(pglm 8xbpy1 c7e9g ;r p0u3ffation of the mass?

  A rotating flywheel can be used to store enerj-mr9t6 g9dzm gy. 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 inertiasol9xnlkux57 7ck*d/ 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 x8hv 8r,/lz8kn bg(mq i1 pq6qfrom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom onx /p(6kqz8v8 rlh m8,gib1qq f the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.hl4 ,hcza7 q4k 6r3h0ju6tmop 010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming cua lmoqjth6746r 4zh0 kp3h,to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is relea8z 7sr.ybsj 4)q;oqzgsed from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a verticalrs qzb) 8j qozy;4s.g7 distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping 3v6x zbaz ey3:down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inerti6: 3eybav3z zxa 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 ;.:wghg gnpema 3f+*rfog8 k6 gq8-rlmomentum 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 .hi tct5s7;t+5:s ;aw u lmpygmoment 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 i,tw t- iyfa/p h r14.(vko 5-*y djsy5h7sotcanertia o-h7fk .1r 5 ajcv54d*( ywtts ,y- ha/oytsiopf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?