Angular displacement is u*;goi +lbeo0 ffv sz n2b: )uk:+ttz4qsually express in units of

  Angular velocity is expresse zcqj0*2v0crh llgc ;8d in units of

  Angular acceleration is expressed zko 4e3nap f09+z*cf)0q r jr+rs3 ezv1+hianin units of

  A boy and a girl are riding on a merry-go-round which is turning at a constv-k* ( qntic8lant rate. The boy is tv cnl*k- i(q8near 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 turning am 6f7blw4x3yc x:p cgk*1xwt3/uv8 jat a constant rate. The boy is near the outer edge, and the girl is closer to tuyt 4:wx1fw8c3lkp*3 jab xvg67cx /mhe center. Who has the greater angular speed?

  A boy and a girl are ridin3, ys:k9lyrf yg on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is:r fk,sy9l 3yy closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whhm 4buh:)k gm8ich is turning at a constant rate. The boy is near them: 4umg hk)8bh 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 at a constant c rufdx5(1 -xaop9 tfoqi+ .n 5cg/2ufrate. The boy is near the outer edge, while the girl is closac rgq fi5( 1 u-9ouxpd2o5ftc+.x/ fner to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurlg1: :el o4-iiw*rv:e 1 dggaxate statement1 d*elg: xg- ag4o::rv1eliiw?

  Rolling without slipping depebn-..w f/ a4d wh9ghspnds on

  Two equal forces are applied to a door. The first force is app( nwz9wq8e jc-lied at the midpoint of the door; the second force is applied at the doorknob. 8 9wweznjqc(-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. The first force izu +/e03f a8vpkeb bpn 2la4s6s applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which forceu3 n 80a4pee6fzblkpa+v b2s/ exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Thixk:,pg 2yv; he first force is twice as large as the second force. The ratio of the torque of the first to the torque ,py hig2:k;x vof the second is

  What is the quantity used to measure an object's resistanhegzgd :fssl), p h(p*gmt098ce to changes in rotatio s:p dgf ,)l*89(hmg p0gehzstn?

  Consider two uniform solid 6do+4sfvx a;ugugnev*pl./ h-g nd 7)spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger momde vvfp +d. l)gg*oxa sgn u-u7/;6h4nent of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has jrq 4m)v vlk.n (1um(btwice the radius of the other. The ratio of the larg1mu((nvr) bqklvm j4.er sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass .lu a;tr6tgf 2,6 siozand twice the diameter of the other. The ratio of the larger moment of inertia to that of th6.sf tuzrla; oig2 ,6te smaller moment of inertia is

  A uniform solid sphere has mass M a 8ogw7xf3 z6of:f 7ulhnd radius R. If these are increased to 2M anxo8l7 :o6f zfw7uh3 fgd 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that ob;+ics n;nlxj0ph ,c.6p +xbpeject will

  The moment of inertia of a solid cylinder abe:scvczm: 1ptuo. 0* nr f;g0wout 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, onr21hzx,gu2 e3c ymwu *e wheel of which has a mass of 10 kg and a radius 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 uniformr2uwh ex,c*z1g3 u2ym disks.

  Suppose a solid sphere oaw, 1+7x0fxx yr*spey f mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline7+xypx 1r0yawesx , f* depends on

  Suppose a solid sphe5 r j9ja3 8pzb/scoxh*re of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends orzajx/sjc 58bh*93p on

  "The total angular momentum of a system of parti7 wz/om+18qftprf o(dcles changes when a net external force ac(o17/8q dot+pm fzfwrts on the system." This statement is

  In what circumstances can the angular cd xrd2s 9 d+k2djt7) d-)qszwvelocity of system of particles change without any change in the system's anguls )+sr d q)dd-d7wzdj22 9ctxkar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictiu *o2bb+:j ow0vc x9 /i*int zrg8xiv0on which may be present. Whag b x 08+vrbc0n*/io oi2zjt*9w uxiv:t happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As4q:r euc.j-m e the Earth moves close to the Sun, t mue j-qc.re4:hen which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a p t :r;*,qrtjn: -drbpgirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axi- *r bgptjtdnr:r :;q,s of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hkd ;mr o*0lo8h.jk bq,is outstretched arms close to hisooh8,l*q;.jmr0 kdb k body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a l(q5pv et;wr e;tb w/s8diq 99fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of in v8;;pwwee9(d9qtqi /tb rls5ertia about the axis of rotation?

State the law of conservation of ay ,xk 6oawi-w1ngular momentum.

  What arc length does the Earth 8 wok(hd3zv(/zpe+-n;9 kkafcd0k jwtravel in a three month period in its nearly circular orbit about the Sun with j;d (z8hekv f09ckwoap k3-z (dkwn+/ 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 tip hjex/:pw yv n b-a )ry6 nkxd,(-z9k;nof the second hand sweep through in 3 minutes and 45 se)ynn6nz:;b -j y9hwvr,/x-(apk dk xeconds?

  How many rad/s is 25 revolutions per minute equivalent to?;rmat ws,czhd 66s 2c-z4xy j.

  A bicycle wheel rotates un tz+ tizui 3llz.a5uxden*6gv21 /gq5iformly through 2.0 revolutions in 4.0 s. What is the frequency of *5glqi+ z5xgt2 z.lva i6 nuz3d/1eutthe wheel's rotation?

  A pulsar (a rotating neutron star) emj n+pw93 n s-:h6jz)wkum )sonits pulses at a frequency of 0.40 kHz. The period of its rotatisp sjn:9 -wom3zkwh6nj +u))non is

  A phonograph record rotates at 45 rpm. Through what angle does it turn ida2r*v 5 z svqd3oog/9nj/ru*n 0.20 sjg5vqdnor*zsd*u a2rv/o / 93?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer tc*nb8r*ipt91wlelg sw3)jd2 yw k,*rim move inr sgd9wp318y)w**njl2tt wbcei * k l, 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revor-/pee;bl,oevsu ); s lutions in 4.0 s. What is the averages;s rebo/evpu- l,;e) angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.58artdvk3lb 8d/m iyy iu(;(o What is the linear speed of a pointrm/(ti; 8(vkab5ydd38i ol y u 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distan (vm). n+ s)6sq-pe7fylooadnce 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 cardmo.n )pny sofl -v6e+a)q(7s to make the trip in 12 minutes?

  A wheel of radius 1.0 m ix bd(9(7vsgk gpx/g*0u kac0n s rotating with a constant angular speed of 2.0 rad/s. What is the linear s( sg/uv7gx d0*bakgp 0k(9cn xpeed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed ,/h8:- nqb71vvqdxk 0:2iq cgkhu(wph9grdh cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear , 18h k h dvcq9u7:ri(:kpnv/d gqgxwh2h0b q-speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant avawe4.okr( hs; pt4)cngular speed of 2.0 rad/s. What is the 4;vr e)khs t4a(powc.centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycui:bxz(p4ew bz,f4q l vg. *,ole wheel of diameter 70.0 cm when the bike is lvp, .4:qz,z weo xubib4 f(g*moving 8.00 m/s?

  How many revolutions per minute (rpm) must 8d), v 8es inphq3 hlkjuul)e4s9l5m1a circular, rotating space station (r = 1000 m) rotate to produce an artificial grad3l5 )q) 8kh,1sihvm8se 4jnup 9ulelvity of $9.80 \; m/s^2$?

  A car is negotiating a flat ci*bbz b ;ab*w6yrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) isab6* *; bzybbw $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/l/ )mda*y-rme(z /8* vdqsyfs;j1xzg fpza1 (s. The maximum centripetal force (provided by static friction)y*j(ap)d- f/f;s xle8 mgam1 1z zy (dz/rsqv* is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of kg+/wo .c0wc9vt .hxra 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then9cvwx0tok/ . r+. wcgh what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of maiyq5 axmb9u 0gm,a-g d2gfd1/ss 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lmxuqaa g i 9 5y-bg/d2d1m,g0fane 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 angular accelh b2fbpq w89)zeration 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 constantob p7 r h3ujdob99fq+- 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 0.30 :rvxjb*tm c-0q:on6+d .gltw.okk 8o0-m radius automobile tire rotate after starting from rest and acceleratino-.rqb+.:v:mx otwd0ctkko* n j68 glg 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 angul ko3zh/ +*;gvmyz-z3noyp (izg 6pfr)ar 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 angularckg /-na du8jf-wll7 ) acceleration on-)dklg /8fj-l c aw7uf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularbs q839uux2f)p r6wu q speed of 6.0 rad/s while turning 8br2quxq pu wu)6s3 f9through 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unizd x .puc:gh(+formly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comh(dx:cuz +p .ging to rest?

  A wheel of diameter of 68.0 cm slows down yui y k2, u4/c(5x1dlm4echasuniformly from 8.40 m/s to rest over a distance of 115 m. What is the angum (aiy1du s x,kuc4cy45eh 2/llar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re/igho ;)x)sz bst over a distance of 115 m. How long does it take for the wheel to come to the stop?gsh i bo);/)xz

  A centrifuge in a medi*k +;tc9a;gbx ds-elm 1lxus4cal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it ag+;cxt4l e 1*u9 lsdbxsmk;- rotates 50.0 times at a constant angular 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 tightening to a torque of 90 Nm. If n1f8i2pvzo 4q t, cll-a 30 cm long wrench is used, what is the magnitude of 812zlv-oql ,ni tp4cf the force required when the force is perpendicular to the wrench?

  The bolts on a car wh:e7 ,gli5/gx bpkpw7l 0 9x f7xunpdpky*s d38eel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required whe0/es, kglkpg:x 7xy83ppw bn7dxl75df* upi 9 n the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in y6h) xvai n203xypg7uertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled0) rifujqf -6,dcp q1s as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is thfr,j)6s udiq qc- p1f0e moment of inertia about the origin?

  A solid cylinder of mass 10 k-y-n e*h 6h23o nk3as2hwb .jfd:m jjwg is pivoted about a frictionless axis thought the center O. 2 3ejw hy.w-o *mha j36:-djn2knbfsh A 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought theozdlqj)c5 dl+avi0e15 (6bm k center O. A rope wrapped around the outer radijob)6+(5 5dl c1mqliz devak 0us $R_1$ = 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 horia2spt q ,nu37 b (hl-sgn(c7zpzontal position, 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 enanzguc , 2s3stl77( p h-bqp(nd is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Negltk,z-i-n8lao38n2fsr lmu ,,3 jw jk9a.yl poect the mass of the axle and sprocket. If a force of 20 N is applied tangenwj.8-k si,oarflptu m8-n3 yz9 na,l2kjo3,l tially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fd6p gyjv kaqmkk1b71 -2-j0fvrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. ky1qfgdv--061pbk7avj j 2mkWhat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley-wfnjy( cpl+jiei;)p ;o) jx 1 of mass 7.07 kg and rl x+j) )i pi;ewj j-y;cf(1nopadius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used tn,(w*m ux*p1eor ygf,o store energy. 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 ofa *s a.3nujw+1zug fhg-v/nd0 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;vh, ,ex4amkc and rolls without slipping down a 1.0-m high inclined pla4c xe, ,mvhak;ne. 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/s. ph7-)jw movv * How high up an inhmpw-ojv* )7v clined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is ogzjqv b6(1f -released from rest and allowed to roll down an inclined plane. How fast is it moving after droppinjqvo zgb6(-f1 g a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slip3wcfh1)ps2 aq ping down a 35e incline that is 7.0 m long. c) pqhw3f1s2 aAssume 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 u,c dja3zzvf21f58zwgeva99 momentum 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 in/3g*eotmyii*l9 .v wtertia 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 +og5xcpl+b( ua moment of inertia 5 l+o+cbp(uxgof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?