Angular displacement is usually express in units o s.fx k1*0rartg3x + g,wvt7xqf

  Angular velocity is expressed in units 0-i mbj u -j4b0f7moaxof

  Angular acceleration is exprcmuz6csg3eepy6y8 7(o hj (8f2nfv t-essed in units of

  A boy and a girl are riding on a merry-go-round which is turning atzc uj*u7w-m5t a constant rate. The*jcu5wt mzu7 - boy 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;-jufgo6cve 7vs j/-olp/q (o-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the g(qcu;ev7 j/sf6 - -olpov/jocenter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which c+/ssm; .oo pnc(j6d9oxhicyu5.lu4sgv/ m) is turning at a constant rate. The boy is near the outer edge,oldcm )ciom/sh4+ ;u sx9 u.5g p/n6j(so.vyc and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning azpz ijcv.fc7p.5ne1ya+8 o 0b t a constant rate. The boy is near the outer edgej vz1np7ayf ozicp5 . e0.c8+b, 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 co6cgr-lpr oo *vt hab1m7/l.u8abg7 (lnstant rate. The boy is near the outer edge, while the g1 l-*pamo8.lurl 6hgb atcgo(7rv 7/birl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body unayfbg.39 v1fi k7 pzu8vwk6 x.u7*othat is rotating. Which of the following is an accurate state f1kyv vo*u7798kp.gzn3auu.bix6w f ment?

  Rolling without slippim ; a ;ja o.ia40,+vvoh2jrg lvtskn6+ng depends on

  Two equal forces are applied to a door. The first force is applied at the midpoe7l r2n.+ltfwint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the r.+l7twfe 2ln greater torque?

  Two equal forces are eu44bp7 dht+25qyq edh9aw 0mapplied to a door at the 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 exerts the greater torqda 5q yq7+bw0h 4e9t4dp2 emhuue?

  Two forces are applied to a doorknob, perpendicular to the dooaqnokk ouq* p9 aip 4f1a7/(f v,(dun+r. The first force is twice as large as the second force. The ratio of the7 pakkuv1d,qn*(o9fi+ / ofna aq(pu4 torque of the first to the torque of the second is

  What is the quantity used te+m7r2js :qnva,* x abo measure an object's resistance to changes in rotationm7 r*ne,2va sjab qx:+?

  Consider two uniform solid spheres wher.cm-umk v58 vie both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to thamv vc-uk85i.m t of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but h s b;kf-,,eseriddn+7a 0fb0one has twice the radius of the other. The ratio of the larger sphere's m,,ds+7;dnfer es0 ab0kbh- ifoment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice thk23-cm/o .zcyo-v m9+ut bxqubk rc ,h;r60g se mass and twice the diameter of the other. The ratio of the /xg20c ;uc qk9krcsmvrhbou-o+ty6 b 3-. m,zlarger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these -1sm4o w9qdjq are increased to 2M and 3R, what happens to the sphere's moment of inertia aboq -moq9dj41 wsut a central axis?

  If a constant net torque is applied to an object, that object will/kpsu,x6/+ eo l)xpq l

  The moment of inertia of ddk)urt1xa qy/ ,zk03 a 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 kinetic energyxz1q0 kd3yk/ a)tur,d is

  Consider a motorcycle of mass 15j6.xza6r; yy e+xb7 / nasispne8;:x g0 kg, one 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 b ;xnrs6 g.a7pys;/xyzaei+6xnj :be8 ike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M a n*1-0 c1iaqdl1 8c6nrh gc,zwmytng,nd radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the spher0 6ntdgn cgc1w m1q1,la-zcrh8ni*y ,e at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withna15 dtn psl)tn:h1z(l r dbav+)8xd 1out slipping down an inclined plane starting from rest. The angular velocity of the sphere at tlz vnan11n)+pd8 5sr bdaxd)t1 hl (t:he bottom of the incline depends on

  "The total angular momentum of a sysm2 .;inu.l azrtem of particles changes when a net external force acts on the system.zruam; .ln2i. " This statement is

  In what circumstances can the angular velocity of system of particlwn h 1gxqr4pc9wy,o0(es change without any changn,( 9royc0w gxwhq4p1e in the system's angular momentum?

  The Earth orbits the Sun in a65wc 5bx5 izpag v;u 3*:uw/dman1tdnn elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momezn i1 dutn/a 3565xw;vdw5u*bcp: amgntum about the Sun?

  The Earth moves about v; u l .7j(jnmtb/4uohthe Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describvt. mju 47/n;l jhuo(bes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast vul nbw:)0fd s ;/s-yispin) by pulling in his outstretched arms close to his body. What happens to his angd vl iuss-fwn b)y;0:/ular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullingxx5*p-)ehc x-gqr jt; in his outstretched arms closex -;5pgjhex *t-xcq) r to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast sp k w0.9iao7tohxbtpvb3* e( .tin) by pulling in his outstretched arms close to his body. What happens to.w3.9bktt pioxbea t*0o7hv ( his moment of inertia about the axis of rotation?

State the law of conservation of angular mom1:u bad, zrxo.entum.

  What arc length does the Earth travel ib9 otg cc6d0tjdee p**+qc5rb ph1d*,n a three month period in its nearly circular orbit about the Sun with a radiusgt bpjr1+ h0ec695od*dq*b*ecd,t pc of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance doe3+ qaqwi eu:po/-vvqxyxlr2mx 4+4zzf .* oi(s the tip of the second hand sweep through in p q/3:i4 yv(xzo qfxl*iwauom+v. r4+x 2e-qz3 minutes and 45 seconds?

  How many rad/s is 25 revo6rop;*n(bhf rlutions per minute equivalent to?

  A bicycle wheel rotates uniformly thr(3btqm - dzlqg.by4i9ough 2.0 revolutions in 4.0 s. What is theq(9 tlz4g3d-q .ymib b frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pucb+qij709h2cwm(syv)o i2s:t xt g1rlses at a frequency of 0.40 kHz. The period of its ro9 0hcqvi1i72jt)rcy:g( xsw msot + 2btation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20j3. 3z-)jyfc6y1 unmsq mhhb2m rr6 ;u s?qr61mnbyhh ru2)zf-.;cm jyu sj336 m

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outerd1xb 7b)5;dh v5 mjxqw rim momd7)x5xbhq;b 5 1vdj wve in 2.1 s?

  A bicycle wheel rotates unifoo;j f8ao .x-tqrmly through 2.0 revolutions in 4.0 s. What is the averago.xo f8-;qatje angular speed of the wheel?

  A bicycle wheel rotatesinvv7m), ruw/ hes;6k uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center re/ s;nk,v7uim6v wh) of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 kscm/q) k1d olp+x3)uj m. 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 tripcu kl) s3mo jdq+)/px1 in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 radz-r3z+ -; ts2ia+ bwsk en0msu/s. What is the linear speed of a point on the w-sz23tz0e;sbnk ua+i+-wm sr heel's rim?

  The cutting cord on a 5umkn ct*lw5kk(xc4,bmy1n: gas-powered weed cutter is 0.16 m in length. If the motorby,kmmx(*k5wc 1l c5n tk: 4un rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a consta s.f qlo0 +fohm,/s7dozim/-ynt angular speed of 2.0 rad/s. What is the centripetal accelerati/d fz07ymosofms+l. /oi,-qh on of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyclf5 lnw d8kgz2xfe*0xij f(54ye wheel of diameteri2n*f(j klx5f zxfed w0g5y48 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cwtv 3l386ahtlircular, rotating space station (r = 1000 m) rotate to produce an artifh8 l3wl3 at6vticial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circula *rwo7sn:*fx e*7mniez*i h :br curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provide7m*se zi*fr* :w:xhbn7n*eo id 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 3pu bke8xc*3 wof radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by sta b8cewu3pk3x *tic 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 strin tn/pv8ydx:)kg, is whirled around in a smooth level table. If the maximum tensk dy8:xnpt/) vion that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass gcgky1t4/ 0.zey- gqdr+xf+n 8dd0vp7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at y0.kdd+ y8 pg-vgtxfq r4+c10z/ egdn 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 constantlu8s4. uqqq1 i 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 constan/ 6j :hpad)c0atmrr 4jt 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 auto7i b;;+mrdn9-r*iqu v cbto9gmobile tire rotate after starting from rest and accelerating at a constant angular acceleration of rvrd -q c9 bm; t+9i;oug*7inb$2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, andlmt2:xmx 5f 3gby/tv c9tco r9,(2iv s 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 decetp 0f*wu)j5mi lerates with a constant angular acceleration*05u)ifj mt wp 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 rad/s while turninu*bs zt2 94btix 9n)lfg tfbu4 xzsb29 * nt9)lithrough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t -rmhd kh/eo5/o rest over a distance of 115 m. Whatemr h5d/ /hko- is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly cn0v uy867hhw /olxgzvj i*55 from 8.40 m/s to rest over a distan67 5*lh nhj 058uxy/wgicv ozvce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/;dr k23/ ;b xvbsw0:anukyzr/s to rest over a distance of 115 m. How long does it take for the wheel s n/k3 ;a0yxbr:vr dwu zb;/k2to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev:.cc8u ld 2 -zslkz8ez/min. When switched off, it rotates 50.0 times at a constant angular acceleration befcl .-zdzz 8:2sckle u8ore 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 2*pse3 x hy f l4hsm0ug527ihitorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required fx3ip uhi5s2lehmg7s*42yh 0when the force is perpendicular to the wrench?

  The bolts on a car wheel require tbuzx5 d1x0xvy(f 4g/*lkb t)yightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of th)z l0 4uxkgx/ fy1d(ybtbv5* xe force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o b51a7lgz8/ -z 7 /ghxmhemgstf 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 modelem:w-ojp70bgb lh (mr2d as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momlg mbw:brjm0h7(2-o pent of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the p(zcmgheorstajzc* ;b57 d3v-:e6l/ 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 sectcz lo/( -:p*hr;j gszdvb5e 3ec76 mation of radius R2 = 0.50 m exerts a force F2 = 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 r3j2ggod mv 4.3a-m sqabout 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 = 6rsdqgja.3v 3m4o2 -g m.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 sxk,k ,ei 6; c.t(jthdone end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is rel xe,6tjsidc h k(tk;,.eased? (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 kg. N:m 4g-pro 21 xk3 vc7bcbuv5lyeglect 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 doecg3- ublr7b:2vk mo541pxvycs the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionljz.*mn: p tgbi1 7,eijess disk pulley of mass 7.07.1iznt gemj* j7 :ib,p kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on v*2xfpk,y 2huzeh* 4 gzh* m7ha rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0v*g7h*e z2,hh kzph 4my*fxu2 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is rii47m;;s rsrpt:1 up wequired 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 inertia l/dg::w u z n6 zlbxu v*4.fyzt/5bw-wof $5.00 \; kgm^{2}$ 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 rollizb(aq;d;/lnvv2m+9rzp m5 plj / 0mfs without slipping down i0ljq;p/m 9b (amfmdl; n /r v5pzv2+za 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 0.010 m rolls with7-qeph y8cwc, q+ pf4n a speed of 10 m/s. Ho 8fh+q4e 7p-,qnpcycw w high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m anavg;hv /.u*nud a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical disug*v.vuna/ h ;tance of 3.0 m?

A solid sphere of mass 1.5 kg and rag+sn.aphu; )is/ll7ay ip u0+dius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Thel/u0hpypa+u g ia n7)ss.;l i+ 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 mome-h9 jd3 yyzpt* n2ckf6ntum 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 inertk*k xd44c6db, bgr9 jwia 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 5z* ptjp136rih .00 rad/s with arms extended has a moment of inertia z3*pr16 tj phiof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?