Angular displacement is usually exu94 ne /.us0uf+bg; mc mltiu,press in units of

  Angular velocity is expressed in uni(bngy1 ,;27wqmrd glbts of

  Angular acceleration is expres s*ekz/.7q: vrsdk. swsed in units of

  A boy and a girl are riding oi/ lad.y/l(e 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 angular dii/o(e dl/.ayl splacement?

  A boy and a girl are riding on a merry-go-rou-aegtl7rssis-c; 78 cnd which is turning at a constant rate. The boy is near the outer edge, and the girl istle -s87 c-g ia;crs7s closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which i+u)t(urxx1 5gf4 ys jjg1g4ea s 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 sey tf4x g jg5xr4uj)1s+a(1ugpeed?

  A boy and a girl are riding a*fri ( un r:vh9g h)lh4yf94v ,6ufrnv 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. Whoh:lh v(4uf9ghv6v rfnuy,4*i f)9rr n has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant rat; nvaz7yaya5 0e. The boy is near the outer edge, while the girl is closer to the center. Who has the greateanva75 yz a;y0r tangential acceleration?

  Consider a rigid body that is rotating. Whichab-b lg x-t -f3 cec (;b/1i/lnx,kjng of the following is an accurate statgnfxcb3-acn-/b e ; ,igk/(t-llj1bxement?

  Rolling without slipping depends oeets 5p-4-qu cn

  Two equal forces are applied to a door. The first force is applied .dm(a:.s0egz jikytee50y s) q op0 1aat the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greatezqg:i)s(.a0ma.j eo 0tsypyee0d k15 r torque?

  Two equal forces are applied to a door at the doorknob. The first force is applo5g7ahobhrzm1 p 1 38na39pb5y* tvljied perpendicular to the door; the second95 jz3ablt1o o5 yhg*nmb1v 3pah7p8 r force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied tod umd(n7h .opek7:c+p a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratduo m7hn7dp.k+e :p c(io of the torque of the first to the torque of the second is

  What is the quantity used to measure an object'sn g --28g*srk:ifkwpk resistance to changes in rotati2r8:s-gi kgw pn-*f kkon?

  Consider two uniform solid spheres where both have the saritdh5+f.e 0 tme diameter, but one has twice the mass of thfti+0 5 dehr.te other. 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, but one has ee cw5bmn1: /atwice the radius of the other. The ratio of the larger sphere's moment o emebc :/1an5wf inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the m9scir wh rjqz*.+,6.dj ym :wxass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia isrrdzj.* scxy6+qw. ,hi 9mw: j

  A uniform solid spherk x-taq wp0.1 8;zxvzwe has mass M and radius R. If these are increased to 2M and 3R, what happens to the spherexakw t;zq- x0zw .1pv8's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that oo0rexr: gg: 1yf9ox:w9 r 6axibject will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 v56vut(u:scr MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy tus5vut: crv 6(o its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a massoel4 j(/m/ vlvriko3h.h /2c g of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the whe/il( 4v 3 emh/jholr2.c/kgovels 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 slippn.1* uwlb8m9ma zt -fbing down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depenfu.1 -m bl*89wz tnambds on

  Suppose a solid sphere of mass M and radius R rolls without sbyw:9a hpqa: 8) lpbe1lipping down an inclined plane starting from resq1y 8: )b:e w9lappbhat. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sys0 bpe/apo6r(k2u/ (h: glgmtutem of particles changes when a net external force acts on the system." This statemen/bl6opm:/0(t p he2ur g(augkt is

  In what circumstances can the angular velocity of system of particles change wit4eyn rn3pxc-. hout any change i3ep-rnn . cyx4n the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignorzvq9 a9 0ly0tcoh*4v re any friction which may be present. What happens over time to the Earth's vv*yz0ta ch lq90o9r 4angular momentum about the Sun?

  The Earth moves about th.txa 27lmvd7 ae Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes vla.axmdt 7 27the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fastg7fk/d:khl08 y v6;( uip((y.u ahhamsd. uie spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum:7g iu(has0 av8kp(kml6 ue(/ yd.hfi.;dhu y about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrez xews m3)3rl7tched arms close to his body. What happens to his rotational 73r)smzxw 3el kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hi 594kwekp: wj k4xuue2v 1vvi*s outstretched arms close kkpv5vj19wx2* ui wvk44:uee to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conser*0hl d4 ll0u fwz6+ptevation of angular momentum.

  What arc length does the Earth travel in a -lpx.bw*9zq+l8ko zm three month period in its nearly circular orbi9p-o * wb l+.lkqmz8zxt about 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. Wha b d)v55 s;-r n2gixyn tv16*tulmb19h9otji bt distance does the tip of the second hand sweep through in 3 minutes and 45 sei 9n5h dtjl2*6o yt nsr v)bv-bui1g1t b;x95mconds?

  How many rad/s is 25 revolutio(1/zd + wm( krm31p szlh0yaonns per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t buex;sn j6;4 f/r8lod n qld4em8-:bche frequency of;4x-n e:cr48/m8 fdnj6ql b odbsle;u the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses ab i4 u*rz)*jrxt a frequency of 0.40 kHz. The periodi zr )4**uxrbj of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle db9 z* 6td zkn:qxr+f4qoes it turn in 0.20 k6z b *rfzx+nt 4q9qd:s?

  A wheel of diameter 26 cm tur76v 7 :nydr xsr*+ 0ab4jr rqruqi2jh;ns at 1500 rpm. How far will a point on the outer rim movx0 *brh7 ;rq d:+4jj unyri2aq6r7rs ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2p (8fnieanubvkt9,5 mwm 55 r5.0 revolutions in 4.0 s. What is the average angular speed of the whe5mk 9n m pvatru58e 55fw(nbi,el?

  A bicycle wheel rotates uniformly through 2.0 revolutions in )0crhyp:3clic.rngw7eu5m1 y.ir 8 :f7jq oy 4.0 s. What is the linear speed of a point 0.10 m from the center5:m.1c . r)83pwcrlyi yoyf7rucjh7 n:e 0q gi of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. pcuu15f)c( nf The cable which moves the car is driven by a pulley with diameter 3.0 m.fun)c5cp f(1u Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/sp 9z+g 7 *fwjjdpuhr+qo f/24u. What is thpjphrg*z++dj q/u27owf94 ufe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0lpf/f-i.gq tvj35vayo/- h 2)g ouap/ .16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate 2 opgu ja) ly-fg./v f/ah o/3qi-5tvplinear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constantmy8,va9 l-pjl4 7eyu7p+vevm angular speed of 2.0 rad/s. W v4j7vypul+m al9- 7m,pyeev8 hat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle mpb72-: bt l4/iuock qwheel of diameter 70.0 cm when- m:iuqpk/b cbt7o42l the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station; ,dh-xjir cn. l7yf9b (r = 1000 m) rotate to produce an ax7 -y;,l.hi cnr fjbd9rtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/sktwt 6 i,o3q5h. The maximum centrihiqk5wt 3t6, opetal 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 circulas9v6lnt 3ztq , frve)9r curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided9lz,9s 6ntev )rtv3fq by 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 whiu0ip:ktvipy3(rdiau-(2; gw rled around in a smooth level table. If the maximum tension that the string can iw0i2r i u-pa3t ;y(du (pkg:vwithstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg 8cvss4);qhz s and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m;cs vhqs 4)sz8/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 acceleratic.qb.6j:3zbk 3 b5. e.2cxkhalcqwtyon 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 of a:l4 1l my*oxu$4.5 rad/s^2$. 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 0.30c k*71 hucxx8b-kkx-s0-m radius automobile tire rotate after starting from rest x8-u h kc-b7csx1xkk*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 anke.6 q (*/ fxg,t40wy.r xrqdk )xxynqgular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s dece 2 axrt/l6gyx7lerates with a constant angular accelerati2ltxagx yr7/6on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a ovl.*w/ yzb,:kbbi q x6x7t*6shx4yln angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average ang/i*y lyq.6zox 7,t:b k hb6l*w4sv xxbular acceleration of the wheel?

  A wheel of diameter of 68u4*mnfe9j 2 xa7qb0d6 a: dsqp.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 9b2*ud j6p7n0asq :dmqa 4efxthe wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovmhq l(q/30l 6wdlrrz3 er a distance of 115 m. What is the angular acceld/3lqr60wzl( q3lmrheration?

  A wheel of diameter of 68.0 cm slows down uniformly from rln: 3cc 3vxl c02wbbgv)f8,n8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the s ,f wnc :)xc0l33 2bg8lcnvrvbtop?

  A centrifuge in a medd:9c(0)c dr39g fhb8bhxmwq n ical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.h: 0 bnmhq)gd8 crf dc3(x9b9w0 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 requw., txz63 fpxzire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force r3.xztwp f6 z,xequired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighr vbzt)n2riqu0; i 0a*nn.(jk tening to a torque of 90 Nm. If a 30 cm long wrench is used, what is thej( ;k2)0i0tb uvqn nnrr.i *za magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment s a* jz3.ohy* h py3mhh3u-zx5of 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 the orig cy/,rk cds ,u1u dbc3 luzb5n dzw(,v8nq,l,2in, mass 2m is at x = a, and, mass 3m is at x = 2a. What ilv,ydbu1 uu3 nr(wb/czkd d,l,28c,zn q,c5ss the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlesnyb*m xd.e.,lr9.oz xs 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 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylix .or. dl9,*mzyexb.nnder?

  A solid cylinder of mass 10 kg is pivoted about a frict8e3c2h.it (p wcyj*ftionless 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 righ t(ihp.c y2tf8* c3ewjt. 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 atrv;imi -wxa,q3pct:u37 x ya7 one 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 released? (The moment of inertia of a rod atx 73a -v; 3cwa,iyiuxmp 7q:rbout one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm a3)jsv:uhf- tand mass 1.5 kg. Neglect the mass of the axle and sprocketa )jfhuv -ts3:. 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pull00t2ugr.fgo uey of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thturo2fugg .00e pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley 6,jt8 u wr3jerof mass 7.07 kg and radius 66.0 cm. What is the acceleratio3ej,wtr8j 6 run of the mass?

  A rotating flywheel can be used to store energy. If it is re-o az-6a*r+sqcs mn(1saxh5kquired 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 i 3mt cpev 4qep7-ua*4r1si/t a1lt1hv nertia 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 raw 2jn0du339y wju na d+b6,u, chpd40.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottoa6+p,whudu,bnd0 yu34nr 9 23acd jj wm of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010a+ dko-pzx1 8;r1rmpt m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to r-x rr1paotdpkmz; 81+est?

  A hoop of radius 0.50 m and a mvb +gp.sz3fb) 1 3v,elv*m gnoass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after droppvno z) sb3v g.b3f,1 l*+epvgming a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping ywok62l xa b+q, 7u,psdown a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia ol7 xs6bq2,kuya+p w ,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 chk n1zjn(. dasy:..mwi anges 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 momendyv.p96 eio *xv6pr4lj(epe*dp0s*r t 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 momen ot:ecn-n+ )gwqdg4.mt of inertia odmn)-n4t +qgwge. c: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?