Angular displacement is up(zr1 :raffe*sually express in units of

  Angular velocity is e(b)e.kmb( cmv gj;n* do1 gum(xpressed in units of

  Angular acceleration is expressed iy i(3iz 9or5khn units of

  A boy and a girl are riding on a merry-go-round which tp(z,f ;2cc( xc7 wcrnis turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centz( f,c c2x(cc7;tpr wner. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whid afjf0g6w +o7ch is turning at a constant rate f6+a07d ojfwg. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are zr) /1tb,ql h iq-vuzh:1atn 5riding 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 grv q)5 1 ,lrhzz-u bnq:h1a/titeater linear speed?

  A boy and a girl are riding a mge bg 6 l58gfwmc:,4zfq46xzferry-go-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 accelerati:486fze wgb f,6m4g l gzf5qcxon?

  A boy and a girl are riding a merry-go-r e);wq.yt-f1xoi sspj z8.l b4ound 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 tangential ye ;s8ibl-ow .)tq4x jz1p.sfacceleration?

  Consider a rigid body that is rotating. Which of the fol7 3as0.qgog m,m -g(x)kl* v6lcoum xjlowing is an accurate statement(g3mxogls k*7-mq,x.6ua) o 0 jvgclm?

  Rolling without slippin2vk6+o+vb kjsg depends on

  Two equal forces are applied to a door. The first force 2:)* gzzar;yxyn p6 kais applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied p z xg)*py:;y2zrana6kerpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied uvh639vqq z,t8s wt 8oto 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 do3o hv8qtz6qsvw,tu 89or. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpen0shm r) /scxj2dicular 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 t xr02j/hscsm )he second is

  What is the quantity used to measure an objectr3hz 4v 8s 2fe1. htjr( fzfirc42nheg22sq -v's resistance to changes in rotatizc4g rz2h n2f fh( f-1v 8res2seqvj4. rth23ion?

  Consider two uniform solid spherjjrh9 )c4 qzlxop( 89iz uv3xd*t25 cwes where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia h)icqr 289pxt(5x*jz wzo3 ju9cvd l 4is

  Two uniform solid spheres have the same mass, but one has twice the rpyp*;k k*em4v adius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sph4vmk;**pyp e kere is

  Consider two uniform solid spheres where one7 o8)vv6gjqv w has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of to 68v)7wvv qgjhe smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these arwfdu5xb yxo,3nupz j5gk 8 0*f6.c9rge increased to 2M and 3R, what happens to the sphcgffn3yo 8r6 uuzxkxjd9 b55wg *p .0,ere's moment of inertia about a central axis?

  If a constant net torque is applied to an obje qc+-v3pvjs 4wct, that object will

  The moment of inertia of a solid cylinder a1/ bgf07-yo sg-4q a kmx86mbaf nirs:bout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic ener4b-6 1 g om7xs/ yg afsiq-:0amkf8bnrgy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg andidb 1v/ .8poym4wgzn 0 a radius of 301 bdv nowp4/0yimzg8. 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 and radius R rolls without slipping d*d7ulh */ ogn5;yvykjown an inclined plane starting from rest. The linear velockyy /dj on*7*5hvlug;ity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping ywwxrv -b:m 8 k hjgo/+9g56ktdown an inclined plane stagm86 9x:j hb-5r tyw+gvkkwo/rting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chy ;spj2 uiur,*anges when a net external2urj*spyiu,; force acts on the system." This statement is

  In what circumstancesf/:b rs(*p:zw)5ersowe (jte can the angular velocity of system of particles change without any change in the system's an*t5 r(frw sp:s(:z)/eeewjbogular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore a yao7ue 442wbbg u-ws8-l.qb nny friction which may be present. What happens over timeq44yg-s .auoe 8l b7bb2wuw-n to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. A w zl1if3vi26*zzw i7is the Earth moves close to the Sun, then which of the folloi1l w* zf673vzzwi2iiwing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstren h g 9tp/xrnv2r5px*b471of btched arms close to his body. What happr nxo4/1pbbh 92*t7fpvgn 5rx ens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette v,/- yu9c ts+fwpy9xf(a fast spin) by pulling in his outstretched arms clos9f yufs pv/t+9cx -yw,e to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulanx)2dbr-al 0i-a juqrx.7 pn:t9 fcg,9ws0xling in his outstretched armf7sax-r ,b.anx gjt9:2p a0c )9wuin-xlr qd0s close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of/ o /b6q9yd pd26+betabdp n1z angular momentum.

  What arc length does the Earth w )gq8dhpsb *5travel in a three month period in its nearly circular orbit about the Sun with a ra8g)dwspq 5h*bdius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a le)o q1/ee9tg 2qpjo6 mingth of 0.30 m. What distance does the tip of the second hand swiqqj6/ )o1om gt2e9e peep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute jp: vns0emo/1kdrp c5xn j*+iqw/o, 5equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionsiaj.ufdyo o2 ,i2*7 vi in 4.0 s. What is the f2o.jya,ou 7f 2iiivd*requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a freqkubkr1 8c q *kf6f5by:uency of 0.40 kHz. The period ofqybk b:fckkuf1r 586 * its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turnf2,xqvt n ez 34:y2yxosot7f3 in 0.20 x stf3,4 fon72qyo3tzevx 2:ys?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the out j8j2zx7ix9fn6s, jozer rim move jx9xsn7z,oij6f2 z 8jin 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutit z+va oh4*.yoons in 4.0 s. What is the average ahyvo + .4*tazongular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is un6cu6 p5xv:vthe linear speed of a point 0.10 m from the center v6v :c6n uupx5of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thsn 346q: 2cgyznjd/aoe 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 th /cngndjqo z3:26a4yse cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is .. )y4 midzfc 2km8i23mxbgsj/ f(ts 9okdf*wrotating with a constant angular speed of 2.0 rad/s. What is the linear speed of (dm m /tobci8fimg92zx fs 4syf2 d..k3jk) w*a point on the wheel's rim?

  The cutting cord on a gas-powered weed cuw+sflg aym kk1xv . 1-l+v5:n6d3itdgtter is 0.16 m in length. If the motor rotates at the v5gdl g3wvf. s t: mn-16x+ial1d+k ykrate 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 constant akoby1o vv -n 0iy q:kwd0.u;g:ngular speed of 2.0 rad/s. What is the centripetal acceleration of a point on td vwo ::;uv0k1in0 y-ybqko g.he wheel's rim?

  What is the centripeta+zk*vp a1 vbas(k 3r)jl acceleration of a point on the perimeter of a bicycle wheel of diameter 70.s+a vzkrkja)b *3 1v(p0 cm when the bike is moving 8.00 m/s?

  How many revolutions perfir,)-2rb f kd minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce airffd) br2k-,n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed oajhum 9yzy*+*zq:f: qf 20 m/s. The maximum centripetal force (provided bhzqy*jq9+a:*m fu :zy y 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 with a speed of 20 m/x9t3: 6tekcnoea8po7 hm t, 2fs. The maximum centripetal force (provided by static friction)o e2hxt: n37tf mtp 6oek9ca,8 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 whirled arov7r7r oq76dphund in a smooth 6d 7rpqv7hro7 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 break?

  A bowling ball of mass k hi( w+dlb :9f5kyepd,8 9uve7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at9kh(,ek8 iey+ vu5b:dpl9f wd 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 bvd)tv z z,8*ka constant 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 c8fq6gkmwbaxl*+p9 8n bmk. 1 sonstant 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 tire8 y1yjyeth*: p:w/vw vvzk 7)e rotate after starting from rest and accelerating a vzypwkv * /) 8:hy7e1wje:vytt a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest,( a*b9:ra vtn-v p9jf0oo /won 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 deceleratesn 7c7 )+3w.cilr itqam kxr3m* with a constant angular acceleration otwn mq +i aikccr73 3*x7m)r.lf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches lyshe,n o,a,1an angular speed of 6.0 rad/s while turning thro1ley ,,,h sanough 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 to rest over(8qx)ibsval n aj9rd0fc2/ p6 a distance of 115 m. What is the total number of2 alrsd(ivq b6xf)/8j09acn p revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cxv0ep,f aif*qy1y ,a -m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angayi,yf1xfq,0* vea- pular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40l5sik5240 kj(t7xdk;uivpzba:zteq3 5. gch m/s to rest over a distance of 115 m. How long does it take for the wheel to come t75kcd4(zk3ljsipe.tg5kzb0;iaxq v t 5: h 2 uo the stop?

  A centrifuge in a medical laboratory rotates u h.,re8ztai3) * bonsat a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before itue*)nz bs,8.a3or hcoming 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 o2 5ef y7vjdnexh)x71k v*l;u tightening to a torque of 90 Nm. If a 30 cm long wrench i*dlnxy; 2h5u f 7e7j)vk 1vxeos used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighteningg nzibt 6d xn 9k/6hwg15y.5hc to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude /9n t whghin x1d y.5bgkc6z56of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o0w5nat4eopq6s o i+/zf 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 f1n7t; b*4 or ptronu*aollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m *r7; r*o1anpu4obnttis at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivok d fsf9wl9kg ;10./tugaw 9oqted about 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 thgfk/ f9q19. 9;dsotl w auw0kge 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 cylinder?

  A solid cylinder of mass 10 kg is pivoted abprbjm+nrjyc7;0 j)(f ujwgl + t5n o,:out 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 = 6.0 N downward. H0j:yo;75j nu +b,j ftg n(cprrl +jmw)ow 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 he(ju2 e j9eod wki1w/;ald 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 about one end is ML2/3.9;(wk2oud/ae j 1w eij)

  Consider a bicycle wheel to be a ring of radius 30 m5m*u(s+b(iye hcu9 di 7m3pl 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 4.0hymm5eu(b9 s+pc7*d( iulm3 i 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 d n:1xlz hp4cex/6; rrlisk pulley of mass 7.07 kg andlcr x;4:h 6/xzr1p nle radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arobtz8a*w gz x ,p;qy,3pml0e/ jund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratio, yzq*0,/x twmgbp8epaz ;3jln of the mass?

  A rotating flywheel can be used to store energy. Ifwk,w3 xv4 8cas 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 i jfq7 ,ro)khh m+v-kwbc34b2knertia 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 sta) 54jrqjnx-wen:x m(jzy f3 8frts 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 bottom of the inclined pwxf53jnyxezjj: )- (8n m4qrflane?

  A solid sphere of mass 1.0 kg and radrhh jl1 g/b4p3xw+ud9 ius 0.010 m rolls with a speed of 10 m/s. How high up3+dh ugwb/h l4x19jr p an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and wrkvkfy a/f.t6 0(x0p a mass of 0.20 kg is released from rest and allowed 0 k/trfv(w0ky x.f6 pato roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wit1ke( ( ypl dc-p.d5htvhout slipping down a 35e incline that is 7.0 m long. Assume it started d(k.51d(e vh-tpcly pfrom 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 momentum changes by ( fq7m1 qiuwe/$20 \; kgm^{2}/s$ 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 my37i5wpei: v ry4nv2 moment 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 r m *x :vta 4jaadt0a-fc)ezjidn**i ):ad/s with arms extended has a moment of inertia offi e ijdt:avd4a))ja z xn*a:*mt- *0c
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?