Angular displacement is usually express in uni,6x6rw qedcrg- w8hfpfj )b g4.ey 42its of

  Angular velocity is expressed ny2c*wf-. znxrr )a 8a +d5zslc4 0fngin units of

  Angular acceleration is expressed i-6wq.l9mog)bx0 yntii p9p 2kn units of

  A boy and a girl are riding on a merry-go-round wkgw ,q 9ik+t v0v.nr3which is turning at a constant rate. The boy is newnvvt i.gw3q,k90r+ kar the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding 5rtj ;yuo0q pc77xiqvj fv/2 9on 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. f7t7vr q ip v y2x9/0;qojujc5Who has the greater angular speed?

  A boy and a girl are riding on a m9 u yev-;7gh+yxe,b76 plltqherry-go-round which is turning at a constant rate. The boy iv yqg;7b hphy6 lxet,lu 7-+e9s near the outer edge, 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 whic pfdk zasn--60kn- .- nf6id6ibhv/x ih is turning at a constant rate. The boy is near the outer edge, while the girl is closk -ns6 k6-if-fpzd6. hnv-i0/in xbdaer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is t;( necp 74erc1mq bx)wyg5l q0urning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangenegm q l;ycce7x5)1bn40pr w(qtial acceleration?

  Consider a rigid body that is r5kbu:xg 0ib)dotating. Which of the following is an accurate statemen0 b5 k)i:ubxdgt?

  Rolling without slipping depe(ytzf)eu71 z4 abtup9sn*x 5 tnds on

  Two equal forces are applied to a door. The first force is a(o g).v-(rdoifv as2g pplied at 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 greater t-ra o2 g.dvf(i)(sgovorque?

  Two equal forces are applied to a door at the doorknob. The firstgx2+adq.y la 6 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 torday q 2+lgax6.que?

  Two forces are applied to anp r mn 4 w**x3ueo-+,l7;csk,z mrird doorknob, perpendicular to the door. The first force is twice as large as the second f - *w ro+smnn*dpr; iermz4,7,xc l3ukorce. 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 resistance tgp -. qi8slue;o changes in rotation ;8e-lsgpqu. i?

  Consider two uniform solid spheres where botxa en4 q-ln/,qh have the same diameter, but one has twice the mass of ,-nqal4x/ne qthe 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 h-)j to/*(uiik(vjol q,n8o;bsyw ;1kheo p.bas twice the radius of the other. Theboi s/ 1hj ;ejuw;on)i b -lyt.v(,q8okp(*ko ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the massal82o fy7si:h and twice the diameter of the other. The ratio of the larger moment of2:ahfy oil78s inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incr-um m (zdgk6y)eased to 2M and 3R, what hamg ( mk6du)y-zppens to the sphere's moment of inertia about a central axis?

  If a constant net torqmr waj e);drt/; v)h:bw+llrp d3.t8 yue is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. yb*jw2u c g)h*tc9 l)-vsnin. If this cylinder rolls without slipping, the ratio of its ro-9) l2n*sjcit vn)ygw*u .bchtational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150m7lv 9s eq8;ji+md8 eb kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the8e9l +mb m7qs;jvi8 de 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 3qw9nc sre;jy 5 d3j6.vvd .6 oh.2mp-jxhcceR rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at9 qse. cjvj.ywrx;6dh2nj-v.ch53mo c 6 ped3 the bottom of the incline depends on

  Suppose a solid sphere ofyjaj/j*4t eaz g*6a1q mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere 46eaj agy/*jt z1j*qa at the bottom of the incline depends on

  "The total angular momentum of a sys+f 5zy.2ii zvx-ogov;tem of particles changes when a net external force acts on thegzzi2i +.;fvx o- y5vo system." This statement is

  In what circumstances can the angular velocity of systetsycid5w x .5eno c.1q8:z 2cam of particles change without any change in the sw.5e:i c5qcxya8s z12t ocn.dystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore id hqjiu*4tqfu8 o 1*:md7vu-st u4i2any friction which may be present. What happens over ti 4toiiu2qihdj81 :* vu*d-7qf4uutsm me to the Earth's angular momentum about the Sun?

  The Earth moves about the Sunq yqd1 uy*+h0ud 9n,c8(k:x3-o yr vrdn kbt-f in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Edntx :n vq bcd-qdryy-3k810orh uy,f+(9ku *arth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in onc a1-/d*idg vq y)u2his outstretched a)qyg2oa*c-/dn d1u ivrms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spif1a7kh4w/f7zq zg .kxn) by pulling in his outstretched arms c/g7xw 4z.7hqkzf kf1alose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a c)lx hca t2(/ l1ya.b d3:vdinpirouette (a fast spin) by pulling in his outstretched arms close to his boa31.( yxa l/ : 2dd)tnihclvbcdy. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum: ph(44yxlrcvpr8e/b bhn 44j.

  What arc length does the Earth travel in a three2ic t9,buc9 zf month period in its nearly circular orbit about the Sun with a radiu,bf2u9 z9ccit s of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has al(uen8t1:b3. pab3w/ hxe l wx length of 0.30 m. What distance does the tip of the second hand swb te3/:hxu1n(plx3l. waweb8eep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eqummk)ck k+::rbwqs2 sq1 alw;7ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. kbz;c pd +)vc;w9 yz3uWhat is the frequency of the wheel's rotatiozu;3cv9w c d ybkpz+);n?

  A pulsar (a rotating neutron star) emits pulses ) bb; 30wtgme u6al;jcat a frequency of 0.40 kHz. The period of its rotat)j;m6;3agbbu 0 lwe ction is

  A phonograph record rotates at codszo*mw nyi31;k ) (p8l3aj45 rpm. Through what angle does it turn in 0.20 s?33nj)a(ymp* s;z1lo 8 di cokw

  A wheel of diameter 26 cm turns at 1500 rpm. How far will aapbpck,oj12(uwf g8/ point on the outer rim move pgfa2bo/jp8 1u(,wck in 2.1 s?

  A bicycle wheel rotates)kygpcd0h b 80 uniformly through 2.0 revolutions in 4.0 s. What is the average angular sp0y 8kpdg0hc)beed of the wheel?

  A bicycle wheel rotates unify r1b o rr.ej4(-pnceqn*gc/ee.s, v5 ormly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheel(5 rb.p. *ecc e, vsjr4gnyr1eo/en- q?

  A cable car at a ski resort carries skiers a distancklo6twsj5058g-n n bj e 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 car to make the trip in 125 w0s-lnbjtg6jk 8 5on minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s.6g qh wij p(i7y.tmv g9o:n;t( What is the linear speed of a point on tmii .7:(n(vo wq69t tph; yggjhe wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If nt-( lhs6/qhj; fni(h the motor rotates at the rate of - ( hnhqsi hfn6(l;tj/20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating w)-k- em- rm7bbht cc5tith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whtrm7hm bk) 5b--c-ecteel's rim?

  What is the centripeta 4 zegb)j;;gq.gf 61pweg 1dusl acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving1w;qb;e1ge du4p g jg.s6fg) z 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space40ig -bp: lbut station (r = 1000 m) rotate to produce an artiftp:-4ibl0 bu gicial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve oic98 fpdgx ,m-f radius 50 m with a speed of 20 m/s. The maximum centripetal force (propd 8cixm,fg9- vided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat ci7*lj 2gz1h) y c9i pofpwnv/q)rcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (2fv yo n7/c q1hwgz jp)ipl*)9provided 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 en so m+b1apn9k*d of a 0.750-m string, is whirled around in a smooth level table. 9smka+1 np*bo 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 7.5 kg and radius 9.0 cm rolls without slipping 10 m dow;szpgyp70t5sll m z, 0n a lane at 4.3 m/s.l m 5,0ssz7t;glzp0p y
(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 3(, xsa xxu1p7 spdfvfq5k8(u 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 constant awbefp f) is4 tf)byc/;p: sn-:ngular 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 tire rotate afte;f7g3 9t-u5iwton pfmr starting from rgowu 9;tf7i f3m t5p-nest 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 angular acceleraty+t :/brqtyo q-h :+bxgx, 1cbion 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 angul;xgilx 2: 2wtm24*b:2e0oubqj c d1-atlqpjdar acceleration oflbla g ue2do1 xdt 02t2-c4qpbx2:i;j*j: wqm $-5.0 \; rad/s^2$. 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 whii 0bu 1aalz7as6l*/c lle turning through 2.0 revolutions. What is the average angulc/ s0la*lzb6 1a 7iualar acceleration of the wheel?

  A wheel of diameter ofz xx9d ingyppd(.3dx j28y5 (u 68.0 cm slows down uniformly from 8.40 m/s to rest over a d gn( x diyjx2dx.puz9d(5 y8p3istance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slow 1r4x13vhumm ps down uniformly from 8.40 m/s to rest over a distanch43 pxmrvm1 1ue of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformedvp )*njl8dwgn2. ftk,r :+sly from 8.40 m/s to rest over a distance of 115 m. H8lnfs, r.j2d *) evg:+tkpd wnow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotamsm 1c 9.fa4o1xb7z/cx juwl*tes at a rotational speed of 3600 rev/min. W*.flo 74aj11c9xmcb zsuw/x mhen switched off, it 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 a ry2vce( vjc+e:ug); Nm. If a 30 cm long wrench is used, what is the mcvera(ejy;+:)2vguc agnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car w4;;anln6 1(aepfbc ymheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requim 4n fbny6; e(;a1pclared when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o,:gky*f) qz)dt ba3 rxf 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 origin e4,d z .;up-giid3z( cns6,uzjnzju 7(r ;nln, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inl,n zn 6dzd7j ;ip(u(.,sg;nz ncu uj3z -eri4ertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ay bg q.sdmf k99gz+w67xis 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 +wgkm99zd 7 6sgfbq .ysection 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 pi; gs1g*zz+* tgvc xfe5voted 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 the right. A second rope wrapped around ano+v5gf1xesg gc*;* ztzther 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 at one end. Ty(hn+us r t)*:iuw -gthe 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 t)ht*g y:rwu-s uin+(of a rod about one end is ML2/3.)

  Consider a bicycle wheel too+pl*-qc lyy5 be a ring of radius 30 cm and mass 1.5 kg. Neglect the masy-q5l opl+* cys 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 achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulleyywju)a5ea9ka21 / fye 3/ fi2n wpop*q of mass 7.07 kg and radius 66.0 cm. What is theo/9a2*)fe 3ywf5 pa ij e 1ny2qu/pakw angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlesa ezy 1v0v6wn4s disk pulley of mass 7.07 kg and radius 66.0 cm. Wh1n0avzyv64 e wat is the acceleration of the mass?

  A rotating flywheel can be used n5w17yav u) q0u oae0jto 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 of in,+s3bhci jeaa n )uoegd0-r (;qi*qrlk +(w 0iertia 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 restt1 oot:: krt;d 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 planeko:o:1tdr t;t?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speedpq.1jlp a rirqvxs06j5;yt. 6 of 10 m/s. How high up an incline5vjqrp; t 1. lx6p6 arj0.ysqid plane can it climb before coming to rest?

  A hoop of radius 0.50 m ie pu(lg:2z:iand a mass of 0.20 kg is released from rest and allowed to roll d( l2euz:p: giiown 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 without slipp1p,du 4fmlb8k ing down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia opukf4 8bl1dm, f 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 moment. lt .uioo0c yn3bbx-+h,poi0mo;c7 pum 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 w(w6huqcb -pft+e xm j.v*5 6tmoment 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/szp+fiip :d.2f with arms extended has a moment of inertiidf .piz: fp2+a 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?