Angular displacement is usually express in un qf w o81sqi8+tq,f3uqits of

  Angular velocity is expressbdg. lq3/4 udej8w wdl7(0pxm ed in units of

  Angular acceleration i pgd1p9 1,galts expressed in units of

  A boy and a girl are i1x(su7jxk e)riding 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. xi7ks )euj(x1 Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning knz* 4dc:0a; 5ey rwdeat a constant ratda0 *d;5yewz4n: rekce. 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 riding on a merry-go-ro3 8vpj+h3 3cwvvw+ff xund which is turning at a constant rate. The boy is near the out3+xwffjv3pv 8w+ c 3vher edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a m):c* c+xx sb xz2s(ttlerry-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 gst +x:z)bc*l(s txx2c reater centripetal acceleration?

  A boy and a girl are riding a me +:pp7)u5v,vr;bcm d.vnrby yrry-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 tangential acceler.)c+ y: rpmnybp,drvuv 5; 7vbation?

  Consider a rigid body that is rotating. Which of the following is an hx:ank.u ap7w/h h ;/8w pimh5accurate statem :kw a5m/ .apxnu/hwh p8hih7;ent?

  Rolling without slipping depend 7 p4ub 0.dpwxhyph3(bs on

  Two equal forces are applied to a door. The first force itnu o) zt6, n9wl)sg2rs applied at the midpoint of the door; the second force is applied at the doorknob ru)2ngz,t o96nw)s tl. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door+.mk58. )l3sn r stfh uq;vqtp at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of q; nh)rt.+tp3 m8lqvk.5s suf the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. +jv*x dw--7kcmgnv)tThe first force is twice as large as the second force. The ratio of the torque of the f vn+*cv-j dgm7k-)t xwirst to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotat2 xgaxa20 iqwbu7 p2s6ixp6a7 0uqi22g2sxa bw on?

  Consider two uniform solid spheres where both have the same diametv eje28zcjbm i7e p.h(:wart9zhx,-) er, but one has twice the mass of the other. The ratio of the larger moment of,h9h(ex ze2vw8-m.c7tepjizrj a)b: inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radizc71y9t e1k flus of the other. The ratio of the larger sphere's mo c9yef 1lztk17ment of inertia to that of the smaller sphere is

  Consider two uniform solid 0ht o.(2bxuycspheres where one has twice the mass and twice the di hu2 cxot0by.(ameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R.j51vc,dinfw7d86r drax)r7 l If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axd71 jarr,vrd ) 8dic56lwn7 xfis?

  If a constant net torque is applied to an object, that object will+ 1z1uos p3 jqaft2ttc2 o3s/f

  The moment of inertia of a solid cylinder about its axis is givz pz r l6,sm*uv(it44jen by 0.5 MR2. If this cylinder rovp6 rl*jumzs ,(i4 tz4lls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of w :,kp :;isvpzyhich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels t ;s:izpk v:,ypo 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 slip lfd)(0b wb+t 3zs3fsiping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline d( f 3dfz) 0bsbwli3s+tepends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an i* l;.x t eahbb,uqy+;t2sxk6anclined plane starting from rest. The angular velocity of the s;;sqt2a*+e,b.hxku ly a6 txbphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net ex62 vk8fu dl:yrternal force acts on the systelryd 2 v:k6fu8m." This statement is

  In what circumstances c4 +l5udw7d xyur4fy3han the angular velocity of system of particles change without any change in the system's angular momentum?u3 urwd4 l7 hdf54+xyy

  The Earth orbits the Sun in an elliptical orbit. Ig;rhr wmpm7cg; .m* s(:j :pfgmnore any friction which may be present. What happens over time to the Earth's angulr .mj:( :*fcmppg7 hgm;s rm;war momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As th, . ,wyne4yk.m 9hxh6 gnpd4kme Earth moves close to the Sun, then w gn m ,w4 h9mpy6,.xk.hk4ndyehich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spins58qjuih35 ww) by pulling in his outstretched arms close to his body. What happeijsuwq 5853 whns to his angular momentum about the axis of rotation?

  An ice skater perforh4r ;+bl.op erms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational ki4bhr.pr+e l ;onetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling gp3n39 xjv kr s,9osl9in his outstretched arms close to his body. What happens g k3jlsro93x 9 v,9spnto his moment of inertia about the axis of rotation?

State the law of conservation of angulardr7j6tx ow 06k momentum.

  What arc length does the Earth travel in a 5mqomm 19u2eqthree month period in its nearly circular orbit about the Sun wieq52m 9 1muqmoth 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 p,6q2fjm l/o+k skeq jey50b3 the tip of the second hand sweep through in 3 minuqbe3 k60, jo p5fl2smj+ykqe /tes and 45 seconds?

  How many rad/s is 25 revolutions per minute equival) 6axwhvup; 0xbwyuyri 5,gh 5m.w**gent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wc v/;d)9esasbtq4ob *hat is the be;vcts94q)*obsa /dfrequency of the wheel's rotation?

  A pulsar (a rotatingu8y8cd6xjv*v4uru-uqvz n h 5) fau1g2/4 heq neutron star) emits pulses at a frequency of 0.40 kHz. The peg8euq5)nzxuquvvcr6y 4u/ 12v4h hj8f *d -uariod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doesu1qqwg,lbxccxl* j12z2k9 ;l it turn in 0.20 s?;g21 x,u2jlzcqbq * xcl9l1kw

  A wheel of diameter 26h9j6.kdy+pla uc kp0. cm turns at 1500 rpm. How far will a point on the outer r 6pd+ u.kaj0hclp ky9.im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.4 lxh x(3trd3( ehx t *8n45to mgfgun4qb*-ob0 s. What is the average angular speed of the w 3tge*4q4ro5lbb8 *dxh((ttmxfuh g o-3n xn4heel?

  A bicycle wheel rotates uniformly t/zv, mv0afa-c hrough 2.0 revolutions in 4.0 s. What is the linear speed of a-0a cmvz,/fva point 0.10 m from the center of the wheel?

  A cable car at a ski res;nwxnu-vb90wmygr.k c omf+,s9z b72 ort carries skiers a distance of 6.8 km. The cable which moves thfv-so7 mw 9unz+; gbb92 r0ywm.c k,nxe 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 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular spe84rl p:cuony0ed of 2.0 rad/s. W 0 rplc:y8nou4hat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16tlcmr6qsek6b( r7s -2 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximat( s6smer tkrblq726-ce linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed o:.a;i,ugfgupu: -nxt f 2.0 rad/s. W a.p:i-, u:uxtu;ngfghat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetalbj;ll66mx6sd 4 jcw -3ib, zfn acceleration of a point on the perimeter of a bicycle wheel of diametebm c6bjx n6w3dz,-6j;lfi ls4r 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stationrpow i.8*k p1fjua3d . (r = 1000 m) rotate u *8prfok.d1ji.ap3 wto produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cif,;5p wb-a evircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by5;-we if,a bpv 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 spewanhbj0y:5-fsaj 0p -ed of 20 m/s. The maximum centripetal force (pro-j 5:a00 nybsphf ajw-vided 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 whirled arouzgv+i xnh,l k5b-(k7und in a smooth level table. If the maximum tension that t h7kl+zi5 knb(x vg-u,he 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 4ris1 pjq:u 7)ezuhi 15f3dc mand radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/izm r q ei1h5:f c1uds4u3)p7js.
(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 const/1gzvqc :bg 2*eb(d eeant 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 lzb wzwri:z/ 8)qt- h6constant 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++oc5h 2poct v.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleratoo2phc++c v 5tion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceler-h 21r uv hebs;5r9ou-r,dowh,x kqol8s.* gjation 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 7bug8ygg*c8l a constant angular acceleration o*gg bycg7l8u 8f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular )+o rco-k.)h9uu8uhlxkpk7x( hxdyc,h 4x r *speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration o)d -47 hokx krc8rpxhk ocxl*.+()hxuy9u, huf the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ki gny 5y62 wu/h(f - y0a+q/k/duam 2bac*rxvover a distance of 115 m. What is the total number of revolutions th bfa2+u0d* 2r w/h y56cnv-ykuqaa( km// giyxe wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dox xw9gz64ze 5fwn uniformly from 8.40 m/s to rest over a distancwezz4 g9xx65fe of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dabjq 6by pv tz/9.g/rh0:d;beown uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the stjbq0egy.;d: 6/ phv9b ab /tzrop?

  A centrifuge in a medical laboratory rotates at a rotational speed of c 6i nifxfrt*9*et3k 83600 rev/min. When switched off, it rotates 50.0 times at a constant 9fkit*3 cx68rnife*t 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 tigins2 qze8+ c3thtening to a torque of 90 Nm. If a 30 cm long wrec isqezt+n823 nch is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm loe21 ml18axjjdn,b r k0/jgqf/r s/c .sng wrench is used, what is the magnitude of the force requir,cl//axjkfnd j2 .q81esb mrjr0s/ 1ged when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiahl+ c2 ;7xhxavsc.*tg $3.00 \; kgm^{2}$ 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, z-thaun,w 7kw6yj0 o*mass 2m is at x = a, and, u w7onz j-ta0*kwh,6y mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted pac(z , sgu0xn,u9dx. about a frictionless axis thought the cenpg,zu9 x s(0c xua,n.dter 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 cylinder?

  A solid cylinder of mass 10 kg is2 7clgo3 v-ayj pivoted 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 another section of radius R2 7 2lyg cv3-ajo= 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. The cxzfq s)xy+i5./rxpcgl. *;m 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 ofrx.;m+yps5)xczi x./ lqg cf* inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring o.r0cpny 4x w405 8- xvkwrhajdf radius 30 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 4.0 cm for 4.1 s, what linear speed does the w5.wrk8x4jr0v ypa hdnc0-xw4 heel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu .4;zh w;jed10zg 68iqee mypelley of mass 7.07 kg a1 6;.e hezy ;ezpj4w08mgiqednd radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskp s0drk z:/ne3 pulley of mass 7.07 kg and radius 66.0 cm. What is the accelzrs nkpe:/d0 3eration of the mass?

  A rotating flywheel can xkyshdtajlj * e c)il7*is9d ((a:2 7abe used to 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 inertia of a w sx2ou2z gk114t2ad4s 5rdg$5.00 \; kgm^{2}$ 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 mjw;rhwd 0c8- radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclinew8rm- ;w cdjh0d 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 anyxpfy7-8 2mv95rg ybad radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb befo v-g8 y x7yyba25mfrp9re coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 ,ix: ggry5 t5jkg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vert,r:g i5yx t5gjical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls q7*k-kue src, without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given ,q-k k r7*cesuby $I = (2/5)MR^2$.
(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 mom( df.0rox7 cdhentum 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 ofan5*u5mvqiti n *ly 1:ze+07bj cln9w 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 withrw 22zq aj:l)e arms extended has a moment of inerti: lzeawq 2j2)ra 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?