Angular displacement is usually express in uniuuuu1,awo t-oks/+ 9v tx;*p rts of

  Angular velocity is exprebs r.z9e)sb( fwc y)5kssed in units of

  Angular acceleration is ex s8ou 6q0gzgz42x s:hm z)xzr:pressed in units of

  A boy and a girl are riding on a merry-go-round whinj(c85xem a npt.)cq93 uk) j+i+mruich is turning at a constant rate. The boy ak)+j n8mxrte iu q5)j(p+m ui nc3.9cis 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-round which is tkgip: .scl0;j8c - cwourning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grea losig8; :jp0w-k.cc cter angular speed?

  A boy and a girl are riding on a merry-go-rovz4e 9bmy b//x:eapx/ und 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 linear speexeb m x/v:9p/4 zab/yed?

  A boy and a girl are riding a merry-go-round which is tur)clpj yzq(x q*f /e8p9ning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the gre/lq *)j(y9pzcep qf x8ater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a co*r oxzzt)k22onstant rate. The boy is near the outer edge, while the girl is )ztkoo2xzr 2*closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of thjzc(ywx *v-g6b-i-x*f sd7qj e following is an accurate statemvid qxj- - *yxwfgs*7 -6zc(bjent?

  Rolling without slippik.+77fjma1mhd8e pu c:wapj ew04zo 7ng depends on

  Two equal forces are a+lnb6s.*w/ar3 f;lydjvnp j-hw3* wupplied to a door. The first force is applied at the midpoint of the door; the sec/63w ;h jdls-f*u3jlr bvwna+yw * .pnond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appli+z f lh 2t;f/tvpeb b,v*c6oe-ed to a door at the doorknob. The first force is applied perpendicular to the door; the second forcpote/ f-b bc+,* l2tvf zhe6;ve is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpenxo6i 9a;4aeuokzr 97xw gre b4v3,z8 idicular 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 theab 6,ge4r73v9oux;zozk4 9 ea8iixw r second is

  What is the quantity used to measure an object's resistance to changes in9564 lf2ddglrqf11 w+sc oqsr rotation? rr df5qlq wf91+lcso6s4d12g

  Consider two uniform solid sml0tdael j;oz/u/(: ypheres where both have the same diameter, but one has twice tu zl/dm a/l;yj0: o(ethe mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the samejb0lqp* um9gqj((dl c*aj) r9 mass, but one has twice the radius of the otheru9q (0rpj*b dm)qj g9cal *jl(. The 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 mass and twicwq+a8j x:s*pxw/ ny6 fe the diameter of the other. The ratio of the larger moment of inertia to that apw+xq:6x/nwfj y s8* of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased kkeal:, 3np ek lwj* -l9.l4)ah-tvltto 2M and 3R, what happens to the sphere's moment of inert 4k)h. -,aj t9e3*kltnwlvale-p :llk ia about a central axis?

  If a constant net torque is applied to an object, i xx w--lro8bf: g1gj7that object will

  The moment of inertia rtlgty1rb6 +7kw*21ef : pv-sn.d lljof a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatio+v.wrtet jl2brg:fp1 l -k 16ynd sl*7nal kinetic energy to its translational kinetic energy is

  Consider a motorcycle/mlyg: wpjz4na9/d1h+ jpk8g of mass 150 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 kinetyj/j np8m dg1lhkpaz /:9w4g+ic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withouta ivxe/:4;nem,,cm oe slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depxiea/enm 4,m; vc,: eoends on

  Suppose a solid sphere of mass M and radius R rolls withc(pvhdv3f6.n)h mx9pcj h /;rout slipping down an inclined plane starting from rest. The ang vjcxdh; rv.mfhp( hn/3)cp6 9ular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a syste k ae;x550qv k ;jusje0co/* gyu,mnu2m of particles changes when a net external force acts on the system." This uv/ju 55xkonj;0g;k2qucs0 e*,ma eystatement is

  In what circumstances can the angular velocity of system of particles mxrrp-km3x,2k, d:pw change without any change in the system's angk2p,kw:pm-rmx3x rd , ular momentum?

  The Earth orbits the S(z,xrq dwi8w 0gxv p.:/y w+idun in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momen 0w(+ ii r /wy,qpv:xg.wz8xddtum about the Sun?

  The Earth moves about the Sun in an elliptical osiyr/lj h 77rq; s(tu,gf.*b xrbit. As the Earth moves close to the Sun, then which of the following best7rq,hs ;rt7 f(g/julsx.y * bi describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling hao)a : 0pml-r,8y(e3fv)m p wtplkwd ):j/ygin his outstretched arms close to his body. What happens to his angula8v0 llpr)ko3/ :meg(w,t pjfdh m):) y-wpyaa r momentum about the axis of rotation?

  An ice skater perford (*: q1xdkxtzzy 77 hq)hryi7ui (uy4ms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rota(dykti:z7yqrz dx 7hu)xyqi(7*41 u htion?

  An ice skater performs a pirouette (a fast spin) by pulling in-:pcesax z0 mxtr1l4. his outstretched arms clxxc10l -pmrsz a.: te4ose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conrf1fmnx f4) -dv2 sor+cur;14 z qb9hpservation of angular momentum.

  What arc length does the Earth travel in a three month perix:nm y-b4twj6od in its nearly circular orbit about the Sun with a radiusy4n -6b :tmxwj of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lent* lw4h8e-*v wnqga0p 1af; ipgth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and *tei1wwfhvp* a8g qa4n -l 0;p45 seconds?

  How many rad/s is 25 rev xtkyc 4p-y7a;g5gf:rolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolution )(7gelaxxoic3 54me ns in 4.0 s. What is the frequency of the wheel's rotation4 37x lix(gaec)oenm 5?

  A pulsar (a rotating nem6tz7 swmg*y 6 i q/(ntjio/o/ro4 :zsutron star) emits pulses at a frequency of 0.40 kHz. The perio: zms z476(roit*6/qg/twomy /o s nijd of its rotation is

  A phonograph record rotates at 45 rwtshsz* 8dvtd*2lyhe v/ x:: ; n4fyx-pm. Through what angle does it turn in 0.20 sx2y *d:lstt*; v:y 8edhn h/f vswz4x-?

  A wheel of diameter 26 cm turns at 1500 rpm. How far a.b )6;hioauh will a point on the outer rim move in 2ui .hb6) aaho;.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutio.jopqef9zin1r*jz .(-l:y nz ns in 4.0 s. What is the average 1 ijr:-9n*l zf(yn.o zj pe.qzangular speed of the wheel?

  A bicycle wheel rotates uniformly through;dc)j p./p/2.r balew 6 blbra 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheelrpjcbw6/be .a;d2 l /)bapl r.?

  A cable car at a ski resort carries ski n2ddxnefu:6 /ers a distance 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 th ned:nfxd26 u/e pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a ua:a 2 .y,3is p.gwxfgconstant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's, ug :iafgyw. sx2pa3. rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the moto if-2:s 9 sasqs7e1cyor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cqc9oi1y2sse7 :a - fssord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0)nkn/0s5iw,ma eo9(m foki*a uvi9r) rad/s. What is the centripeton9 (*)/rsi0 , ki9makn ui5awoefmv )al acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bim)u7cef) hxow8-ch ;wcycle wheel of cww;) mhc8x ho7uf e)-diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (r9;4hb +jmfbpa = 1000 m) rotate to produce abm +4f ;hpab9jn artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cgz)sb 2ex-zew mm)q3 +urve of radius 50 m with a speed of 20 m/s. T z q)szgbmxew2+ 3-em)he maximum centripetal 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 circular curve of radius 50 m with a spekc6l-v+5 ljo u ox2mn(ed of 20 m/s. The maximum cenm o6jknxu2(o5 lv l+c-tripetal force (provided 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 stringd4 ddflnv 7ut;9;zx3 r, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 25 ;d9;uvlrxd4zndf37t0 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 k 2,a3rmfli5lkg and radius 9.0 cm rolls without slipping 10 m down a i 2lk3rla5,fm lane at 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 constant angular acce5gq(9 hoiep8p0*othq leration 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 as u08y9qu/vg1vs2fq 3r yy*s n constant 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 rdze adr+;ybhi (b 9053i x k+d2dlt3yautomobile tire rotate after starting from rest and accelelb + d5z+k9y3edxdr 3b tiy(20dihar;rating 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 ang(zf bx*xc; .prular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s fvjqk:q,j*(cmt qvf0w09w++ hg ir 5qdecelerates with a constant angular acceleration owkc j,jq 5mvg:9wi* 0q(+hqvrft+ fq0f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest anj zq4, y/ljxe7d reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average ang,7 qejy4jzlx/ ular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly feu6cjb7x )o )zrom 8.40 m/s to rest over a distance of 115 m. What is the total numuje)b6 c7z )oxber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter d0vcxd2c,) i qck*bs2of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m0c2sxc,2qi)d kc *vbd . What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforkk u b,j10vfg9y9wz-a mly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to twzkf -, jv 9gb9k1yau0he stop?

  A centrifuge in a medical laboratory ro/tnq9*o 9mtby tates at a rotational speed of 3600 rev/min. When swi q/t99*nmo tybtched 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 Nm. pi xhzj/ i o5*9h2y2we If a 30 cm long wrench is used, what is the magnitude of the force required e2io9xh5y z*/w 2jpihwhen the force is perpendicular to the wrench?

  The bolts on a car wheel r; ix)tyi3msxa;n r;+ kequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the fkri;)+ xn;t 3asix; ymorce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia zf6hv,yzpp 0e 8 1aa wq)km*0h$3.00 \; kgm^{2}$ 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 icaw wd8 1w4vi8 + yvik.f8ejl9s at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about thd.viw8 8v i8kywe1+a lcjf49we origin?

  A solid cylinder of mass 10 kg is pivoted about a f m yw2-)fkuzu1rictionless 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 a1-m2uwfz )ykungular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionp 7l3.0bzevzx b0xd u1less 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 e.3e u bz70bzxdvxlp01xerts 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 en*z pov0f6;o8d wuv3twd. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. 6 fvov to*;wdu3wpz 80What is the angular acceleration as it is released? (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. Neglectt 4 *pkuop7m d8gli/v41vc2if 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, wg upf vol474i1m tcv8*dk/i2 phat linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless 2m/ z z,ppawt19qdiz *disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleq */ 2w i9d,1mztpazzpration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlessz hyy 5x*(scy7 disk pulley of mass 7.07 kg and radius 66.0 cm. Wha 5xysy( y*z7hct is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is *c gzh7b6q:dligf2 ) fe1jzd2required 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 npc,cl u1+f 3 oi6cse11sx.vfinertia 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 reb hrj(m-jlxaf e-jlf 7.;g x(2st and rolls without slipping f.lhj r2(e7l -b (j;j fxx-magdown a 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 with aram-u*b u 9, t0ppw:ew speed of 10 m/s. How high up pw* -b,r t0u9e:wpuma an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a i+2bmpf* hiem4jim1t bz09y ,mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How jz2ef0y9 h*4i,+1m bbp mitmi fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 k l:o/9ewdkv/ r hmba ,p3zatn89 a7jw,g and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momentea/h9w,8n9 / mwz ptla,ovd7k:3jabr 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 3qz4eb-5j*n a jsc4 :kcw ll ch8)pm4pchanges 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 ix:8y dau- jf3pnertia 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 rotat c, ayy0rqy*0ting at 5.00 rad/s with arms extended has a moment of inertia of0a r,cy0t*yyq
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?