Angular displacement is usually express h.+kuhqlf 2g3 in units of

  Angular velocity is expressed in unit pr:x )ke: 6uwm5knl,*k3mnzds of

  Angular acceleration isaec e m ; y6t/sfszlabh7135a1 expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning atlol : ,*e4ibmy a constant rate. The boy is near the outer edge, and the girl is closer to y4om *,ile b:lthe center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant r7 2e cernb4ju6ate. The boy is near the outer edge, and th6cnu be7 r4je2e girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning aqns;o7 dv/ 0q,tdx ml( *qxyn)t a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wh sn dx)0od ytnlm,q*vq;x(7q/o has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at afh/j)c(o):1 .h 0 ktqdb ioynj constant rate. The boy is near the outer edge, while the girl i oq(nt /ibk)jj:d1oy0) c h.fhs closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-roun4a e1li-4 xe pne0bvn5c/ gt)ld 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 g)t5ep40n acbi 1-ele xn/l4v greater tangential acceleration?

  Consider a rigid body that is rotating. Whic y2 tehe/p89jch of the following is an accurate sta /e8eth9 j2cpytement?

  Rolling without slipping depends on q;n3j+a*dlvf

  Two equal forces are applied to a door. The first force is applied at the +3sa7,l7yg g elo +jhdmidpoint of the door; the secgo7+ ,e+l3lhy7jgsda ond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are ap+wba9t;*pp7 xgfi l 1gplied to 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 door. Which force exerts the greater torqut7;+gfblxwp*p a gi 19e?

  Two forces are applied to a do )85s no)myosrak,p4zorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torqus,5osapz )rm 4k )yno8e of the first to the torque of the second is

  What is the quantity used to measure an object's resistanc)vo zw: nsm/v1sm1r1p e to changes in rotati )smz/:v1snp o1vr1mwon?

  Consider two uniform solid spheres where both have the same diameter,3xbnd )dw*dnd+)1ehso v eg9( but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertiahdnod+ (n*b)x3vw91sd de)e g is

  Two uniform solid spheres have the same mass, but one haxofv;b,* 8f vss twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller f8xvb;osf*v , sphere is

  Consider two uniform solid spheres where one has twice the mass and twice 342yzsj 2py wgthe diameter of the other. The ratio s gw34 pz22jyyof the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If dy9xk.l ,any l4ezxw.( rla,* these are increased to 2M and 3R, what happens to the *ex4a ,,. 9la lyz rxw(.ykdlnsphere's moment of inertia about a central axis?

  If a constant net torque iqf7x2etd ; 5qclc)2wi1o r/gvs applied to an object, that object will

  The moment of inertia of a solid cpa1jh gyer45kvk2/c4. yx u9pi k5b4i ylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratiokx4 9c 52 ebkhpj45/ivk14paryygu. i of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one whed bswa0 b v) :7evwad1grr5-i1el 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 translationg 5r 0av1dd 7b:sewai-w)r bv1al kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of ma x0flf8hc2g b1cnt3f+ ss M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphehftb gl208c+1fx fcn 3re at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rhn j0x(n/6vs fmiw7 )dolls without slipping down an inclinefs d0()nhimvn x76j/wd plane starting 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 changes when a net extecz-8focjwap lqci wh sy;/ af)); 5y(3rnal force acts on the system." This statementa- cqy 5c )j/)3z;fp;hs(oww ic 8fayl is

  In what circumstances can th9id 1 3,nemksom* 7q( 0v0* jiopxufpee angular velocity of system of particles change without any change in the system's angular momejmde7,ov91 i0pus03 ep(k* qxmonf*i ntum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mayh (t31 am5iclu be present. (ma1luhtc5 3iWhat happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Aqk7: vj.trjoa s*1oc9s the Earth moves close to the Sun, then which of the folla 1j*7c9ktr.oo vjs :qowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling x0h0 h8z.dmnn in his outstretched arms close to his body. What happens to his angular mh0dnzh. 8mn 0xomentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) x ( vek82;g ryxn33qdhby pulling in his outstretched arms close to hx33grevq2x; ny kdh8( is body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs d tu0v 2mm 51khbml2npxnki w) 4u3;1ja pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia abo 1;ljmb)twm2 3pn5kv4 u01i2dkmu nxh ut the axis of rotation?

State the law of conservation of angular +.9 s3ixfeld8 ah9klvmomentum.

  What arc length does the Earth travel i +x/u nc t 7)blyu9p2opgha30vn a three month period in its nearly circular orbit about the Sun with a r30a2y/9+oh7lxpv ) nugupc btadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thhz.v.h( ywd bsei,5a1hodsh )8p as/:e tip of the second hand sweep throhaa5 8shv .hhd.y,do: )(spzsw1 bie/ugh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions p3l 3 u+hq2(nk:aecitu er minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolution zi1fp j)9uda6s in 4.0 s. What is the frequency of the up 1jf)z d96aiwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fxr8(j a- rd4y zp)zg)yrequency of 0.40 kHz. The period of its rotation4a(yzz) yjdgxp )8rr- is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.201d;zt ,4uymaa: al/le /m4l: ; a ytu1adl,zeas?

  A wheel of diameter 26 cm turns few9o 7-zf ,m5j1yx joat 1500 rpm. How far will a point on the outer rim ofoz7 x 9jye5,fj1m w-move in 2.1 s?

  A bicycle wheel rotates un g 3.kbcw 8vehvot0yoan xvjc820f:14iformly through 2.0 revolutions in 4.0 s. What is the average angular spee8co w2 v0o th3j a8vyncg1bv.efx:k40d of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in ql:tr8 jo -(fe4.0 s. What is the linear speed of a point 0.10 m from the center of the wheelftqerj(ol- 8:?

  A cable car at a ski resort carries skieanno5o,+h1 bv rs 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 the n ,nhobo+51va pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 w3s4 16lkddda m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the 46lkda 1ds3dw wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in leng ytyab5y3j p7v/6pgn,p +3sgjth. If the motor 6,3v5+7yjygp/g3 bpsnjtapy rotates at the rate 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 conk 9 c0c63fz0tum 0jxftstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wc0mcf x 0z6uftj0tk9 3heel's rim?

  What is the centripetal acceleration h z xp)i30;+ ow /0/ymfyolztbof a point on the perimeter of a bicycle wheel o; y03/hftizz 0pw+bym) l/ xoof diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must ztjcx s:1( 9xr*;yntfa circular, rotating space station (r = 1000 m) rotate to produce an artificial cn(t1tfx:j*sz9 xyr; gravity of $9.80 \; m/s^2$?

  A car is negotiating a flao(l hwqv2x7h0t circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal for(h xvlq2hw 70oce (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 ce0 6-hxs:c hfgurve of radius 50 m with a speed of 20 m/s. The maximum centrip eghchs6-x0 f:etal 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 string, is whiw*xk 4s -9wawyrled around in a smooth level table. If the mw*- k4w swyax9aximum 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 sli6 mp vefj2 rldb)/+u:ox6rg0n pping 10 m down a lane at 2 b0 pren6ougxj6:r )d+lf/vm4.3 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 accelerationt8 :cdz5g25, bbvz ybq 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 +qm -dtl8ufb :/7hsb la 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/y3 t:u.o tooe.300-m radius automobile tire rotate after starting from rest anoe/o. ty:otu3 d accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and haky.vtur1su cr,g840es an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatingnrj ge4 /kt5r) at 20 rad/s decelerates with a constant angular acceleration ofkrt/4gn5er )j $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an 8 u/r-nb*7 wlyuat du*9g+amsangular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelerati8 wlgt y-d9bm*u+u u7nr/asa *on of the wheel?

  A wheel of diameter of 68.0 cm slows do dapuh9 qttdbh32.-3iwn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel r3u .d9hda t3-2tbi hqpotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to restfe)e s7:ey :o pqsu26cig--yrs, 9uwt over a9- ie-ysc7f,otu )p:syer 2q:6gws eu distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 06ajf j6j- t4jlkq-zc8.40 m/s to rest over a distance of 115 m. How long does it take f64-takc jjzjlq6 0 jf-or the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotl)e s:dzm.,;x eqp3jiational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accele,:z;x)s me 3dp eilqj.ration 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 aa:j 3 nw *3i7*s,krngx6rfnupqpo18 require 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 force is perpendicular to the wranw7:s gp1aj3qku rn* ,p3x6*ri n8ofench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm l 3t n+umpty218mwee0km9 mr9iong wrench is used, what is the magnitud9n 18 mmm0m ir2 93ypt+tuweeke of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment *u9q cr:f(v c)tn6 kgjof 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 fol6pw *8gfv; coolows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Whc86*fwpv og ;oat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axim97wss. l;4qr bj5xsns 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 bs9qs5s m.nwl;jx7r4 the cylinder?

  A solid cylinder of mass 10 kg is pivoted about ak2zvw:zn : +kv.er ( wf)injc9 frictionless axis thought the center O. A rope wrapped arounv w rkv(n.j9c+:ziz )n2:fwked 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. 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 rod is initially held in the 2sl7o anp*m sbq1zl- :horizontal position, and then released as the free end isa b:ps2on* m71l-lzqs 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.)

  Consider a bicycle wheel to be a ring of radius 30 cm ac7jl8x,3 urqcg lwj1y2gx ); knd mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tange7 )cwxu;r 3 jylclkgx 1j,8q2gntially 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 r0sfxfzc7+b5 7u xed;a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the puur7 ;bfz0sx 57d +efcxlley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlessckl* awtki,g- ofu2 5dj 7y8j9 disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the miu-29c*j 8j57t fg,kolw d ykaass?

  A rotating flywheel can be used to store energy. If it is required to sto- w8ikkhs83 wore $1.00 \times 10^{6} \; J$ 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 gis 3akks7,ead68g-k$5.00 \; kgm^{2}$ 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 ay*sw8 * -xghdrc(xl m9nd radius 0.010 m starts from rest and rolls without slippingsx- lcg9( w*mhxyrd8* down 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 j5 65na 3tb mfafi /y;9quczc(rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming tof5if5b6tcq; amu/3nay9 ( j zc rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is r qz gb(etig5y,z:0:tveleased from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical dist,gt: 5yzzei(bgt : v0qance of 3.0 m?

A solid sphere of masv1f hlsg,qya41 (iti7s 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume,v7sfq 1ig4 hytl( ia1 it started from 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 js+8+ 7q rc-sif*t6 moxw0exnmomentum 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 momq9 ib f3zd*ya 123k.fk7cpblvid7m8 aent 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 e i3f( iwsz- vj7kkja:1bh 0yw:xtended has a moment of inertia wh0fkw z:a17viji(3 -b s jyk: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?