Angular displacement is usually express in u 8v0z4c qnof;2xeim ;x+b, koonvc /1fnits of

  Angular velocity is expressed in unitsj w38k1kzke3 w.tb de7tq.my8 2tu;i w of

  Angular acceleration is expressed in un:rk9isrn s+7j*4cu.rs j*8d ogh o1wzits of

  A boy and a girl are rin28yba* w,h erk23zgig (: eboding on a merry-go-round which is turning at a constant rate. e3 ygkwinr2b a:2oz(h8*,gbe The boy is 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 turning kb 4dna10ng5gk/qrz(4r) bh rat a constant rate. The boy is near the outer edge, and the girl is closer to ther4rbk0k g1n 54nqrdzh / b)ga( center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-ry,gdp jl ;;8wk vo6g(bound which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who kd l;jwp(og8y6bgv; ,has the greater linear speed?

  A boy and a girl are riding a merry-go-rounj4 naa: 2wv7vq(jq9mvd which is turning at a constant rate. The boy is nej vvnv7a(wm4qj aq:92ar the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turn6o;-ce- v1ak,7v pjr vul pyy)ing at a constant rate. The boy is near the outer edge, while the girl is close-cyop1v);p6 r-jy k ,ulvaev7r to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followinplnvk;ih 0 stq -o185bg is an accurate statpnsvo81 b 0l k-t5ih;qement?

  Rolling without slipping dependv:tje,h5 z.ni8 xpv(ds on

  Two equal forces are applied to a door. Tyb4e9zvd4vs 7 l,pi4qss* gp8he first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forv7 4pq*s p e9dgl4bivz s4ys8,ces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a dooc6rgya2;hi j( r 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 f6 2r(ahic gjy;orce exerts the greater torque?

  Two forces are applied to a doorknob, perpendiculak8vpqeeg82t( q 7v2plr 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 the second is82vvlp( ek72g q8q pte

  What is the quantity used to measure an object's.adg jsw*+7ik90enr 1 dj6mrgzh 13ux resistance to changes in rotatio 6.3m d+ drsiwe1ggj 9j0a7*uzkn1rxhn?

  Consider two uniform solid spheres where botzi jek+ m 6lz .*gauk: /t.eabe1o3yd9h 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 e o3.j b+a ly z:k1d9at/g*kiez emu6.smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of je ,a ;xx(5lf-x5,kl 94 wpkei1jbxxt the other. The ratio of the larger bpwxix ;5je4, fj-xk lte1(a9,l xx 5ksphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres g:hg(ecj tos z79d8.o where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to tha(gs d9tj7o8zechog:. t of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. dv sve52*e(x g ubrfha:f.u1;If these are increased to 2M and 3R, what happens to the sphere's moment of inertia(ux;r ae 2f5v :dgb1us .vfe*h about a central axis?

  If a constant net torque is applpi 9d+x-oli 4(d g;cbaied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 28cp 3 shkaa aoyd(s(; 9ei.d y45vcxqMR2. If this cylinder rolls without slipping, the ratio of its rotapa3a ac ydh( k2.vxdis549(;esocy8qtional kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass o tah no,,7f3cojbn0pd3m k v53f 10 kg and a radius of 30 cm.3k t0 ma,n375pn, jh cdo3vfob 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 g .lo0v;y-ds,slp4 jpe86fay radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the-pa8yflg 4;lsp.j6 0 vd y,eos sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wvjk9vg2pk:;khd*z )eithout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incli)zj;9: v2g*vep dkk hkne depends on

  "The total angular momentum of a system of particles chakf 1qylf7i-jiuc (g c)(x7g7k nges when a net external force acts on the system."giflyk 7kqj u1ix 77(f)c(c g- This statement is

  In what circumstances can the 6,fkh lg7 o(ib.icy 7bangular velocity of system of particles change without any change in the system'so(6y f ,ic7.g7hb kbil angular momentum?

  The Earth orbits the Sun in an elli ncsz4 e+2lu8wptical orbit. Ignore any friction which may be present. What happens over time to the Ea lcu2z4s+8w enrth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves dybgmwu y-nc6::7v l4close to the Sun, then which of th- 4u ym7cd:bg 6wn:lyve following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a 1(wfx+ ( vv8iepo/irzpirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to hv i/fi8+px oewzv1(r(is angular momentum about the axis of rotation?

  An ice skater perform3 q,wpk)k /d7f z-j;g dwtqu(zs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens totzwj7qf - d ;wuqd3)(,k gkz/p his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b/q6 oh vrdr4, bsju;8t23hsvky pulling in his outstretched arms close to his body. 2h4bt,uq36k ojhdv8r s;vr /sWhat happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mog c2j 00fpnc8nmentum.

  What arc length does y9 nk0qfh4vzd/dln u6;w0: pxthe Earth travel in a three month period in its nearly circular orbit abou /9d00nv4hyz wu k:lqf dxp6n;t the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng9jruw0dxv/fl q ,pq (5th of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 4w,0u qv9lfqd(x/j rp55 seconds?

  How many rad/s is 25 r mbf eppt9ql-, 5.wdx/evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s da d(29t lue hvd6aesi0g.u(:. What is the frequency of the whutad is2ld(hved0a .9:e6 g(ueel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40( eahulmgv*ebpu,8 m,h0x4 y, kHz. The period of its rotatu g pvx8hm ubh,ey(mal,*4,0eion is

  A phonograph record rotates at 45 rpm. Through wkuz( )fb fhjh4yj3f kpm lh*5 lf1i/x+b -3/eyhat angle does it turn in 0.20 zj-/kl hjxi pff4b5u/(3)b1+ em*yfyh h3flks?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on thy4ze 2o 9vu cxiur;h ieb4:3j2e outer rim move39coevrzuj;ei2y 4x4 iuh b:2 in 2.1 s?

  A bicycle wheel rotates uniformly ti*wp-l9rgld /udy-/i,j 7s afhrough 2.0 revolutions in 4.0 s. What is the average anr7dd, /s iya jwp*9 f/luli--ggular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whac1gn93blcal 1)yqnb2fy s:m0t is the linear speed of a point 0.10 m from th0sy1cq y 1 b2mfna3l9n:)glbce center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. c a6f2ibhde-mt7rygd 2sz (62The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulleyfa 7t2(dzg2hr6 2dmce y-ibs 6 rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m ;b/-f /puwus wd8fe k;)vqi5 bis rotating with a constant angular speed of 2.0 rad/s. What is tfpvfbk ;8uq)/ -w;wie5u /sb dhe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered 4fx k+v. )vx nf ynvm.m;)x8moweed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear +nv kv; 8 m)xfm. 4nxmo.vx)yfspeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angulak6e(b*cos c jg0.l0 pkr speed of 2.0 rad/s. What is the centripetal acceleration of a pecp*kscb j(gl0ok. 06oint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of mdur )civt5:ojd+il2)wh ) e-a bicycle wheel of diametuvwiml-ti 5:dh2j+ )cr doe))er 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spahe;6io di*pg5 ,h)iq4tx i r(lce station (r = 1000 m) rotate to produce an artifii*x6 r p)ihig tl hq(ieo4d,;5cial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 mviv r0uyc)3a gg-rdd+,gq7.r with a speed of 20 m/s. The maximum centripetal force (provided by static friction) idiv7grg-a ,v0uq+g)dc.ryr 3 s $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flatm.2onaex b)2o circular curve of radius 50 m with a speed of 20 m/s. The maximum centn bmx 2oae2)o.ripetal 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 stringu 9sv6(qo e ,4idb2jfv, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the m of 6ivd9j q,2bsuve4(ass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 bcrk 14 .)ck2,lk8u tysd*/t0r uawvrcm rolls without slipping 10 m down a la t)r4 ylru *k2w8v,cksduk.tr 0b1/ac ne 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 constanta4epuwt nwr,m5uejgt9)*i v:5 rq*,o 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 constant angular acceleraj uvxocu*k5:vd.m 6q*tion 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 after starting fzntg./ui e8*9qvt 1xx rom rest and accelerating at a constant angular acc.gi8 tvxztuq/ex 1n*9 eleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has a-wopz xu b;0r4ryg1;zn 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 decelg 21ptd *o t3du,)fctxerates with a constant angular acceleratio )dt 2pfo1tdx*, c3utgn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and re.ipx+xj,( er qxvw ,e9(btb r1aches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of thr9 (t+rpvjb(,eixx b q1.exw,e wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rzm 6ghy5 2uu9jest over a diu6jgm2 hu yz59stance 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 slows doh6nklps ;* j.qwn uniformly from 8.40 m/s to rest over a distance of 115*q6hl sknpj .; m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r sxuc;bs b:ig j*z-3f0ok +mr;est over a distance of 115 m. How long does it; imb; *30zkgfcu jx-+:sbsro take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotlydx. b sc 1hrdq4b8 pfx15*b7ates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comc1 8pd 7b5bfr xxds14h.bl*yq ing 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. If.)b1tmgvf3 pid 7z2ld a 30 cm long wrenctz3fl7)vd2g b1.pd im h is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel requ1eh,wus w 1)izire 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 fow,) eiu1 wsz1hrce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia +e jmz:lb9 a,p$3.00 \; kgm^{2}$ 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 ;tga,4)iyvd mthe origin, mass 2m is a 4,dt)gvim y;at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mv7rum0 3eiq.dass 10 kg is 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 t3vqu di0mr7e. he 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 h 1y7)xrj+wt6v0(g ix.di nivmass 10 kg is 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 t6xh0.dxgij 1r(v nyi +7i)vwt o 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 horizor)g0/p fzzbq. ntal position, and then released r / bpzq0.gfz)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.)

  Consider a bicycle wheel to be a ring of radius 30 cm and ma(aauo1* ow 0 gfl)(cdxss 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 wheel achc0x(fgwl1 o *o(uada )ieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a friction50tflr3) h06e2 fmcjnt glg:g less disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angujln:t5g36mclr 2hf getf0) g 0lar acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu q.-+d 3grt+*;sn zld:citvdklley of mass 7.07 kg and radius 66.0 cm. What is the acceleradtngci vs;-3q .lr+d*k+ :tdztion of the mass?

  A rotating flywheel can be used to store energy. If it is r*wxwf;5v0y5oce r5syy:jd-c 0 v1d ydequired 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 ofpytim 8z iu q7r.,t)*y inertia 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 ams1a 5 c2cf*j5p9uoahgs;( wdnd radius 0.010 m starts 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 thewucsaomcj(d *; fhsa5p1g5 9 2 inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rols0/ n .1indnkuls with a speed of 10 m/s. How high up an incuds1n0 i.nnk/lined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a massow);0lq6490 bgug: akcz dmiq of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is itl6ag;qzo4wqmiu) 9g0bd :k0c moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass omqw6q(( raj9*vhm)i 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 mqr*jv( )hq9m6w imo(a long. Assume 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 momeny:0:yeryrt;u tum 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 of iner5y( v02tn zzb0frfn7 ztia 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 wit 554qtmrdty 0eh arms extended has a moment of inertia oyem r45 td0t5qf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?