Angular displacement is usually exp4l9x ll *l5smiress in units of

  Angular velocity is exp3-ttvze lz 6r0ressed in units of

  Angular acceleration is e1yut( c+j idj6)hao ,:coa2iexpressed in units of

  A boy and a girl are riding on a merry-go-))4d7oqatr fe:*v nnd +u 7zokround which is turning at a constant rate. The boy is near the outer edge, and t )f odn:o7ur7nd)azkv* eq+4 the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridikfh67ff( z:iprh7 42q pxne(fng on a merry-go-round which is turning at a constant rate. The boy is near the outer eff(pzqf2n( khi:77perhf 6 x4dge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridisn0wqr :kovp77 v:if3ng 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. Who hakfs: :v3oq p07vinw7r s the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at 4o; vy2cmgakp+i kp8hae-4 k1a constant rate. The yp2 k8 a;kie1v m-4oc p+h4kgaboy is near 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 turning at a constanwfq3v*7br yq2qypb :h2o 0hi ci2+ xj+t rate. The boy is near the outer edge, while the gii2 qq3:2yv rfhcjqowy +p0 2h+*bxb7irl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Wc-q a:l:dz//ixawcw/d. k((bt.r a ufo 2-el dhich of the following is an accurate statemezw /-t. :lar/uk:l- xd caea bw(/i.od2d(fqcnt?

  Rolling without sliplud,qd8 w0e 6eping depends on

  Two equal forces are applied to a door. The first force is appdne( b:/-id7hlb lp 8glied at the midpoint of :ed7h-i lgp 8nd/l(b bthe door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. Thegogsg8(+b6gi /fqs 8k first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which f/k6s s g8gfi ogbq+(g8orce exerts the greater torque?

  Two forces are applied tot08 wyma/z -zv)2jrnc a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque mr)-jnat 8 wy/z vz2c0of the first to the torque of the second is

  What is the quantity used to measure an objecy 9ut v nf,(/9.ccclvit's resistance to changes in rotation?nit9l9 u(ccvv/c.y, f

  Consider two uniform solid spheres wheinp3i;k p/aeb qc*u 6l o+,z8ire both 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 smaller moment of inertiaqa bok3np6 , iu;iczl+p/ *ei8 is

  Two uniform solid spheres have the same mass, but one has twqlmh3 t :*5h36ebbl tnice the radius of the other. The ratio of the la* b3hbnmt6l l q5eth:3rger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice thebx fq8hycr: 4qpgw b64/ z74re diameter of the other. The ratio of the larger moment of inertia to that of the smallerwz7pf4 hx r/gecqr464bqy:b 8 moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2dvwqa /a/r 1q7M and 3R, what happens to the sphere's moment of inaq raq w71/d/vertia about a central axis?

  If a constant net torque is 3+udii3qry p .applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. (f, yp 5vg bsyq2+s bbt9:nc0mIf this cylinder rolls without slipvs 5fb s:b(bn,0q2+myg9 ytcpping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one w swlm*:/ l 3nctg8alh4heel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatimll8ta4 lgs/w3 :nhc*onal 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 R rolls wi/xyl bu-y); kcthout slipping down an inclined plane starting from rest. The linear velocity of the spher )/-k l;ycbuyxe at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an); uxm :muu+gt inclined plane starting from rest. The angular velocity of the sphere at tx)+ugm:;um uthe bottom of the incline depends on

  "The total angular momentum of a system of particle+g sm4q6i j5 oji:/7h(f ft8gswutl8i s changes when a net external force acts on the system." 7 gs /i tmglq+:tsufihi8(5oj8j f4w6 This statement is

  In what circumstancemi/h f- .5vm jsc:2hj04 tymor;c(qfms can the angular velocity of system of particles change without any c4 .fhsv;mc:c mt rhm(m2 0ji 5y/-oqfjhange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which c,d:k ui (toj-may be present. What happens :t(c,kj i- douover time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cl91 hhte)pfo vccgym * s8tb*(0483uqc4yodkp ose to the Sun, then which of the fo 3ysgc*kc9heudmtcp tov4o14y8bh(p8 )q0 f*llowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his ouehj-abqu ir x1/qs 65.tstretched arms close to his body. What happens to his angular momentum about the axis of biqs 1j5 q.ae-x /hr6urotation?

  An ice skater performs a pirouette (a m sb/25 m7dcpk(6s zaqfast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis o(qs m65az 2c/pmbs7 dkf rotation?

  An ice skater performs : fpgf ad6uk+zn69e9 ea pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his ked66afgp+nu9 9e :zfmoment of inertia about the axis of rotation?

State the law of conservat(khrfx: zgyey49 (6sm ion of angular momentum.

  What arc length does the Ear-i 3e/a oi5cxoth travel in a three month period in its nearly circular orbit about the Sun with ae 5oixc/o-i 3a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Wh* gm/a( f0 vaf7bic q28miyj;szs,jx7at distance does the tip of the second hand sweep through in 3 minutesgmifczxai,vqb s;y8j0 mf7 7(*a/sj2 and 45 seconds?

  How many rad/s is 25 revolutions perq)(albh u(0nt; ale e( minute equivalent to?

  A bicycle wheel rotac9;zwwk r .pq(x kx6s 2vhaqgm 20,b5ytes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel'9kvx.gmq2ryqa5w,b2sx h k;cp w0z6( s rotation?

  A pulsar (a rotating neutron star) eflg h2 k:4*hc94u qmrmmits pulses at a frequency of 0.40 kHz. The4h9 q* u2h:mmklf4rgc period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does is vt-hw 1dfn a* jr9:fz:dw-g3kpq+3tt turn in 0.20 vd3:n fwq1p+- 3 z fjg9d:tahsr *ktw-s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on thepj,y aa 6,amm; outer rim mo 6;ma,pajyma, ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. ej z3f .y:/qfq What is the average angular speed ojyeq q3/zf .f:f the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluti)e:x sv;t )iuwons in 4.0 s. What is the lineats)wi ;u:xv e)r speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers;zixbm j-2*4efgiw :k 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 pulley rotate for the cable car to makg*bzx2jif-mwke; 4i :e the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a cjun/s1k:; urd- ./yv kj(x tslonstant angular speed of 2.0 rad/s. What is the linear speed of a point on th yujk(r1k:d uxt-n.s/vs/;lj e wheel's rim?

  The cutting cord on a gas-pog puupou+/i ps*ya/)zm0ky ,2 wered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of p02*kzy/)o au/yispmpu, g+u the end of the cord?

  A wheel of radius 1.0 m is rotating with a .,.twh:6h au mi tr2odo01negconstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whhgrnw0.t. a:t ,2eo6ihm o1udeel's rim?

  What is the centripetal acceleration of a point on the perimeter of a ,4t 0ggjx 1uwdbicycle wheel of diameter 70.0 cm when the bike is moving 8.00 dg u01jw g4,txm/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (w +)rl5f -iz.hn v7*26xfbxj sxza uy;r = 1000 m) rotate to produce an artifici);zbfu*xhlxnv+ i z6 fw. - ay752sjxral gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with at; 7-ktlwztixx9j 8 s2 speed of 20 m/s. The maximum centripetal force (provided by static fr zxxsltitjt 72k9;w-8iction) 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 withrrdv(:xz wmn (wdy;pqsqm y;.+a,0 c0 a speed of 20 m/s. The maximum centripetal forc;qv;q y0,r mdr0z +m(acwn:ypxw.(ds e (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 whirled around h/p )+eb p.gznin a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maxihpeb+ zg.) pn/mum 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 withoutl+k4;3q7tqg4fjv9a:; kyrtk eon +ut slipping 10 m down a la:v k;+y;rjt3eutqt7 4qa of4kk 9 lng+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 constant angular e)kpx:(;(gsy2g fgcx 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 acceleratiual ,xoq5ebmaw+h*n/ 4e6id (on 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 automoxxpw 7cpbvf:6 8ge.s k)u4de7bile tire rotate after starting from rest keuvgw:)xp7c bps786e.d 4xfand accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, 2hmq m+t)j2, l4fshy9dpk3hg and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating dfwsov*s 7tr)+ ,*ojm at 20 rad/s decelerates with a constant angular acceleratio*tss*, mof + v7odrw)jn of $-5.0 \; rad/s^2$. 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 while turnb++9 (tvqi itbing through 2 +biq(ivbtt 9+.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rid- j6aj/t4tp est over a distance of 115 m. What is the total number of revo ptjiatd/ j46-lutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fra49pdz.w6 2s-l9y gpmus dx)nom 8.40 m/s to rest over a distance of 115 mlpg suzad-96dw4.9y n2)xpms. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over , ;os3i:pf )/yb0vfa)ptnt ik a dist,sia ffo3;n)k /:y 0)itpvbptance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a roe s27hlkqhdk: 9m;(:* xhferq.au4 kr tational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest 4*hfr( u2q9 l;h.:dqr sexek:amh k7k.
(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 tightef-rv 9) x6cnxkm j7*lqning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the rq 7 6cljnxx)m-vkf9*force is perpendicular to the wrench?

  The bolts on a car wheel require tighten01hk1qbp3 qy hmt 4uy1ing to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magk1hy4p 3yqb1uqm0 h1tnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment g( ay-m.ha)t zof 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, mass ;f,o f3aqoaj ueh1/m 42m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia aboutoa3a o m hqe/1fu;fj4, the origin?

  A solid cylinder of mass v5te) xy up3g410 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 the right. A second rope wrapped around another section of radius R2 = 0.50 m ex)ypx5g 4e 3vtuerts 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 pivoteds;l(6yw ii 6vw 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 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in 66 i(;vswiy lwthe first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is-6rdz f )-spkd d7pe(t hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. Wht()ks ded7-dfzp rp6 -at 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 rzxt6trej hsd5q n,6/o; d- /7/ rs/e5mukkoq hadius 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 /,e55//kr; t eumds x7q/hkq6jhon dt-zs6o rspeed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of massflb f;o(:qh8g 0xzx b- 7.07 kg and radius 66.0 cm. What is the angular acceleration0; xfolq(-bf8x gh :zb of the pulley?

  A 1.53-kg mass hangs on a ronpe5 mufro n06g4/;uj pe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is 0 4fug;/6ejrn5 np oumthe acceleration of the mass?

  A rotating flywheel can b9 63v3uhjjxrx/ 1 bqvje 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 inerit2gj;lhzhzs6q:, cq 1o (+ el+dof a+tia 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 rest and roloh6dl3 gmy1 d1ls without slipping dlygm61doh3 1down 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 a speed of 10 m/s. l +iwcsk16 cn/po 60ia How high up an inclined plnwlck+ pa0s6/i 6 co1iane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20i. o2;eu*mptp kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a veru; em2tio *.pptical distance of 3.0 m?

A solid sphere of mass 1.5 kg :u mb /tv4kjm e5b gegv(2g7 6p-ggz)hand radius 15 cm rolls 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 giveng4t )h67mm/g jkvp ( 2gvbb z-g:5uege 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 changes )inj. *st +kmyby $20 \; kgm^{2}/s$ 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 inert.ye v(ver7j 5ol:t b)lia 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 rotatir.* ti5 er-koing at 5.00 rad/s with arms extended has a moment of inertiert ir-ko .5*ia 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?