Angular displacement+ /kj)smcjm.w4dlb pyw28 zk; is usually express in units of

  Angular velocity is exp:ws e1 8utojh:ressed in units of

  Angular acceleration is expres57qw2i cbbnf)24kynssed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constan7 f tk.2-5hduvbqwm (9 d ylxd74tr+zrt rate. The bo 2rbr mfyh4kv7zdud-d9l7 wt 5x(+qt.y 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 m d3+(t)jg6 au vehkqk6erry-go-round which is turning at a constant rate. The boy is neaqkv(e tkah)u6d g6j 3+r 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 merd-vp5)2z2mfw* hlue gm9njb /ry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer lgm 2v*/-m)5h dzb2wenfpuj9 to the center. Who has the greater linear speed?

  A boy and a girl are riding a merrolc m9l dqg4ed:p m;3wpnm fv0 b0 n*hkv6.v(4y-go-round which is turning at a constant rate. The boy is near the outer edge, whilekofv0bwm npe.3m:l d6nv hv;g*ld( 04qm4p 9c the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riam slwioi* +vms;w4eso.(+*c ding a merry-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 .o4ww*issco sv(lieam +*+m ;has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which ojj3)mc+y gv. ufsd7wr2 rl(d04jvl i3f the following is an accurate stateme7yu+cj.30j rw)(gmirdv v d jl lf234snt?

  Rolling without slipp;5sev4 zu0 dat06r4ujktyb q0ing depends on

  Two equal forces are applied to a door.:a1o8xkt h 1dz The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are appliezx1 t81 odkah:d perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a 2 eh/fwbis-fnz otcr5lr +s67 //5cyk door at the doorknob. The first force is applied perpendicular to then rbzt-5ycfr /ih6c2k/ws5fs/e 7+ol door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the dho-bvj5 xy1-a*oluan9v+w*y-wns ;woor. The first force is twice as lwv -*9shj;v5lwa- n+ x wyny*-oa1oubarge as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to change zous0ve vp;(45cijf5edbf 4y1+ cb6ts in rotation?i sd4 4b bz0;cc vou565+ffje1(vetyp

  Consider two uniform so)pdcs5l6iv *2 zut 5ipio/:knlid spheres where 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 ipiskod p/ vz:c t2 i6)u5*nl5inertia is

  Two uniform solid spheres have the same mass, but otyu5pd45r3yb r.8dn 6j(qavc ne has twice the radius of the other. The ratio of the larger sphere'suaq3dyrd ptrb4v5 6 cy58(j.n moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mfxpy.y7+ p58wwd)as eass and twice the diameter of the other. dx7. ) 8wywys5ea+pfp 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 radiu b.o6mk 7kus4wmdw**b s R. If these are increased to 2M and 3R, what happens to the sphere's moment of iwm7* w.b*kmdkso6 u b4nertia about a central axis?

  If a constant net torque is applied to an object, that -kt8 qyy +6bbhw;c:n tobject will

  The moment of inertia of a solid :xjb,.oob)x w cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kine.obj :wx ,xbo)tic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg andqxntdv 7ef+ -/ a radius of 30 cm. Wq+x-t dv 7/enfhat 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 radius R rolls withouklnh6irr 20 gg3uax2 5ajz,zb ks65;et slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inclgz0552h;zeln a2brrsa3ux6 6j, kkg iine depends on

  Suppose a solid sphere of mass M and radi-qky u.+mix/+hmzc ;nus R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere ac qy+h-i.kz um+ n/x;mt the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a nec rk2 6fa-vgt02eudrkjr42* n4vqcle6t;x 0yt external force acts on the system." This statvd gkrkf0 6c2;xtq6c*a u4 er2e4-t 0ryn jl2vement is

  In what circumstances can the angular velocity gpom a0yh-p15of system of particles change without any change in the system's opag1 m 0y-ph5angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fruae8t nks 4t-(iction which may be present. What happens over time to the Earth's angular momentum about the Sutns48tueka-( n?

  The Earth moves about the Sun in an elliptic.za5(7db8fetb djgh, . 6bzqkal orbit. As the Earth moves close to th87zb (j 6htq,d5z..e afdbbkg e Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroue (h hm*zp,kujmdhpo13 ,hcb(+qawl)9 tte (a fast spin) by pulling in his outstretched arms close to his body. What happens to hisqc)z,+1 j wbl9o,a(dum k*3phm(hh h p angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling m, x0y9cqa(q0 qhvhzze2 g h)1in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axigmq9z0xq q2)hvyz c,eh( 1ah0s of rotation?

  An ice skater performs a pirouette (a() ztex-2 apwq fast spin) by pulling in his outstretched arms close to his body. What happens to his moment xaze-p)w2 q(tof inertia about the axis of rotation?

State the law of conservation of angular momv lt1iu .a6/o9crqw5qentum.

  What arc length does the Earth travel in a three month period in its nearly ci )rb q 34 hyj*3nyxvo(9tr909ggloncn rcula3(9g0vn b* jton xlrr9ghncyqoy)9 43 r orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distanuh./ec1td 8 lsce does the tip of the second hand sweep through in 3 minutesc81teluh d/ .s and 45 seconds?

  How many rad/s is 25 revolutions per minute equih4clyxt(egvg 86o x/(valent to?

  A bicycle wheel rotates uniformly through 2.0 revo+ljk/ -) dz t+1vojjgd*o +hbxlutions in 4.0 s. What is the frequency of the wheel's r+hk*djoxbd+)gj + -/ 1z oljtvotation?

  A pulsar (a rotating neutr4d71hyy esh 4ohis68*,xau a uon star) emits pulses at a frequency of 0.40 kHz. The period of its rotadyh8x,*h1 oya6u 7 uhsa4si4etion is

  A phonograph record rotates at ir +s2btwwo).y(o.u u 45 rpm. Through what angle does it turn in 0.20 w u(+swuy2or .i)o.tbs?

  A wheel of diameter 26 cm a0:9uet-iwzv turns at 1500 rpm. How far will a point on the outer rim move in 2.1 -:v0itu wa9ez s?

  A bicycle wheel rotates uniformly through 2.0 revoluttf+;1bkbsz 9n)6we/a+qros7imub x -p0 jy. yions in 4.0 s. What is the averan10qw;zxebt)o 7y pr +b9s.-yu 6smjbki/+fa ge angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0o4w2u fb 2/nuh s. What is the linear speed of a point 0.10 m from the center of the whe h/uu2fwb24n oel?

  A cable car at a ski resort carries skiern0 iz :+ xikz/4grqik4 ly*p)kb+ov+d s a distance of 6.8 km. The cable which mo4r)xq+ 4lkiin i*kv/g++ ydkzb :poz0ves 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 make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular stun) .s4 *ddiid ;ojt5peed of 2.0 rad/s. What is the lineatisi*dd uj .d;)5t 4nor speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter ic0im7 v1qdz (1ed5t ons 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate lin0 1n1mvt c qe57id(zodear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatinpxye- zgu:; m(t7 n0deg with a constant angular speed of 2.0 rad/s. What is the;p7x0d :mteuny- gez( centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on a ay,vc 0 d(k44 ke8smu2vlyog:zp6:mz;sr4sthe perimeter of a bicycle why,u:(kg 8 aok4ls0:sz6 drc;42vm sy m zvap4eeel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per mug0zln/; en7 i( *lv5vuox6duinute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificiavou*5(xig7 /nnu6 v elz ;0ldul gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20warh-)v qy7jx 8n4tp(g: 2hcu m/s. The maximq)(:t 4yuxvn 7rp w8ha-j2gchum 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 )ar dm9fw 6/itradius 50 m with a speed of 20 m/s. The maximum centripetal forcedawmi ) rf69/t (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 ej qh +a ,hsm5 58jsc(,*utosxynd of a 0.750-m string, 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 mass have if c,5o5qt8*s ahu jy+sx, smh(jthe string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slippi,l4 lcvk/atx 5ng 10 m down a lane at 4.3 ,kxav t/5cl l4m/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 constantq eyh476l 2:6qag q6sefrd/iq 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 acceler*hb xido )9,cpd dsqx6ww0 aq s7i2r2-ation 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 radiusrz)yzp8k( z59ufd3 :+xtgnw(od0d gh automobile tire rotate after starting from rest and accelerating andf0)kgy zud hg :zt9r o(p3zdw x+8(5t a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an uvw5bwr;d eo44vm .y)angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 5 13c6 okdt10ze02am-kflzan: in zimrad/s decelerates with a constant angular accelerato51kz0 e- a0mnctln3ki12m: f iad6zzion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular3ipxkjt0gy0o x f9v.5 speed of 6.0 rad/s while turning throu00pf.9k 3j xotyg5vix gh 2.0 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 rest overje6 st* ady- l(2lft)t a distance of 115 m. What is the total number of revolutions the wheel tsy edl6)jl(t *ta-2 frotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov 0lz(yfcsgt59 er a distance of 115 m. What izl0fys95gtc( s the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to revihx6,,re * kest over a distance of 115 m. How longk* ,i 6eevh,rx does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotas3j 1sgxqwov; je:-w 6tional speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constan;j:s3gqw o1x 6wjes -vt 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 tor-cqxon9 m)r0bik: 4 elque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force r4mqkb n o :celx)0r9i-equired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 )*hn-1aztpwct*u ) ;xta; u2uamahqbv/ *o.kNm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force app b*/ttaaatz*muc;nk w;uv) 2 x- ohu*pa1)q.hlied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertviqeij83) 8ex(. br ftia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fohx2f*a 6,cmgkowsg) )llows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of io ,m*6 ) gkwsh)fx2agcnertia about the origin?

  A solid cylinder of mass 10 kg is pivoted a/u2 mb/rosep3bout 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. (See Fig. 8-1.) What is the angular accelerationsr 3bu/ e2pm/o of the cylinder?

  A solid cylinder of mass 1prqs)g de+uf ;7,az) t0 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 pg + ufeq,s; )d7tz)arF1 = 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. n bnmr jn (+qz1h7 +kwz3.gln: The 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 ren znn3qh.nlj1+7wg+(kzr: m bleased? (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. a+4or:c kzis0 Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentialr40c+az : kisoly 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 wra)grr+9r2j fgh pped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration f 2rr9g)h g+jrof the pulley?

  A 1.53-kg mass hangs on a rope wrapped around sgs; , xsthc9(a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?s;ssg9xh t,c (

  A rotating flywheel can be )z,qs (z m6kvmused 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 ,idiqzfpc dib 73 f704of $5.00 \; kgm^{2}$ 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 0.01wnt8ybo10qgca3 sv2 70 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the 78os1b0na gcq w2t3vysphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.0, kqag2w*si80 ex (wem10 m rolls with a speed of 10 m/s. How high up an inclined pl8wie x*s 2 gmkew(aq,0ane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releasedp xij qm-7w,5y khr8,m from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distan,8 yrx5hkpiqw,mj 7 m-ce of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls 1qyikk) 9h037 rxua- swtmajrj4/ ;njwithout slipping down a 35e incline thak 0x9it a4-un7 1hrksjry ajjq3;)w/mt is 7.0 m 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 momentum chanz/k8-zap -)h xfsnc.n woo g/,ges 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 momentpft+hi6d 9t n0 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 extended has a moy 5;ord3lr+3y oylb3fkov l3( ment of inertia ofod;o3+r5kl l ry3yf blo yv(33
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?