Angular displacement is usually exmqq4v3 /dl hl+press in units of

  Angular velocity is exprerc d(ai 6eq. 9-ijkc.fssed in units of

  Angular acceleration .v;m;d vx 7ucsyn 9-l;o3fojois expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant p-ng9*0r e;jnp mmgh/rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displac ;e-gg0* hmj9n /rmnppement?

  A boy and a girl are riding on a merry-go-round which is turning at a con ;iu-qvg3jts0lx3 orew bvn9x)*jd9 2 stant rate. The boy is near the outer edge, and the girl is closer to the cej; s3 -jl9x vbonv0)gqw*3uted2xir9nter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turni;/ij(r* lummgrmk eslg,y, /9ng at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear eijsl,rk(/m,g; *rug9 /mlmy speed?

  A boy and a girl are riding a me*lefs:tt7pv,id- 3x d8 dp 9cge- /tjcrry-go-round which is turning at a constant rate. The boyt-8tg9*ddpvsp: el, xdi3f/7ejc -c t 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-roun,lromrz )( 5i1k /kz.v yocl/md which is turning at a constant rate. The boy is nk1 /,i)zrmz.rool/ yvmlc( 5kear the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the,4*wya )aqmebd;w,m 0ds l 8sv following is an accurate stat adbw;0a*)y ,qwmdl,4vsm8s e ement?

  Rolling without slippinq6 e:-ohya m6tg depends on

  Two equal forces are applied to a door. The first force is applied at y1ejd (t2njl75 (:luova n 3aithe midpoint of the in (lu1l:ya3 oaev527jd (n tjdoor; 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 /hjskz; +nu umm(:badc(fos5 ph 7s95applied 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 s;7kpa(s5dm fuj:5 / +shou hcb9zmn( the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicula/z a31k8yjap o)2qlwo i03opor to the door. The first force is twice as large as the second force. Th8/31 aoyij)kpoo qlzw3a02po e ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an oak 9d (jhnz-(gbject's resistance to changes in rotation?j z ak(gn-h9(d

  Consider two uniform solid spheres where both have thjv,k)ic)let xlxr 5.5yi.fg :e same diameter, but one has twice the mass of the other. The ratio of the larger mol cv 5f irxl.5tk.e :g)ijx,)yment of inertia to that of the smaller moment of inertia is

  Two uniform solid spher adbb zqlzkq.+r:l:q3) ky;y *es have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of t qdrl q3b; y+kq::)*z yabzlk.he smaller sphere is

  Consider two uniform solid spheres where one has twice the mass .lh +g5kb g7ybrfe+2e and twice the diameter of the other. The ratio of the larr2f+klb eye+h 75g.bgger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incredu6wp6- 3lsdd ased to 2M andw3dd 6pd -sl6u 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torp7)6vu s)ju pf) p8zxai5s44m je-+i blo9 neique is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.uzezcre -3a3zr-6r4 e 5 MR2. If this cylinder rolls without slipping, the ratio of its rotationzzr34u rzce aer 3-e6-al kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass:yt3 vgi 8f bmfq:7ie)6ua:q g of 10 kg and :qfat3v6g)y f:eimb :87qigu a radius of 30 cm. 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 radius R rolls without slipping u0m: gu6q0ya ibzi 2:cu yx7ll -.8r4fheu6l xdown an inclined plane starting from reslx ic6u6b:egm0z:y2q.af uiulh yru487 l-x0t. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R ysswico 1(4 5*0 d;hcztuwm7drolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline de iy mw(t1 4cc7ssu;* ddw50hzopends on

  "The total angular momentum of a system of partiwov:v0 s2xzgro+9j :bcles changes when a net external foj zo:v9vrwb:x + o02gsrce acts on the system." This statement is

  In what circumstances can the angular velocity of system aeic2v+sjf)6 of particles change without any change in the2es )+6jcaf vi system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. 8o9ekj(b g*fvvh u-dq/y5v8 yIgnore any friction which may be present. What hdyf- yu v j5o/q*g 8ehbv9(v8kappens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an 0rh1cug3 wuaoov7n;n j 97.qxelliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orb;v9wgo 7.0auxu3cj qho1n7n riting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by p46dq:f3kg4 es:n fnvve(j7 mfulling in his outstretched arms close to his body. What happens to his angular momentum about the avf 6:g n4nsk4fe (m:3 edjvfq7xis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstret(p.il rl sn2tny -0jb*ched armspri .2(ltyjl*- bn0 ns close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hisvf5u7ib5pz,q w: 79j+j3reo fir n(ca outstretched arms close torni37o( w57p e9i5zfj raq+ j:fbcu v, his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular moment;vjvdew*h m(m+ * y.qf::dpleiyfd3)um.

  What arc length does the Earth t8be nsprl:8 2 vja* av5fiwgh)l3pu:(ravel in a three month period in its nearly circular orbit about the Sun wita) e8f silj(5bng3l 2up:*p8 r:avvw hh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock haj *h(uizgq32e )wdnl/s a length of 0.30 m. What distance does the tip of the second hand sweep through jqzwe u/ 3hlgi* n2()din 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivah rsf7e i2dtw f e/j(1+vah/a;lent to?

  A bicycle wheel rotates uniformly through 2.04 nazwz- c; v6g8,aluk revolutions in 4.0 s. What is the frequ ;,c aauzw486gvnkz l-ency of the wheel's rotation?

  A pulsar (a rotating neutronk -71qgpa-ivg star) emits pulses at a frequency of 0.40 kHz. The peri1-7vigq pka -god of its rotation is

  A phonograph record rotates al1 y+zvvg v1 c :rwnjn)epbd3)v20 bm1t 45 rpm. Through what angle does it turn in 0.20 :wbyg)l31 evj)2rdv1v+pv1 bzmc n0 ns?

  A wheel of diameter 26 cmv8/v1nsnpu /kuga x.(n- 8*m rdj:ksq turns at 1500 rpm. How far will a point on the outer rim //njx *knsvm8-8q sv1.p :a g(rkuudnmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t8 n1bjy8:gmvfhe average angular speed of the wvf: b8g 81jnmyheel?

  A bicycle wheel rotates uniformly throum y1g+ 0kfe8e5mehgt2gh 2.0 revolutions in 4.0 s. What is the linear speed85y e20ftmgmh 1 +ekeg of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of b+5r 6jz7:v lv(du ldh6.8 km. The cable which moves the car is driven by a pulley w7hl d (v+u:z6v5dljbr ith 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 speed of 2.t/(edek o) vlp-z(y8g0 rad/s. What is the linear speed of a point on the wheel's rim?ve-(tze dk8)y (gpl o/

  The cutting cord on a gas-powered weed cutter i v(/l*3vkzh*m. nm .wk qyhu+vaj,7k s:p id9us 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of m 9 .zuvlni k*uhk:/7+*pk vsjmdyvaq, w.(h3 the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/sveh5zcf435xm1eam 8 a . What is the centripetal acceleration of a point on vca3 zf545hme1a8xme the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyclex)o8c 0-me dj nr*wv5jv6c+ dz9,a oaa wheerjja)zxo80 ao,a d nmv- cv9*w5c6+de l of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mustl 6h9z, j.rb)zvd2pvt a circular, rotating space station (rrp6hlzbvd9 z. v2jt ,) = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circa69k :yqzyd /yular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided bka6y : dzyy/q9y 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 speed olyf8 stqnbk8t/ )eg r;mb/(9o f 20 m/s. The maximum centripetal force / k 9fy mgo tqnt;8(brs)be/8l(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 whirzh6j :e8elq3 xled 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 l:ehx j3z8q6e if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm re3cy0v .ek(lunm 3a-iolls without slipping 10 m down avn33-ye( ki ae l0.cum 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 acceleration of irk.ev0bt7u vi430 ;gl0* k mgncv)e n$4.5 rad/s^2$. 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 ro6 4q *spxtokc-4:fx/ rin +nacceleration 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 rov(g y gt 7v(g .j576yo-rgxfpvtate after starting from rest and accelerating at a constant angular accelgogy((6 5jv7 v -yp. t7fxgrgveration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration ofu(co41 wlz -r3-6 l.wr 8v prhyv:wrde $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rx,(-ln/cl bt2;e fdcw ad/s decelerates with a constant angular acceleratio;el l ,tbf c-d(/cw2nxn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularjaxovvipv h2,8q-m / ( speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelera8xojp iv - ,v2/hvam(qtion of the wheel?

  A wheel of diameter of 68.0 cm , 8/fzljj;( 4+;gnqt gtrexq hslows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions tg+,qzne rh f48jl;gx;jtt /(qhe wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest tw2g :9, m3orcd6 mcifover a dis icm,f9todmc2 w6 3:rgtance of 115 m. What is the angular acceleration?

  A wheel of diameter of 66hmcz1v4/rr 5a 9ja x z9jlm rc(*kw)dpe7+gs8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come tmdz ewc(v146rk xpls9jz m/7)5j*ca+ 9agrhro the stop?

  A centrifuge in a medical laboratory u,db/rewqj+1 rotates at a rotational speed of 3600 rev/min. When switched off, it rqd1b+uwer, j /otates 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 yaw:mdgr +kb-sjps:h;j ,f 14 a torque of 90 Nm. If a 30 cm long wrench is used, what4rhad j m,:sp:1-jgbywk+ s;f is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If h4q dy -:efepk8*u;t o( jq5mya 30 cm long wrench is used, what is the magnitude of the f4k 5f m*uyy(htp oqq8j;ee :-dorce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i3d7z5 af;i.b wdyjq/lnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is 6i80 gm hr,ite6i7pjtmodeled as follows: mass m is at the origin, mass 2m is at x = a,hj,6igei8t 6 7i0mp tr and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kgn p5;r/,roxdf8nzr mee-akb2n+ ,xs8 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 exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular accelee5rdbz; frer x+8 nan 8n sk2,p,/xo-mration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frih.5enju+ t.xcj 3wu* 74wtp vyctionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F.t*4 y.t5jucwne7j 3+pxhv wu1 = 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 hori rw/* *pyzz4ll/ 1i23zxz lmrjzontal position, and then iz23r*rj4wzyp*x lzl/ mz / 1lreleased 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 ak3w/h:9bp bj hs4 o6aond mass 1.5 kg. Neglect the hwh j6/o9p:a bkbs3 o4mass 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 achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mrv.jiw xmvb4c uk(3 /*ass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thbj4w(3 iv u/xm .vckr*e pulley?

  A 1.53-kg mass hangs on a roppb361e*s,c du8 k cdnce wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is th18pd n6s*cc3de,cbuk e acceleration of the mass?

  A rotating flywheel can be used to store energy. If itz.zb x5kx ee+sl gm*b+f* 7/cr l kt202otkp*s 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 of y tv) wiytymn-g.g;v/-q1kj/ $5.00 \; kgm^{2}$ 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 startsd)5a+. v wyanih.0kml from rest and rolls without slipping down a 1.0-m+d)am .k. ali ny0w5hv 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 o)2+,skm czke speed of 10 m/s. How high up an inclined plane can it climb before coming to rest?mce,+ kk2)szo

  A hoop of radius 0.50 m and a mass of 0.20 kg is rele a:jgyphhvtuj5+x4 zil:*n 0 5ased from rest and allowed to roll xu 5a+pv0 t:jh*z 54inljyh:g down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm r 2v hyw+zp)so3olls without slipping down a 35e incline that is 7.0 m long. Assume it started from reywohz) 3s p2v+st. 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 changes byi eu..gpg*,xny6 c m)h $20 \; kgm^{2}/s$ 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 inert7q6nk w -nh01mm:i,ku o(irdbia 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 rag/11r:j2zuwb) w yo ,q0opa dbd/s with arms extended has a moment of inertia ofgbo0ju / r)1o1qyz wdwb p:,2a
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?