Angular displacement is usually exf8s f.3 7*lysmgtv*a epress in units of

  Angular velocity is expr( w ,/ )-ggmg nn0-xzhlydu(pressed in units of

  Angular acceleration is5 hbw:iot bi8 i3w0+wenea* s9 expressed in units of

  A boy and a girl are riding on a merry-go-round whicjl :aztuqv4 5/kne :1kh is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenq evl5:jkk1:un4/aztter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a const vlzlm+8 +wnv;ant r v+8 zwmnlv;+late. The boy is near 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 merry-go-roundea -l,e-m53 n*lxsuf d which is turning at a constant rate. The boy is near the ou3s- un*fxma,l -eld5 eter edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merrytmuc 22y0n zvclw6d( 9-go-round which is turning at a constant rate. The boy9 lcv 20 tdu(c6wnmzy2 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 constant ratejpbh37yb;da95xv 8 hq. Thevbqa9x 75b8;jd 3p yhh boy is near 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 the7nnhb4b* 1;jky/ tnug following is an accurate st1 jnthbn/ugn4b*y 7 k;atement?

  Rolling without slipping dependrf,h p+ l,r qa2t;l;sus on

  Two equal forces are applied to a door. The first force is applied at the midpw jasykz z//28okj8w2s//z y zaint of the 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. The first force is +a65 v8af9 h fp74nm vwaq8haxapplied perpendicular to the d nv4+78hw hmvqaf 5x faa69ap8oor; 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 door. The fyg pv vpn8x+npg,,+m( irst force isppy+8vn,(pgnm + ,gx v twice as large 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 chan1r18su0 btdh;7p jw grges in rotationrb udt hwrp8 sj;g0711?

  Consider two uniform solid spheres where both have the same diameter, but one had r 3( t-kvn1;uvs hii)il(ey8s twice the mas) u(v1yd-leni8h;r3s k v ti(is of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twi/gili8 +1*ufja0g1tkz mmeu. ce the radius of the other. The ratio of the larger sphere's moment of inertia to that of i zg0u.1jafk*8t/ mge um il+1the smaller sphere is

  Consider two uniform solid spheres where one has t ,y -lj4u*fx)+sxl2a 5uz6+dsfdfw f rwice the mass and twice the diameter *w+,56lfaldxz dx4j f-u2s+f) uyfs rof the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass-y0 n l1wir 4bwn;ic6c M and radius R. If these are increased to 2M and 3R, what happens to ty4n rn- i0;lcwb1wi6c he sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wiljr ue/e3*h f 9: ovs--eu3,wd 6nwxhocl

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. jo,; qsby t8d;vu vm12If this cylinder rolls without slipping, the ratio of its rotational kinetic energy toj1os v,uqyvbm td28 ;; its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass ofacn1,b0nm/x4 2nbqzwgqy3 sprc 97 (d 10 kg and 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 y(,c s/w7b d2mgznn01xcbrna3pq9 q4wheels are uniform disks.

  Suppose a solid sphere of masg20e;mmj(nw ol 4 ,jsmy)kx (ss M and radius R rolls without slipping down an inclined plane starting from rest. The linear vk4)ln;j 0gwm(sy (jm ,s em2xoelocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M a u;xpxlryj5g i b:d.x ygi tex7/104.lnd radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the y.utgx7x0 ; /rebd g5l.1xp:iyxl ij4 bottom of the incline depends on

  "The total angular momentum of a system of particles chanxp:6nkrpeq 4 7ges when a net external fknrx 4 ppeq:76orce acts on the system." This statement is

  In what circumstances can the angular velocity b7z d bg pp3all2 ,geo82r,lz3of system of particles change without any change in the system's angular momentumdg,pbl3 7la 2,32eolb8gzp rz?

  The Earth orbits the Sun in an elliptical orbit. Ignore any :7vn xqvjg kb*( 7i:fzfriction which may be present. What hapgv (zknbiq 7xv j:7f*:pens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orea3sl0zh qf,wuac x gltb.;9;d,u 83a bit. As the Earth moves close to the Sun, then which 8,la dzx9lu;.3t , wcba;ea0q u3hgsf of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche as(1rn+rnh fexb;-*qd arms close to his body. What happens to his angular m(sxnn*r1-;qaber+ fh omentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin v 1dhro l+a,xy2ds8x3l: -auwg in his outstretched arms close to his body. What haavyl-3a8 + :dldsr12 uxowh,xppens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) bylh7+ llrwz81m/2pi /q m1nkek pulling in his outstretched arms close to his body. What happens tolm7rel//plh +wn18imz1k2 kq his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum4p)3myr*kk8o25qx) ndo ru uo.

  What arc length does the Earth travel in a three month period in its nearlln:f -mhyl1 g-,e yrh9y circular orbit aryh -e:n1, lh9myfg- lbout 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. .-ufngchb gyps16;j3 What distance does the tip of the second hand sg.c6b;-1j gfn3pyu h sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute)s1f..-cxym ro mq2pt equivalent to?

  A bicycle wheel rotates npig9rgy,6dnv: 0)zkuniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel':rdz)g, 6gi0kn9vpy ns rotation?

  A pulsar (a rotating neutronwer.b + 1uyp)y star) emits pulses at a frequency of 0.40 kHz. The pe. py1) uy+rwberiod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle 5mx q)p+6 v bkk0.b)5 wtilwizdoes it turn in 0.20 6qmw.l kz0b)wxvi t5b)i+5pks?

  A wheel of diameter 26 cm turns at 150b//h *xaag a4g0 rpm. How far will a point on the outer rigxb a* 4ghaa//m move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 muey ihsc21;h6rsd5 +s. What is the avecims 6sy er+ud 2;hh15rage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolz)e79it-oke0 y meq,vsbk4gz- xr48 vutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of 4)sv0 t be8-i eoer4k-9kmz,vgx 7qyz the wheel?

  A cable car at a ski resort carries skiers a dista1 )uumy5mlgjr8a w10dnce of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, u50m8)wyl1mg1d r j uahow 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 2r;)b) 7go -mb+ioyuke 9o-kj r.0 rad/s. What is the linear smu7y)9k )e kr-jo;-bg oir +obpeed of a point on the wheel's rim?

  The cutting cord on a ofp0rrsas55 018s 3r4yqok bsgas-powered weed cutter is 0.16 m in length. If the motor rota br5 s k3oqfys1s805r0aspr4o tes 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 constant anub;f,use,6h+ m)tx iid8 duj-gular speed of 2.0 rad/s. What is the centr8j )mtu6-feb i,dd h;i,xsu+uipetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicy, sjkh +hgwu/+cle wheel of diameter 70.0 cm when the bi+sujg+h ,w/hk ke is moving 8.00 m/s?

  How many revolutions per minute (rpm) must nyend- py1n4,yg 3 cw)a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity o1py-y)nwg3y en ,n4c df $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of rija7 s*hq+u it+7 ,xodh+d(x20 m/s. The maximumddsh *roia+jh(x77iq+u xt ,+ 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 flate-i)gq1ihag b:b b;:p circular curve of radius 50 m with a speed of 20 m/s.;a p) ::eghbq1bbii- g The maximum centripetal 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 8 ue*lu)6ym ;y -syxbeof a 0.750-m string, is whirled around in a smooth levsuey- ;e8l yym6*xu) bel table. If the maximum 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 radlpoz+mu38 (gu8dm6x zr 2u,n bius 9.0 cm rolls without slipping 10 m down8lg8 xmr o3uubmu ,+dznz(6p2 a 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 constap bx /yve3s8g uo.j4i (4dew5qvu sy4+vhbe13nt 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 accyw hwg84 qc-7 vsw+u,keleration 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 doesp 5z,qi;gl.lv6z a qd4 a 0.300-m radius automobile tire rotate after starting from rest and acceleratazq ,gz lld6 .4pvqi;5ing at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, andsevm09 fljt, ji fqv 4l)/*o)d has an 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 deceleraz2c :53xvceh7+fiwy ates with a constant angular accelerati3cfy vehc:i5 72wazx +on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from resvkz ) nfiwxt2 s84 w)(1rcebml/t o6q-t and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular -bm /n six k2ltv8( owq6c14)z)rfwet acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows downid( d)t , -*ur.tvcx lkc,hzy.+zwhs5 uniformly from 8.40 m/s to rest over a distance of 115 m. What is tk.x,sulitr +.v yc)wd d5hzz-c *(h t,he total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over4lw-7l:emkm r;z6: betryw 1m a distance of 115 m. What is twl7 -r z ym:6:rewm1lk m;bt4ehe angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over 2hj 9yerpci( a198lxm a distance of 115 m. How long does it take for the wheel to9x (m h1lj e9p8acy2ri come to the stop?

  A centrifuge in a medical laboratohph8 ump0306hro q9dqry rotates at a rotational speed of 3600 rev/min. When switched 6 0pq9 hdhro0p8uqmh3 off, it rotates 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 tig) e c45x0itcci;t (lathdyzdvj3z/. 6htening 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 petdv(it zt 0 iy5/)x6hl ce;c3jcad.4zrpendicular to the wrench?

  The bolts on a car wheel require tightening ts4hxzi/db, *t : og)iio a torque of 90 Nm. If a 30 cm long wrench is used, ,)ibigd*t:hz /osx4 iwhat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia x:l3m-czqta-)d21j l+afo kg $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule ipujyj g,y+ym4 jw/j 4/s modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about jj+g,jwpy yj /4 y/um4the origin?

  A solid cylinder of ma + fel/wt:agtkeh.(d 9ss 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:.te (lef +9wth/g akd 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 the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless m.b4xtmj v9-raxis thought the cexv4t br9-mj.mnter 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 the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The-e9x p2 nugww;*k6xkk rod is initially held in the horizontal position, and then released as the free end is allowed to fallxww gxuk;k-*92ekn p 6. 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 mass * v4n gblqi8x24:wvtc1.5 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 doeswc2q *4nv8 it4lgxbv: the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs ohu wx j fr.6m)j 1,x/bc/+lkuzn a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the ubu/)zr, h6m. jxkc/lfw+j 1xangular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope olxdio-)e1 q7d) nlj2 d/qlh,wrapped around a frictionless disk pulley of mass )lhjoxqo) nel2q1i-d/l,d7d7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to s po9;urb1w eez op;e67:34nwakbdiw1 tore $1.00 \times 10^{6} \; J$ 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 qtfv */m erfmd6z( k6av5j2j: u,djt5 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 and radius 0.010 m starts from rest and rolls pgd w*lj),/i owithout slipping down a 1.0-m high inclined plane. What is the speoj, /)g*lwp died 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 wit8 hl o1m rict(.d)bu:ch a speed of 10 m/s. How high up an inclined plane can it climb before coming to u lo8 trb(:i .dch)1cmrest?

  A hoop of radius 0.50 m and a mass of 0.2 4knv/is06ds1 lb -pgooar2q7 0 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping r2s -als /g 1opi0 7d46qvknoba vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rov8e0(j /u2hqd ujef:z 7i4fyrlls without slipping down a 35e incline that is 7.0 m long. Assuhqj40d7 z u8fvyieue/2 r: j(fme 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 moment wjir55aztr o15m )de7um 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 m8p1m kw;0z cjg),h 7g*wmjxwkoment 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 moment ofs xt67wf9m6s86(tx2mdcl kx w inertit8f6(smxwc 2xw 66s7tdmk 9x la 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?