Angular displacement is usually express in u c c8yv+t,cnw)nits of

  Angular velocity is expressed in x,0)jxohs8o -c lcre,j3ny5 c units of

  Angular acceleration is expres axr32 b 8n htna.wv(op/+pp+vsed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a consta,/ j y2b7gd:xmluzm c0nt rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulc72g /xm djul,zb0m :yar displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a consta,dpl1cy xf.2vnt rate. The boy is near the outer edg2fc yv,x1ld.p e, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding ob03 glkki mxr5-i)ov7 n a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girv )r-307 i5mik xlgbkol is closer to the center. Who has the greater linear speed?

  A boy and a girl are r i;w/npma3d7 zhav* i/iding 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 has the greater diwnm7 /3i; h*vzaap/centripetal acceleration?

  A boy and a girl are d 0tqaoe3:b kbx /et+/fq:zxao5 xf0w+m9xw + riding a merry-go-round which is turning at a constant rate. The boy ik0x 5x0 +w+w3:b/a qfatzd x+:ebeq /oxt9o fms near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotati)xfh .w: sg .s-y :zkse.5vcko2pt2 lwng. Which of the following is an accurate stateme: 2ss x:yc )sz..pewl g-2o5k wkh.fvtnt?

  Rolling without slippin0 th :lhe:bn eg5hdr8aoy,n3.g depends on

  Two equal forces are applied to a door. The first force is applied atb2 (p do 5fty-cp+ti1u the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque5ud b(i-f+pop2 ytt 1c?

  Two equal forces are applied to a door at the doorknob. Thwr9b:gz 7y7jae first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exr 7w97:bygazj erts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fl*2 a f hjvrhc(q0;y-rirst force is twice as large as the second force. The ratio of the torque of the ylfv-hh ;*rqa c 0r(2jfirst to the torque of the second is

  What is the quantity used to izu n lm (jza784sbq+3measure an object's resistance to changes in rotation?i(83zbz+luq4a7sjn m

  Consider two uniform solid spheres where both have the same diameterw.34vvwi lok0, but one has twice the mass of the3vkwlo 4v. w0i other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the 7o8, uhb2sa93hezly k same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to 2loeh,7 szu 3h9ya8kbthat of the smaller sphere is

  Consider two uniform solid sll,+hc yjd7 +opheres where one has twice the mass and twice the diameter of the other. The ratio of the lalcy ,+dh7 jol+rger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M andqouhkwb 8a 71/xh;x mqolj.wq xw )*25 radius R. If these are increased to 2M and 3R, what happens to the sphere's mmxajx5w7qwb/ h2q 8ou w; qlh ok.)1x*oment of inertia about a central axis?

  If a constant net torque is applied to an object, z/2p6( o5( h+r xuzxspvoe-butq9p1cthat object will

  The moment of inertia of a solid cylinder about itssz ig+y;h8 i gmy/un;( axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its n (h /gy;uy ;zi8igs+mtranslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which ha4s e (j8c6fj-7 echvtgs a mass of 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 wheels aret(786 ve-hgj fsecj c4 uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping zbd 8wbu v8k6/t8 njc*down an inclined plane starting from rest. The linear ve8/znu86bc8d j*v kbtw locity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mm2 tjg/qxd5greoe 6b1qd :6, hass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom o1od5 egx6 m/d:trbh,jqe 2 6gqf the incline depends on

  "The total angular momentum of a system of par8llm0en d1w a:r9*get d vhq*,ticles changes when a net external force acts on the system." Te l d**wtg:eh a0vr9dmnq1l,8 his statement is

  In what circumstances can the angular velocity of system of particles8(arozj ocp/k o8jj2* s82q qb change without any change in the system'sp*z8/cs8koqo2bj8( 2raq jjo angular momentum?

  The Earth orbits the Sun in aeqs5n f6mlq2:, eml24ht0bs pn elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth' 5e2 0nssplhm2 qem64lbqt, :fs angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As hhl;3(afq w (i,jk4 evbwa-i d y)2y.u h*y-fothe Earth moves close to t f,lhia)yyh3fo4. ;(qdev buw-2jwah ( -*i kyhe Sun, then which 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 outstretched ci 8(t6dt5m*vh5fbn y arms close to his body. What happens to his a c5y(tnb 85tih6dm*v fngular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spinz *s 6sgqb696pwzhz9v) by pulling in his outstretched arms close to his body. zpbws 6g6hz zq9v96*s What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirol -o*lixkkn50bk8/ bab.6x qkawe33 cuette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment ex/kblkna*6wcq ai83k 5kbb30- x .loof inertia about the axis of rotation?

State the law of cons iv:.5vt zo/i ;xivbo8ervation of angular momentum.

  What arc length does th+ px;0 qeobdg6e Earth travel in a three month period in its nearly circular orbit ab0 gobd e+xq;p6out the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has 4-wtv:k)per7y v3lh ya length of 0.30 m. What distance does the tip of)4lryv wvyk3 :e-p 7ht the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 r;z woa8 c;5s1oz 2ydsyevolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whaq(pp .6i ;ba40+mgxy0 dxhbsut is the frequency of the w0spxh 6agbd. u;p 4imbx(+qy0heel's rotation?

  A pulsar (a rotating neutron star) emigc10r tnh o(sy4wk8u3ts pulses at a frequency of 0.40 kHz. The period of its rotations 4c3th(og0unr 1ywk8 is

  A phonograph record rotates at 45 rpm. Through w0e*j6,/o(6 ka u kelln b4kdhehat angle does it turn in 0.20 sl ede( 6,0 le*b kh6/nua4jokk?

  A wheel of diameter 26 cm turns at 1500 rb 80x2gno7hpl2ckh 0y pm. How far will a point on the outer rip gk8yxc7 nohl0h022 bm move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W4nmoa8 it(m )e;pxc 3lx(u1y3sizutxl cl 504hat is the average angular speed of the wheeuteau480 sm(p(ncmz4 xyl1xl3;iixol5 3t c)l?

  A bicycle wheel rotateshthev un.()p ( uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 )t.e(phh uv(nm from the center of the wheel?

  A cable car at a ski resort carries s (pq)bfbq 03 tk gbucwf-ss)7/kiers 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 )/kfbsug wt7 cb-(3pqbqfs0)the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a7hghm z d4x,6 w3 7xcqwmpa:8v constant angular speed of 2.0 rad/s. What is the linear speed of a poqdx 78 hcgm: vxap3 7z4w,hmw6int on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in len6pwy-3c em2 ehgth. If the motor rotates at the rate of 20 rev/s, what is the approximate ly mce6ephw- 32inear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/sr6x4df 1y mznpqzjd 4/6o/s7) nls t+w. What is the centripetal acceleration of a point oyzmslz/ q rt dfso)p 1+n/ 646wnjd7x4n the wheel's rim?

  What is the centripetal acceleration of a poinbqhibv-6 )dc*qzq53kj7 e* k ct on the perimeter of a bicycle wheel hij)*b qd*53 ekzbq7-vqckc6of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mrl;nq)m * 6ljkust a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity mrl6q;) lnk *jof $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve+l**ocq:yo/r2vti b u of radius 50 m with a speed of 20 m/s. The oct+o 2vbl:/qyu**ri maximum 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 fr. i xdg))cjo)lat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stat) gd xjo)rc.i)ic 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 w( 2y tm)qcv2;. o5s)sudgni hbhirled around in a smooth level table. If the maximum tension that the string can with.(isbtc5 )2)u2o nmvg; h qdsystand 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 kg4 w is1pyzds-4 and radius 9.0 cm rolls without slipping 10 m down a lapsws4 ziy-14d 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 consta4x5oo; m gn/iant 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 acc.p5q9(c(+g9qdmu i*3 :g cew bwywobkeleration 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 aj4yxjo5+jx 9;w kgz rl:a+0 wgx5kn1n fter starting froko gwjlnxnw x1j54j9xak+y5 g r0z:+; m rest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an anguw)6yw+j fpm4 vpi-(wrlar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratesjvl3 n3t0(6* fc yvugsr+i sv3 with a constant angular acceleratiov vt( nj*+r3gl0 3ucsfiyv s63n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and req.zk4is0 p9(rr c 1xy)c3yvipaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the ave 3v49(sy0i izr c )xqyc1pkpr.rage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o*z;pl7a4 u bsfywrw04 ver a distance of 115 m. What is the total number of revolutions the wheel rotates in ar*;yu z0bpl 7f44sw wcoming to rest?

  A wheel of diameter of 68.0 cm slows down uniformlyuo hdre63:wx; from 8.40 m/s to rest over a:e;3w6 hxrdu o distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slos9 qx*lil.1o8h)go ygws down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it t)i*lso9l o.g1 8 qxghyake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3hg9e9,t t zf57 dfni1 i4h4qzk600 rev/min. When switched off, it rotates 50.0 times at a constant anguliihz4qgz nf1 9 ,k f74htd5e9tar 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 torque of 90 Nm. If a 30 cm l5fie1pk;s. pac1wztfi+dy*8n 6t l(aong wrench is usedk;d8n ltft6+epfp1 is1*.c y5 (aziwa, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel r s*p hr3jh4o)kequire 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 force arj*3 4ho)hpsk pplied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner+ :x. (jp*qoyz3acm ag/ejpx 2tia $3.00 \; kgm^{2}$ 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 obo3 +a8mtb)og znlnhu -6:u7c rigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia aboo8- +hmtb7ula unb 3nzc): o6gut the origin?

  A solid cylinder of mass 10 kg is p,iypu :e*wtpulxp 5uf.1yk qv,0* ph0ivoted 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 acceleration of the cylinder?:w,p0puvh * xut1 py*50 ,le .pqikfuy

  A solid cylinder of mass 10 kg is pivoted about a friction- t,l8y xzo5moless 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 inlzmyt- , o85xo 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 h01jcbv gwa:;p+8 e2xrt6r(0xw oml zqvvw -8xorizontal position, and then released as the free end is allowed to fall. What is the angular accelerationzj q0ltvgxm ;0xr-p6cvab8we( 2x wwo:v 8r 1+ 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 1.*k 5 b 9pcfvpne94nf;oop.3g x5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is pvonfbogx9 3.pp fk59 4e;*cnapplied 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 wrapped6xt o8k y+3neg around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thenxkego +38t y6 pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlyxrhkz 1p, i.iyl.-t0mhs):fess disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass1:ip y)l .it0rz .skhhmf,y-x?

  A rotating flywheel can be used to store energy. If)lwb irk2pfv (1xrjz 13l6 tp1 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 of r+5tt 0ky.crf*glzk*p7u(w r $5.00 \; kgm^{2}$ 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 kg9o8li4r iesis/hu t b:guy 3)3 and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed i)hiu/usoryt38 4sl ibg93 :eof the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolln7hg fhlgu9+z 0.a 4sus with a speed of 10 m/s. How high up an inclined plane can it climb beff.g0s za ul47hg 9unh+ore coming to rest?

  A hoop of radius 0.50 m and a mass oihl1iqr)gfx* b +n 8uddr:, 5numw5 e3f 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it movin5 d+df15:qn* )g u, 8bhxw3elurminr ig after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 1axux qzaie(xu(*x a5o)k9d, ,3ds/ zk5 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it sa 5xxko9uad az( ,3exz*k(/xs q ui,d)tarted 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 changes b*pj uu;etr u6vh:61b ty $20 \; kgm^{2}/s$ 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 oimgcl e5w1ze 7r41m+ gf 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 at63ivp p yp:7kf5: ytn3htypo7 5.00 rad/s with arms extended has a moment of inerti ot3hyppintp6:v7k7f 5:p yy3a 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?