Angular displacementchi9 (fs;k.og5 7zyy-6j lh ui is usually express in units of

  Angular velocity is expressed in units o pv*q00 ia.gmqqq7jjhn4(g w(f

  Angular acceleration is expressed in uo6e7oq11b0 wfzmk9eonits of

  A boy and a girl are riding on a merry-go-u:iy,- p8reye lbxz2(cuio2 2round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wy-co2 e( ,rl2ixye2 izp :ub8uho has the greater angular displacement?

  A boy and a girl are ridiy6+. z5.7tbn+rqnksw thc 7vnng on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is cw . 57yrbtnk +6+7qhs. vntzncloser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry- n4vo9 gmd2 mq6o+:lgfgo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. o4l:dmv fng+ g26omq9 Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constaqx8da/.elx l8voj/ j+ nt rate. The boy is near the outer edge, while the girl is clo oajjlx x./d8q8/+ levser 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 ra /ygg3 uhbk4:ete. The boy is near the outer edge, while the girl is closer to the c3bygeu /gk4:henter. Who has the greater tangential acceleration?

  Consider a rigid body that is rotaki/vwk y ;pcqt1h/b9 nhs31t)ting. Which of the following is an accurate statemetih c191v /k;n/s3tyhqwb )kp nt?

  Rolling without slipping x:rrr +,jw sex(, sbs:gl6f1bn2zq(d depends on

  Two equal forces are applied to a door. The first force is applied aeb f.t/g r: j5qbm6j5tt the midpoint of the door; the second force is applied at the doorknob. 5bjtj5/6bqg frtm :e. 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 g56 h45ufpbpx. The first force is applied perpendicular to the 5p 5 fx6uh4bgpdoor; 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 firem3)r abnf +;xst force is twice as large as the second force. The ratio of the torque of the first to the toxbfn+m ar ;3e)rque of the second is

  What is the quantity used to measure an object's resistance to chanuu 03j s;4xozu*yc 9tnges in rotation9ocu*j xus ;z4nyu30t ?

  Consider two uniform solid spheres where both have the sam9dvcw5ndf0x9 svz** re diameter, but one has twice the mass of the other. The ratio of the larger dcd*zn *vf90s5xr w9v moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the(ic) 1hl, rzcwa22n is radius of the other. The ratio of the larger sphere's momentzi i2rw c2)cn(1ha l,s of inertia to that of the smaller sphere is

  Consider two uniform solid s1 )l/c-.dvd 7yu tcmbppheres where one has twice the mass and twice the diameter of the other. T1up-vl 7.b tm cc/yd)dhe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mvgmmtk:nk).8 ass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centralm tv k)mkg:8n. axis?

  If a constant net torque is applied to an object, that object willasp; g05ks/ ep

  The moment of inertia of a solid cyc0mvk15fc7n o 9h div/linder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150:jh cq4+kea0: jnq.ya rse;d 2 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What ids.qja2e : j kah0ce+yqrn;:4s 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 Mn0, isxcj yl6(ln2ll ;m g;*wo and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depe(g,yico2; nj;* 6ms0 wllnxl lnds on

  Suppose a solid sphere of mzfko)u/lb0ow*77e fj9b( yf eass M and radius R rolls without slipping down an inclined plane starting from rest. The angular ez oju90)e7(fb/kwyo f7f*l bvelocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net e+ffifc(ow865hiaydv 3:e5k bxternal aoi i8fdf+ 3e k5c(fby6h:w5v force acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles change wit)iz(fog 1oy1 h jkb/:zhout any change in the system's angular momentb/(zkg: 1 y iofj1ho)zum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which maxdc+e5;epmw -hw/jf :y be present. What happens over time to the Earth's angular x jpe-m/ +wh;ce5fwd:momentum about the Sun?

  The Earth moves about the Sunhh- pir)eip d,h) :e8bxka)y / in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Eartay8,b ee-h k)h )xir:d)pp /hih about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling ihf.y5dwj);,: pj yjst n his outstretched arms close to his body. What happens to his angular momentum about the axis of rotati.wyj, jyd 5tj hpf;):son?

  An ice skater performs a pir d2fk(c:pxnb(ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic e dx(kf(:pb c2nnergy about the axis of rotation?

  An ice skater performs a pida ,rmi55*vkf rouette (a fast spin) by pulling in his outstretched arms close to d ik 5*vfa,rm5his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservatibwi /nq m3-ve*q v15qdon of angular momentum.

  What arc length does the Earth travel in a three month period in its neartk1 /khxun1.i920daxflc1 g dly circular orbit about the Sun with a 1nlxk 2 at/fuhd.xikd c1g109 radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thw37z 9c*me ;ty.hla79 9ujurzzc qh)j e tip of the second hand sweep 7h*ryt 3m 99caj;)zcwjuue.l9q7h zzthrough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pvubc e 8a0(b.ier minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions ) ca+l:zyjo4w6e wf(cin 4.0 s. What is the freqa 4:(wo 6cjy+wce)fzluency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits p(pcq,9c,2gfjb 6a cen0t nn/qulses at a frequency of 0.40 kHz. The period of its rotation isq0pc62neqcjn ,, g ba(t/9cfn

  A phonograph record rota .k j d0y.webe,f/u2e(yxb 1voem3r:ites at 45 rpm. Through what angle does it turn in 0.20 s (eboy1bk03um, 2d.w y:ie.fexj/rev ?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point o08k 5uk2k dqd./ kx /dl7rzmxvn the outer rim move in 2.x8u5.kzk kdm xrld0v2k7q //d 1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in (mehk /tfeku 6 ,0-n;n,hmq(j1j upxj 4.0 s. What is the average angular speed of texnu(-/ uj heh f j(,nmpk6;q,m0j tk1he wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whu(l ab 8)1+dznoaqdp7at is the linear speed of a)dzl1 on+ b 78aqa(upd point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 pq-5fw( jpo a957pjla z6u 9olab +i4hkm. The cable which moves the car is driven by a pulley with diameterla(olp j9f455aqw z b+6jpuoi 7 -pa9h 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 an 7gzfv* ,vjogz .nf;y.gular speed of 2.0 rad/s. What is the linear speed of a point on th7fv*fgvznjy .z,;. oge wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If i tc80 4 8ruua0me* ;kjygw3lzthe motor rotates at the rate of 20 rev/s, what is the approx8i gz;0jle *k40wuutm 3rca 8yimate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rom -7zdi79go lj6t9hm qtating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'sm7j9q- toli d 7m6g9hz rim?

  What is the centripetal acceleration of a point on the perimeter of *bi rchb65z wezx(6a) a bicycle wheel of diameter 70.0 cm when the bike is m5(bza h b6*ei)xw cr6zoving 8.00 m/s?

  How many revolutions k() oj+u5xd)xlo(zc pper minute (rpm) must a circular, rotating space station (r = 100)zu5 okodcl) x(jpx+( 0 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circ-kg .0 3kqre ys/x;yynular curve of radius 50 m with a speed of 20 m/s. The maximum ceny.nq; gr xs-yk0ey/k3tripetal 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 9z2.vg/vkm 8 mq:u mudflat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (providemq9mvkzg2um ud8 :./vd 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 in a4i wdg,(v oli3 smooth level table. If tw l4 3gov,di(ihe 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 radius 9.0:6rjx2ovgg2wdkz l -g 0 c-bt-mzi7 4x cm rolls without slipping 10 m down a la7-dig-rl x 24vg2k-zmb gw6cz:xj0ot 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 witrq1/c 0knva,ayf u99 4- ops.ipy9dxxh a constant 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 accelervulv9ff6 l2 5fation 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 ro8;f a4mnau iu(tate after starting from rest and acceleratinu84 ;(niamf uag 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 angular accel37w (,r.qfroo/ e d0ohdf5oi,k t /brteration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angulxsevuea 0k0s7 * ;b;wupsw;0d ar accelerati ;s xu;we0*bwvu7sp0e k0 sda;on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches)mp. es 7n:gdp m4jq*bc6:e ic an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accel 6:c:) 4ibpc.pmdne*sq7ge jmeration of the wheel?

  A wheel of diameter of 68.0 cm slowe2l q4+ck-(d0saauo a+g7ff es down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number oea4fa a0-7sg f(odcuq++2 le kf 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 reskimi4yg 7so6zy7: *-e e5ddp*xpl,n p t over a distance of 115 m. What is the angular acceleration?e :zpy ,e*46-md7iy o*s idk pp5lgn7x

  A wheel of diameter of 68.0 cm slklf+o pcy-6fv- izy-k2 t y4i0ows 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 to the stop?i z+yp2kot-k v6icf4y -0-fly

  A centrifuge in a medical laboratory rotzln z4n *n sz:/ 65r3kwv6f3b8ru zoaoates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befornno4k :6vrs 5/z6zfozzr3a 83ul*nb we 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 requih, x. +w2cp fuoboj*u2re tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of +cou bux2jw,po2.*fh the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tigh)z8 sxsn+sw4sf6)z r)f5id h0 sjd7 rctening 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 applied at dhd)z60z)c xf7sfr sss n4w8 r)5+sij$53^{\circ}$ to the wrench?

  A wheel with moment of inertizgzm55y t1j pc77tq kmsgok2u 3,ip+1a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as f bz:g i jn3fg.9;riuf+jk*fdlz1 1k3sollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of ines j u+if .19jgdkflg*3irzn ;3bk:f1zrtia about the origin?

  A solid cylinder of mass 10 kg i buy,/wwjyl,7b b. e ia*zl(6ur..f oks pivoted about a frictionless axis thought the center O. A rope wrapped aj l,el.wb6(*bfuy,z.rko. wbi7 /ua yround the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionlesdd w4m;zs40voae91;t de5s nys axis thought the center O. A rope wrsd1w4; osdy dt nv 09mez;4e5aapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 rfgwjq.zj 55wugj* i5;od is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratijf;gwzjj 5u*q iw55.gon 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-qt9 gbvo34 gd x9gc+h 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 speed does the wheel aoggdb- 49h tqc9 gvx+3chieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulle: h/ *8wmgt6pvu qm*q6c bmu +ht,j9nzy of mass 7.07 kg and radius 66.0 cm. What is the angul zc:q6m/*96 8uwg+pjmtq*ht,nvbhu mar acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arounw inm-w0ez5o2 qmha 47d a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass 5wiaqze-ow2n4mm70h ?

  A rotating flywheel can be used to store energy. If it is reqi-e, l1 0gw-ijflhhws.5 rc c5uired 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 inere+f)t:. nvrxp 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 rolloq(ryw m11ji82lj:ou vrp; m9s without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the botto1umri ( m8lwj9yqj:21v r op;om of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m roll)ga xul6gv:x, s with a speed of 10 m/s. How high up an inclined planealxx:vg6g) u, can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and al ek;)aj/z.lg9jc1c1t /xf i:eys( yqdlowed to roll down an inclined plane. How fast is it moving after droppij kxzq)/y91dg e jye:;./ilct fs1c(ang a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down r dibpj3 )*1)vxlde,t2f w(hca 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a s*r)3d vx j2dc 1lf,p)(thiwbephere 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 chai:1 uz()fq4en lsh:y it3k6frnges 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 moment of inertiarp+i) rgb 3m7f 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 v/eu;ij)h3z (eqkd c*of inertia ( c ek)d3uhj /;iq*zveof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?