Angular displacement is usually express in u*as;i 3,fy)jovc cp-k*vyvm 9nits of

  Angular velocity is expressed in units oqu0e9sdhb)8 nwko.s0f

  Angular acceleration is exprgz 9n 0enhf:n+t ejp5*essed in units of

  A boy and a girl are rid3 y4eoq68t lfaing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who fy8 4tqol6 e3ahas the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constank,wr+sd4kbgq1 o )sb7 t rate. The boy is near the outer edge, and the g d)bsrob,g sqk+1wk47irl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridi,z,fb8q5ups by +r uc()ki gq*ng on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who hac5r * ,qubpig(+by8kfz, qus) s the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratltf1ak n(t2 3ge. The boy is near the outer edge, while the girl is c(gt1tk3f2 alnloser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which iq. j ,jz. lkgdk7ru:uhf;/ r7ts turning at a constant rate. The boy is near the outer edge, while the : zjru.;k7 j gf rtl.qk,7/duhgirl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is 3afwf68iqz )s rotating. Which of the following is an accurate statement?i6a3f)8qf zws

  Rolling without slipping depe t8cvkwpqc3hd(l7,.c, x ig/ ypk-tl1nds on

  Two equal forces arew ppw )9jj4btz*( -ifz applied to a door. The first force is applied at the midpoint ofipw9p b *zjwt(jzf-)4 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 fir// 5jq;48 sbi:y pfmlik1y xdqst force is applied perpdxb1py4 siiqq ykfm8/l :5j/;endicular to the 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, j7rr- . 0b:p*fyota pdd+;jszm7 l2k fperpendicular to the door. The first force is twice as large as the second force. Thftfr.sb*2d ;rlp: -7zmjpd j0a y+o k7e 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 changes in ;d lr1d-p:tah rotatiol; 1atdr: d-hpn?

  Consider two uniform solid s1 jc vst*p 1jp(1 f2oz,yguta;2dq)z upheres where both have the same diameter, but one has twice tzqt ,pv2pfu;(2u* dg 1o cy1as1t )jjzhe mass 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 mzbnp wh 4knr5j9rl) 24m86h y *kvr gh48kdj8has twice the radius of the other. The ratio of the larger 64vjl hjhr *pgk8 5y82m4k9hk n4zd nbmr)w8r sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sp/ xtbefanlns na;*,tn26 dx(4 heres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that onean n x(b/nf dax,6s l24tt*;f the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R.9xy.ihvqzg3 eg1t15a; mv *dy If these are increased to 2M and 3R, what9mv5 1qa;1 e*vi. gyh dgytxz3 happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that ofx,*y vb7wb0 jbject will

  The moment of inertia of a so tw+ /;fo9v8 yki)w- vtxb7ymdlid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, th mtkv;ytby-fow +wix d9)v87/ e ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass(k-xz m6*.6q-yjlfw:w. yst uj/jpss 150 kg, one wheel of which has a mass of 10 kg and a rax. p.ys m -:6qjl6s fwkwst-zjujy (/*dius 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 slipping1/39lg- wey n1jcltz g down an inclined plane starting from rest. The linear velocity of the sphere acg z-t931 nylg wej1/lt the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippingz3kuc4d7 a) 4fs8pwrtg3xy -n down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline desk)4 4gpcrxd 8ynat u3z3 7-fwpends on

  "The total angular momr.ucv ovcb+l(v *y*( ventum of a system of particles changes when a net external force acts on the system." This (y*v .vvc*ucl( ov b+rstatement is

  In what circumstances can the angular velocity of system of particles chan7v 4o rxt6j9fx s,rh:p ibad/1ge without any change in the system's angula 7b 1,xfvthor ds:4xpr6j9/ iar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fril;4 zl oyi-:vgzbclo b/6, eb2ction which may be present. What happens over time to the Earth's angular mome/,bl; -eolb l:ovib24c yz6gzntum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the ywqr6c(o8)ab1f3ff pEarth moves close to the Sun, then which of the following best describes the orbiting speed b)qa(p3 1of6c8r ffwyof the Earth about the Sun?

  An ice skater performs a piri5-x2y3zmdqk;rtxcq (wt( z je* 2gq9ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the akycd mj(gx2zr(xti 2q; qw39qz* e5- txis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his out7kbv*nw y( -gbstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotwy b7*bn(v-k gation?

  An ice skater performs a pirouette (at qddg//7/e6u hdyd0; vtpqj/ fast spin) by pulling in his outstretched arms close to his bod7q h/jy/ /q tdude/dgpd0t6 ;vy. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentu8pg*.u*:m*k iwx ; dnd5ibiqqm.

  What arc length does the Earth travel in a three month period in its nearluorl+wk--ru :s (sw2csaa*-q y circular orbi-s+s(-l a:q 2cuk w- sora*wrut about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cl4(a fr6-rvo yxp2oa. gock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes -f(2rproo 64aavg . yxand 45 seconds?

  How many rad/s is 25 revolutions per minute equie9p riyr5ax -d dg wix5hi96)1valent to?

  A bicycle wheel rotates uniformly through 2.0i-//ab,lg;u tyb4y fm revolutions in 4.0 s. What is the frequency of the wheel's rota,yigbul y;m4bf/ t/a-tion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz2gk9e x:ciym: 9 l)fpu. The pek e2i):cf9yglu:mx 9priod of its rotation is

  A phonograph record rotates at 45 rpm. Through what anglegxch42;f vci*f phjux- 2ds/. does it turn in 0.20 s?xhgvux;/. 4hfcs fi d2pj-c*2

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on thcplz /rvpvo n6, zq8cby.3sn;* hb9:de outer rim move :/.bhr 8vcsvpn,dpc9y o3;z* l 6znq bin 2.1 s?

  A bicycle wheel rotates uniformly thb3 z(kdxpsz7x 29u2 8xkjqw1 arough 2.0 revolutions in 4.0 s. What is the average angular speed of the whe2px kk9 xx1uajzz28(7b3wd sqel?

  A bicycle wheel rotates uniformly thr,;a7 v9-4/h ed4vgri,vckfg5ax zkk y ough 2.0 revolutions in 4.0 s. What is the lineavkva9g/4e-yz 7 f,r hd5avi4c x,kgk;r speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whi--dbcho 69qmr ch moves the car isb-dhq co96-r m 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 speed of 2.u*trjkle*gn, *n3m: xpm *e-r0 rad/s. What igm n*murejk3et -* :xr,* n*lps the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in leng ai;rzzvw:ep +7.w*v* c1k akwth. If the motor rotates at the rate of 20 rev/s, what is the approximate zer1* ;kk+ww:.vc*p wvaz7i a linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spklrodd6/ + qg/q2 ,jiqeed of 2.0 rad/s. Wr6k,/+dolq q2 /dij qghat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the peckcu 2,g*lyt wjdh9c:d68a 6 orimeter of a bicycle wheel of diameter 2hd6j g8 yla,cctckd 9uo6*:w70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sgcgkz 0 3 n sc8r,al9.dqac12ztation (r = 93qzcnda ck l8a02gsc,g z.1 r1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20f+e bgl-/j g5j m/s. The maximum centripetal force (provided by st l jg5gb-jf/+eatic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circ)zo-cd(gjg o,h: ,c dlular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) i ,j): ,dclcghd- goz(os $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.7508l + mh5eu8m, hck;s2y mfyal5-m string, is whirled around in a sm aslk8h+ lmh,55fmcmy2y eu;8ooth level 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 masgj0gk j*tf . zzbtp,*6s 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane*zzgj,g tbp kf.0*t 6j 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 y*hdgv 97pjt2tk5 c2jjbx/ b5of $4.5 rad/s^2$. 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 accel o9i-ev eo)3/ic-u++k0jtz unm fnro+eration 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 aut iianm ol/:1c( p)3upeomobile tire rotate after starting from rest and accelerating at a constant angular acceleration1e): /lp3nim po( aciu of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angul vp1vexzyp4*a uw3/axn)tl2+ar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotaticn)7 2aw3k.4pwzqsv hng at 20 rad/s decelerates with a constant angular acceleration of .ks7hapwv 3n) 42zcw q$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a :pj+s0e2h9a3i sahh/ mlhg +un angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheg+s 9l shm: a0uh ip3h/a2je+hel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/sd8f d,g1s u3uc to rest over a distance of 115 m. What is the total number of revguu38s,d d1f colutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniforml.; xrarhhdml* jm apc46+(3 bpy from 8.40 m/s to rest over a distance of 115 m. What is the angur; ax+.4capm(3hh6rlj* mb p dlar acceleration?

  A wheel of diameter of 68.0 cm slows down )mk/qk k0-hyvuniformly 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 syk0 h-kk/m )vqtop?

  A centrifuge in a medical laboratory rotates at a rotar9ejc, n,.wp btional speed of 3600 rev/min. When switched off,c n rbe,j.wp,9 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 tighten0t,tbct, th /sing to a torque of 90 Nm. If a 30 cm losb /,th0t t,tcng wrench is used, what 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 Nbl0st01y.3dne +9c z6ffneq q m. If a 30 cm long wn9 b qe6zy0f03dqsne+ tc.f1l rench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of4 uhvea78u z3s inertia $3.00 \; kgm^{2}$ 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 u3(rqe 1*v j du-x6ibokj +c)sthe origin, mass 2m is at x = a, and, mass 3m isueu*jbdqx s( )63rviock 1+- j at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a f o.c6c7) wvyr86w nmm khfqc)-rictionless 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 thomc-7).mrk)cf wqvhy6c 8 nw6 e cylinder?

  A solid cylinder of mass 10 kg 4c9up, gdjm6lt4p5 ym 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 wrapp4u gypc 4,56tl9pmjdmed 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 ho xn( w 7d)t6 -ejrj*s oa5*vems9o7zkinged at one end. The rod is initially held in the horizontams7x6(9rvdz7to o 5a-w*sk)j e*je nol position, and then released 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 and mass 1gkr6up( r *31-t* epfpmv a8lt17lmlj.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, what1rmpj v1 lup6pt*g(ft3a l-l*rm7ek8 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:r (nt8mqd 3wg pulley of mass 7.07 kg and radius 66.0 cm. What is tqmw8gr dn(3:the angular acceleration of the pulley?

  A 1.53-kg mass hangsofn 0p5i2ol-m on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 2mooln0-i pf5cm. What is the acceleration of the mass?

  A rotating flywheel ca0io29kk:k*t2 hbiiz fn be used 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 pr8 epzq *feohst6 .: ;exp63-suxg/gof $5.00 \; kgm^{2}$ 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 qz,t0 y (zo2l-ve khj59c(.n+zf; li nqsbs5x0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the9 qnl(z0yxs.(c ozi;5e nl,j2-q zkvtb5h +sf 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 mzoz ;t2on196utx5iy9r0u8 fu vzj0 u m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before 8zmvyo9 06zu 12nui;5tutxfjoz9u0r coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 k(4nf3) qx5ptfcbg ,e n7xq e;tg is released from rest and allowed to roll down an inclined plane. How fast is it mogq7enn3 5tbeqpf);xct,4x (fving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down hfgm+rw - 6r1vk/go zez 74je6a 35e incline thz 6z-14hre7wfggr6m/ vj e+koat 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 mol *6vay 4eip) arlvc),mentum 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 moment of ibjs59phi vqw/zffck/cgi 3+9 )la+f3nertia 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 extend7t*slg); s u3c uwktd5l.t;v;heqk*aed has a moment of inertia7td;l asgltt;s*. ;ew*3uh cu 5) vqkk 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?