Angular displacement ihb5 mr*i/(yg cpe/h.b s usually express in units of

  Angular velocity is /-p8ztw kis4 aexpressed in units of

  Angular acceleration is expy wka k(w 8aygfns;+: 4gqab-/ressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a cons )l0-pg ;zldw:u)crcc tant rate. The boy ic p)0 -rlc;w:)g zudcls near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round w.+mx rvwx(uog: 3 a4tchich is turning at a constant rate. The boy is near the outer edge, and the girl is closer :w 3rg 4v+muox(acx.tto the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whic,;qqcm/+ y/:bpuciyppq, 5 cu.c x,abh is turning at a constant rate. The boy is near the outec:ci xcqc+5bp /aq,/uyq .,pmb ;u, pyr edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tkhu l bl5d-g9cy:2o2wb(v0 mourning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who ha vhocbm:5y-w 9guob2(d 0kll2s the greater centripetal acceleration?

  A boy and a girl are xus:uw( s.q5a sz0po :riding a merry-go-round which is turning at a constant rate. The boy is nw q 0z:pxss(suu.:o5 aear the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid bodu9 )rl1z )fbd a- rxdg-k(rt8cy that is rotating. Which of the following is an accurate statement?l8d) d-(zag)rf rr1x c -b9tuk

  Rolling without slipping dj t5b4;-76x exno07lxzz twe*1wqcafepends on

  Two equal forces are ap8pfb 75 o fip7ry+xm*ot /v.onplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces areb r o n7o5tiym/.7fv*pxo+pf 8 applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a doorz*g j*vm(ry2)b5r3z qk zx: iu at the doorknob. The first force is applied *)gr 2uv qzjk bzm(* yrz:5xi3perpendicular 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, perpendicular to the door. The firs;fp04ebe6vq ho8g,w tfh 9i a4t force is twice as large as the second force. The ratio of the torque of the first to the torque of the s04gqehiv fpwf;a6t98h b e4, oecond is

  What is the quantity used to measure an object's resistance to chan5zhyx89f bqd;ges in rotati9f5 hdyxz qb8;on?

  Consider two uniform solid spheres where both have the same diam2jh5b) sw 2qometer, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertjm25w q2sbo) hia is

  Two uniform solid spheres have the same mass, but one has twice theinhvp (sby(p.1:ol36m brhdna.;c wn n)9z6t radius of the other. The ratio of the largerl6nv zo(d.r 3: b snyhin 6c(9wm)1pna. th;pb sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice th n*t4qtqc0; cctyfzn w iuh*e89/;c *he diameterqf9 tt4*un; h*e y/z; 0iwccnh8cq*tc of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphehb*2pd45h jc are has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's momen5a*d cj24hphb t of inertia about a central axis?

  If a constant net torque is applied to a:o e7quv*,b ghn object, that object will

  The moment of inertia of a solid cylinder about itj6+ e;t2,geik9f t6 +rx cub kb*zg)vns axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translabf+,g66ktg*ej)riv keu2 nxt+c z ; 9btional kinetic energy is

  Consider a motorcycle of mass 150 k raws1+0tq +gng, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheelrgq++s 01an tws to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M an1 x-)nqeaa.7hglj 4d+h o f(nrd radius R rolls without slipping down an inclined plane starting from rest. The linear 1hogaj (7.-r nnq+dx e f)hla4velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of m f3kjqu9t v2moze9u 3;ass M and radius R rolls without slipping down an inclined plane starting from rest. The angul j kquf9uotvz23;me39ar velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of t l u qmc7 ky6kg zt:36cs*sg4p:v*gi)particles changes when a net external force acts*tc7:g c:gu 6*l4vs3py i gk6m qz)kts on the system." This statement is

  In what circumstances can the angular velocity of system of patuaf; x87.3s83un l:rfze q ogrticles change without any change in the system's angular moffz;qt:gou8 xn.87erau3 s3lmentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictio pxn 3+:mmw)npe0 wtte*l6-jon which may be present. What happens over timee0 lnwtmp o-3 t:jp*mn)ewx+ 6 to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbia nz0qlsss*1a vp.0x (v:0t)ok2stu et. As the Earth moves close to the Sun, then which of then*s(tv)lvap s : e o1t xq02ua0szs0.k following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pb c jiswnlh.0jn87a+ccx i 1/,/iaw 9wirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens 1 ai js +b8l./7ncwnwc 0xch,9i/iawj to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fastu)r* / 6kzeazt spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rota zek/a *t)u6zrtion?

  An ice skater perform9e gpl*(wgnd 0s a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the ax9(d0 ne* plwggis of rotation?

State the law of conservation of angular7arwhd , -vk8ur4aefve /s 4z+ momentum.

  What arc length does the Earth travel in a three month rvt 6us jh5e1351+ mhsbk89jv* q zaizperiod in its nearly circular orbit about the Sun with a rahs186u qzmia 5rezh1b 5k jjv9*3vs+tdius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What ((gt net7bo7s distance does the tip of the second btsg (77 (netohand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equi za,81x:g e6hkxpjrl 1valent to?

  A bicycle wheel rotates uniformly through 2.0 revoaf o( b7lqrd,(lutions in 4.0 s. What is the frequency of the wheel's r,fa(bo l(qrd7 otation?

  A pulsar (a rotating neutron star) e3 r*2ogco*blvs d :s6jmits pulses at a frequency of 0.40 kHz. The period of its rotatiolg:jv2* od36bsc rs o*n is

  A phonograph record rotates at 45 rpm. Through what angle(yhb d)w.n a8l 8que0b does it turn in 0.20 leaw0ndh (b yb8)8qu.s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a ponrz)y,j0m bmjn6; *hir*b7c.agc;p +z:x zl fint on the outer rim move in ,pm; 7ij6rrj )*zmlz y zbfg+: 0ac*x;bh nc.n2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is th u,*j: u8xc;nt 3a*vmeeukgh ;*4wahu e averuwkenc*uh eju*,;x vt*:4; gaha m 8u3age angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W4/ bcd/rjk zw/hat is the linear speed of a point 0.10 m from the center of thec/4wkrj/d/bz wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. T3 /2v)ku- 8kexmm:rdzsqtq 8nm. tmr/ he cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the q rtm v /.rtmdxkk s-n8z/2ue8mq:3)m cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with(idp8uq* 6)y pav y.dc a constant angular speed of 2.0 rad/s. What isq6d8pup(*)yic.av d y 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 lengthmoatl6((1w ej,a h1ev)si; ov. If the motor rotates at the rate of 20 rev/s, what is the approximate linemav te),sh(vi1; ol(awje o16ar speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed c1) tubsqtf-sf) 5su7lg7bhv8kha:c,9 gya + of 2.0 rad/s. What is the centripetal acceleration of a point on they-)8cf q gs),k ag+ 7:alvuf5ubshs7btt1 c 9h wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicbpq7tdh w5wq 3i(4b7pycle wheel of diameter 70.0 cm when the bike ip7b(h 7dw b4pq3 t5wqis moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, roz 369phapu:jo tating space station (r 3j9pho uz:p6a= 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating e n2qied.+3 tp aa,vysto 1m/m3ozjt+,9 twy5 a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by sasmq,+y,2 t3ite/t .two1v9d py nao5e3+mzj tatic 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 of 20 ms9m6s)j lkm*) v.qm ah/s. The maximum centripetal fo.)jl* )qmv s mmhska96rce (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 endb6re/vhx)we8 -0w l31n whzs lmfi -*x of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand izsvhfwer* h- ni 0l/3)x6 eml8bw-w1xs 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*jy8y9coqw81a.j a,:ses9j p , ha jrl kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 mc91po ywaj,asleaj. jj9*8rsh,8 y: q/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 angu+nupfi*ob m m)uu8;2 elar 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 ,skl. osza*b b9.p5n uangular acceleration 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 after star;zd wdnb+ 5wjo53 jlh(ting from rest and accelerating at a constant angular accejndwd+3bz l( w 55;hjoleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angula- g 2p mcfcok 4ix-)wd+kl3/mur acceleration 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 angular plk-kc ps0 l91accelerationcs 0k1l9kp-pl of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from reic1y+ f xxv(h*wf26n ust and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular +yf(vi6hx*cn1 f u2xw acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows o9p+rw;)4g qpqo w2, u7u7lsylxtm.rgr-: s h down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutiouo-s)r7 pl:gwsr9,.+yh2lx4 qq;mp 7 rutwgons the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unhu, m:44lr)fmvg )dmy9vwc5r iformly from 8.40 m/s to rest over a dist g4)ryfmv,4 5w:9)rmm chudvl ance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.04 p nawdbm.:i 34fnla5 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 to the 5 3i pn bma:wa4d4ln.fstop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 reonpf ( 0dpq. vf-s92tev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to res tsf .n-90pedoqpf 2(vt.
(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 rgqigc u 4g2/w*equire 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 forcewg*/ 4iqgu2cg is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90n.0dn xh(yww8t :oem/c2ult. Nm. If a 30 cm long wrench is used, what is the magnitude m .tdow0( y/c. ehw:nxn l8tu2of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of q*a;q asvs0:winertia $3.00 \; kgm^{2}$ 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 origin t/cgzw17 iq(lwk2vm 6, mass 2m is at x = a, and, mass 3m is at x = 2kqcgw2 1/lvm6z wt7i(a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought rc2g3p48j :sx5w, dht2on pns 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. (4dsnxh w8s j5t2gpr3: co,pn2See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis th y1p)t+8ywh:eu rvl*zought 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 in the first 5.0 seconds, if it starts)lty:yrp* wh 1uzv e+8 from rest?

  A 4.00-m long rod is hinged7gz wkciz9k;f ;)s lf) at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration asf wsfkgci l;k9)) ;zz7 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 y0. 8tlau; phzand 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 achieve, 8pay0 t;zh. ulassuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrazeb8 7,oe:eq4k i6 ja6+ghssb pped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratio8ezbi gqkbj a,s+6ohes6e 74:n of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk 0vmno w3:*aljwb ge7v)d d9.cpulley of mass 7.07 kg am3jdw7 )ogb9.vc ad:0w *l nevnd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store ezmmoy6e ;xr, zxa*x4*nergy. 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 inerti 3sayihnu:8ih e* hety);zp3.a 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 rad6q(; u6uvd( ne/rems (i w6ld epkl/,mius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. md 6wu/ q/(6(ke i;( lsnerm lpd,e6vu 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 0.010rnflnqox01 6 9 m rolls with a speed of 10 m/s. How high up an inclined p1f06qoxl rn9n lane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20:3jpd c ycj,4l ofavf55 t5mp( kg is released from rest and allowed to roll down f 5ppof5(5cv ,jcy l:4dt3ajman 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 roll): fdeg*ezi (as without slipping down a 35e incline that is 7egd(iz):eaf* .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 momentum chplg3b+z)rb aeszf 8-x;u 3 z*5d9cumrp,ux+ ianges 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 momet; garg en+zj/yix 2.4nt 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 atu qaie su0k*4 w- 35jxrqgepa52 9xel: 5.00 rad/s with arms extended has a moment of inertia o:kg -l 3ap0ur 24q se weex*axiuqj955f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?