Angular displacement ismg. gehv0 lg9,c xgnc2e,n lfy 6*xb:g9opm4. usually express in units of

  Angular velocity is expressed in units340/ff h nnogs of

  Angular acceleration is exprbp6/q6wyqzdw q*o1e0z s fb ,;essed in units of

  A boy and a girl are riding on a merry-go-round which is turning at 2 r1u6ef*q foca constant rate. The boy is near the outer edge, ando*uq 1frec6f 2 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 which is turning at a cons9 rc 2*a1j+b k,ovr. eu;tsetwtant rate. The boy it e29 ;.utckawero+ 1jsv*,brs 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-round which is turning atn8exqz3 8byy f 1w:ka/ a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater1a 3wfb /yy8n:qk xz8e linear speed?

  A boy and a girl are riding a merry-go-round w4+w,rqpnin0n5c (d sw cvio;6 hich is turning at a constant rate. The boy is near the outer edge, while the girl is closer toq,n0d5v pr;sii+c4 wn6 wnc (o the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which isy*jt1(u6 z cq2 0pxayf turning at a constant rate. The boy is near the oux f102y (up zcjaqt*6yter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of tqw68txj2ylg9. g6e gjhe following is an accurate statemgglq 2.ej6t 86gxwj y9ent?

  Rolling without slipping d. / aflw;kzga9c83yabepends on

  Two equal forces are applied tl ))kc(o6-umw x;iec to a door. The first force is applied at 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 to6 ) lmi;)e-xut(wcckorque?

  Two equal forces are appl+ ykxuwt oyyhay*f/a* 1 6vi qk;3ej5(ied to a door at the doorknob. The first force is applied perpendicular ty y1wv /*3 auh(keaiyk+*5to;qxy f6j o the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are appli3rwd)b*um t,ied to a doorknob, perpendicular to the door. The first force is twice as larg*3 w u,dtir)mbe as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity ul+tp80i j; bidbz6z1wsed to measure an object's resistance to changes in rotation?l 8t0j biz6z1w+ib ;dp

  Consider two uniform solid spheres where both have the same diameter, but4sfj o6fjn(t9 one has twice the mnst9(f 4j fjo6ass 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 twice the ram8i i0n nji22) wjt6rp(pv1qqdius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere 8iitp n (m)n2j0 wvr62p qqi1jis

  Consider two uniform solid spheres where one has twice the mass and1:g*o8pngqz fr0 (idd twice the diameter nzi dd( *1rgofg pq8:0of 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 M and radius 2kxswh m1 tuq79e0g1a R. If these are increased to 2M and 3R, what happens to the sphere's moment ofh9 g17w0ske1ua xm2 tq inertia about a central axis?

  If a constant net torque is ap8t d9hkjua* *x m9jhf;plied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is givee/skxuv utlm. u9):1vn 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 kg, one wheel of which has a fy6 +h2vlg/vy 3uv 3b iy-ch5wmass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total tiuv g2ycwy6b 5hf lv-/+3hy v3ranslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and rk) zl(uh7 7zkdadius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the b u( )d7zlhkkz7ottom of the incline depends on

  Suppose a solid sphere of mass M and radius R q y3xnn2z(*os rolls without slipping down an inclined plane starting from rest. Tn(2zqn o *y3xshe angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of prdd) je:var* 4- ktsv;articles changes when a net external force acts on the stsre d*avdj4;krv) -:ystem." This statement is

  In what circumstances can the angular velocity of system of particles change wi s7e+*) a.mex;/ hwzd9 .dtuxr1zl5vxgt2quathout any change iz)x5d1;emqdtu.lex7a 29 stgx ha+*z/wruv . n the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which 0x.w8xl.e4cwyhp .wt may be present. What happens over 8x ely.4.0p.thxwcwwtime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. vaf cge h/;dh w6n*c/k.m 6t9f As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Ekh.; cfe 69gw/fc6tma ndv* /harth about the Sun?

  An ice skater performs a pirouette (av9btii3 , 0q*o( yb*hc7svbft fast spin) by pulling in his outstretched arms close to his body. What happens to his angul c(7bvqytbs ,9oi3 tibv*f h0*ar momentum about the axis of rotation?

  An ice skater performs a pirob:yb :lkghe 9-c)*luv uette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy:vlu )9 -kbe :hb*lygc about the axis of rotation?

  An ice skater performs a pirouette (a fast 1 ),cdgxyn+sd yzcsh :jn321n spin) by pulling in his outstretched arms close to his b1nxy3ndc1 ,n hs)zy2dg:j +cs ody. What happens to his moment of inertia about the axis of rotation?

State the law of conservatiz0rh lxap:t8/on of angular momentum.

  What arc length does the Earth travel in a b5e* m+(j9cwj emvy9fthree month period in its nearly circular or 5efb+ve *(jmy 9jcwm9bit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30s pm ip+52wf:i)xqy 1v m. What distance does the tip of the second hand sweep through in 3 minutes and 45 secopq1ysw)5 ixpv: +i 2fmnds?

  How many rad/s is 25 revolutions per minute equivalent to? etq19fsiqvpqdr;8kx9:kw 6w 8m6 b+5otira)

  A bicycle wheel rotatenwnq9plun8t.,w.6a+h ; vp gbs uniformly through 2.0 revolutions in 4.0 s. What is the frequency of t +phn.8p bgtl,nqa. 69wwn;vuhe wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenu.o t55fmh+z mas.ywgm zi,8v/5, bywcy of 0.40 kHz. The period of its rv s5,ag+5,.o5tmm/yi wuzzw. b 8yhfm otation is

  A phonograph record rotay+6vhw .n r(5gfkmn jhzm/x)e d( i1-vtes at 45 rpm. Through what angle does it turn in 0.20 s x1f.dr( nkvnwmhy mie( 6hg zj/-+5)v?

  A wheel of diameter 26 cm tf v ;kgcb-w3n1urns at 1500 rpm. How far will a point on the outer rfb;w- 1 cgvnk3im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isty; /b,heim0y the average angular speed of the mh;b/yit y0,e wheel?

  A bicycle wheel rotates uniformly through 2.0 rev*r 7pbp u xj8uwu,uz77olutions in 4.0 s. What is the linear speed p 7zbu 77x,u8r*uwpju of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skie 2itz2 e9 ygoend:b*-77foi kers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. ei o79*et:ezykn gf d72boi-2 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 2.0 rad/ )xgp1 vob.(sz9pvfgh.*o8u b-2 o kpf-fpa,cs. What is the linear speed of a poi p k*g-,scvo-pzh.8obf(bpuv 1p2 f. ogaf 9)xnt on the wheel's rim?

  The cutting cord on a gas-powered weed cut6pu-od5c* bse q.v:on xao;g9 ter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the a-dgpoeonv;sx bcq65. : 9oa*upproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a ux(kqgb6 dl5) 5+ummrconstant angular speed of 2.0 rad/s. Wx+dl5u )6 5q(mk gumrbhat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of aa4wew/*6f ij a bicycle wheel of diameter 70.0 cm a a fjw4/i*e6wwhen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space staticfo;fq pni:- +on (r = 1000 m) rotate to produce an artificial :inp;f+- qofc gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cihqm*c )1 bei+ircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal+q*be im1 cih) 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 flat ciz1; ekd8l.hhzrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) iskl ezhz1;d8.h $1.2 \times 10^{4} \; N$. 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 inw aottf 0qp, 7t:;p1fr a smooth level table. If the maximum tension that the string can withstand is 250 N, thet;rof:t01 qtpf7, wpan 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 cm rolls without slipping 10 m dow+wd zt+h qi2e+n a lane atdhi e2q+wtz++ 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 ak c/oh)jl :k9fngular 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 acceleration u/h 01u jpsq6.ez fk4fof $4.5 rad/s^2$. 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 ro6tgdh 9aldk7m* ;bmqftb q1 1+tate after starting from rest g d11h9 * mmltdbqat7 ;qf+6bkand accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and h pc47e pstfy.x0p ) l+y9yepo6as 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 decelerates with a constant angular if aj5z;j 8(yel2k44u0 fdlat acceleration ofl48fldiy a2;e0 uz (54jt jkfa $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reah iqh;q ,77zgm s33ugaches an angular speed of 6.0 rad/s while turning through 2.0 revq, hi ha3s77u;zmgqg3olutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 b zs91 ff69orxm/s to rest over a distance of f9r 916bozfxs 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.401 ktk3p vh5cwob- en+ (3roym0 m/s to rest over a distance of 115 m. What is ther+0cpthmonk yob3v k315(we - angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovb76nhl) xyfuil )pp2ff) q2p dh; z3c,er a distance of 115 m. How long does it take for the wheel tb,)dq)uph3l l)7fzi6pc nx2f; yp 2 fho come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 revdhx8d+ u*neh*8pxey b (+y+uo/min. When switched off, it rotates 50.0 times at a constant angular acceleration b dh*o+ de++8xyunxh(epu*b8yefore 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 lii/8g+f r 3t(3n oclg qhz z3)h*dqr:cm long wrench i8l*rq3( izgr g)dz ohcf:h/3qni 3l+ ts used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel :d zq a:v1.ocarequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, w1: .zodac:vaqhat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ini skxjwy1gi7tc 4w h2+io l-:1ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: masu x +pbxom7x/n2bcy+ )ek*2q qs m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is c2qobnx)q *u2ye/7 pbxmx+ +kthe moment of inertia about the origin?

  A solid cylinder of mass 10 kg z4 fj/5/ l0ny22q j yxtsfdfh2is pivoted about a frictionless axis thought the center O. A rope wrapped around the ou 2jq/ fs0fj4 /2yyndhfz t25xlter 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 ma9;sv; )dtuk ,dqvgxo+ss 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped arou 9+qv;os kd;,x)vdgtu nd 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. Thefvb +zfs94 gcc nz, /1n1in7dj rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The momescn z i4/jn17czgf fb9,nd+v1nt of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and ma 0**e regb9f. 20s4s 3wcjqxg4rr jnkrss 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, assuming it rolls9sj3 *nc42rwrerkj. f rx 0ggb*se q40 without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fricti+ +aeiv6ax tp47 k,+*ogsv4fot syxl*onless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the an4atx*vae+kl pxi4s +o*stv gf 7o+ ,y6gular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fric;h0ed c+gb 1rpus ./httionless disk pulley of mass 7.07 kg and radiusu /h. bhes gr;01+ptdc 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. Ifufhfm9jnb89w5/c2 )r.u hoki(k it)j 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 ofvg 2bfmz16w 2m $5.00 \; kgm^{2}$ 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 0jsx;to 9 y*+f -kywjfa.c0cr2 .010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when kjj0o yw ; -rtc*+.2xycf9safit reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls*)h/k7s72as deor xw a with a speed of 10 m/s. How high up an inclined plane can it climb before7sraxew*sh72 a) /odk coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released froi*h hmk. 8.ucmm rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vhu.c* 8hm mik.ertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rol 0u8 u+xjl sidb,*0oez,7ta*sab vyo8ls without slipping down a 35e incline that is d vuit*e8a uoy*,bx0s08,bs7+jlza o7.0 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 changes bywq3ey la48ha5o am5 :ol27npx $20 \; kgm^{2}/s$ 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 moo)4n+hyemml)/t-l m 7 )flneqment 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 haof *sch; e98fm:hby r(s a moment of inerti:;fo*bm hs(er h y8fc9a 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?