Angular displacement is usckv h(k.* wm x6ezfdsao;v9og:tu*2 pu;-x(kually express in units of

  Angular velocity is expressed in units 4 hobj+shln2d8ouh+l2jisf x(d2y ; 3 of

  Angular acceleration is expressed in units of:y/)snugm 1 cg

  A boy and a girl are riding on a merry-go-round which is 0+ t8flp :ndihturning at a constant rate. The boy is near thnhl i+p8f 0:dte 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 which is turno*wspssd+sg6 3 lmu3 c0*ulj f8i6mn4ing at a constant rate. The boy is near the ouw66ssl4m 8u s lnsp3*f i*cg3+dmo0 ujter 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 at b /f xty+x 61 7x,qk.qnqku.yxa constant rate. The boy is near the outer edge, and the girl is closer to the center. / y.y +b nkku7x,x6fqt1xqqx. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which i ju -rmgf:y;mhvd48.qs turning at a constant rate. The boy i8mjhrd m4.v:y-u ; fgqs near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round w 0esllo-jtl90xm 7w :sh;ilv:hich is turning at a constant rate. The boy is near the outermtj 9li:xsh es-w0llov:;07l edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of tq(wi4 rb1l1mr c snydj *e677phe following is an accurate sta r4 7i6cdly 1sme1wq*(brj7np tement?

  Rolling without slipping depends 9czeeo(8;ay j on

  Two equal forces are applied to a door. The first force is applied at.joj3 vdmd6j*+4wiud 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 greatej+d4i6wjmd j.* 3 vudor torque?

  Two equal forces are applied to a door at the doorl;z2*pmgs; ga knob. The first force is applied perpendicular to ;mzg ; pag2l*sthe 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, v h 7ul.(rsno7x4f e+cperpendicular to the door. The first force is twi e frvl77usc(+.hno4x ce as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure k7 emhtf2,z rq7rl51san object's resistance to changes in rotation75hk s2l 1,qrtr7zm fe?

  Consider two uniform solid spheres where both nc5ai 45c d-ppg/j7pohave the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller momend-4c55opacg7 j/nip pt of inertia is

  Two uniform solid spheres ,oohhnsejkq f4ef0+73em- r9have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of th9 eo0f,foqh+h7 eksm j3nr-4e e smaller sphere is

  Consider two uniform solid spherese*iqhzw)5 i s/ck /ppah0kp51 where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of iners 05qpk ka*i1 5ipepw//zh)h ctia is

  A uniform solid sphere has mass M and radius R. If these ar9znlyj/0;osboa 3:;l er ,pyqe increased to 2M and 3R, whaljbes3/ ;0yyq a, zn or:po9l;t happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that ob+cf-v yvij g)l7a6uruh /:)v1r8 luua ject will

  The moment of inertia of a solid cylinder hg6) ,geuzqy7nk)x o)g-mw*b about its axis is given by 0.5 MR2. If theogub 7qy)hnkw g) -,*gzm )x6is 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 r so jd4e 36(evr7a-djwhich has 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 ofr -v e(s6oajejrd3d47 the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slq7f 8kut +b4 r.mlo0afipping down an inclined plane starting from rest. The linear velocity of the sphere at the umbq7o t4k l+a0f8f.r bottom of the incline depends on

  Suppose a solid sphere of mass M and radius Rv4 lwsmlch19. rolls without slipping down an inclined plane starting from rest. w.l4 m9svlh 1c The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particllko5 +:cj+0*0;r9o dhw vh/sqtpe gikes changes when a net external force :skr 0 +*qpv/tlg+e5 ;9 ojhdckwohi0acts on the system." This statement is

  In what circumstances can the angular velocity of zt 2ot2arv2 ,esystem of particles change without any change in the system's angular momentum?ato,re22zt2 v

  The Earth orbits the Sun in an ellr wnz1g w5ny:7t:e l6fiptical orbit. Ignore any friction which may be present. What happens over efr 51y6wnn:lzw 7gt:time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Aszm j2;wm(t.q.c auoe: the Earth moves close to the Sun, then which of the following best desc.mujz 2;cqaowe(:m .tribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirou 9:ou2efivl3c ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about o u:el32v9cf ithe axis of rotation?

  An ice skater performs a pirouette (a fast spin) bsx* oqy:(4 ggvy pulling in his outstretched arms close to his body. What happens to his rotatio(svqy:x4* gog nal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a ftv n absts456+ast spin) by pulling in his outstretched arms close toa tss6nt4+v b5 his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation ofdpq 1v0em8x -4a 1 /vimn:psxr angular momentum.

  What arc length does the Earth travel in a three month period in -q3 ajveo96vf its nearly circular orbit about the Sun witj 3e-vf9ao6vqh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock t ) o s:k3rybooe1g4n7has a length of 0.30 m. What distance does the tip of the seyg)4obo3torn e 7sk1: cond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions perc: m-j79wv l8iiohqp9 minute equivalent to?

  A bicycle wheel rota a46qwuwps39fv 4zx pzt tv+,8tes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of thep4 vf8q u4 z,twawv+ z396tpxs wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fr +-s)nq e8qqdwequency of 0.40 kHz. The period of its rotation ied-)qs nq8w +qs

  A phonograph record rotates at 45 rpm.wx*9b*6n h 3n 2 nvo-gqv ng.7kvk0y6derier2 Through what angle does it turn in 0.20 sb gv36dnq022w.* yk knorxe6grhv*v 7n n-i9e?

  A wheel of diameter 26 cm t qe4h6o;6g2 uf3wpzv durns at 1500 rpm. How far will a point on the outer rim m 63egvqh2z4wof p;6ud ove in 2.1 s?

  A bicycle wheel rotates uniformlyv/t;sjknq x9.)z g(v3 ay q 7jys(a0oe through 2.0 revolutions in 4.0 s. What is the average angular speed of the wheeyvn9s7va;q(0 qtx(o szkjae )/ yj3g .l?

  A bicycle wheel rotates uniformly through 2.0 rev6 xgp ox;y;v:ztl6;itolutions in 4.0 s. What is the linear speex :lpt yi;66zv;t;xo gd of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiero;l v8 ufl;l::f +ztqws 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 the pulley rotate for the cable c8 ;+wolqv; l:tffu:l zar to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant anzi i 3j0yhd0-kqok, x)gular speed of 2.0 rad/s. What idoy),ik zi 0-x0qk3hjs the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter iszjn r57va maduh-s ;e,i-*o 7then 1n1 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what in*em1tad ju7oe-h1,a5i7nr ;vnsz -hs the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 k (b/ i7r psr5(psj*zyrad/s. What is 5srk7pbzj(/ (yp* isr the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a pointoo:fu )5uvu2 de i3cd9 on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 d)o3cd uu9ou:if e5v2 m/s?

  How many revolutions pec+hf*i (j1eshr minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial grashjei+f h(* 1cvity of $9.80 \; m/s^2$?

  A car is negotiating a fla7;6n s l+lxpbst circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictln;s+x 6s b7plion) 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 mu24, 7h y k-nfes*qmmf25vfccd-qd7c/s. ,u-7vm27f hsneq 4f2qccydf-5 cm*kd The maximum centripetal force (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 end of a 0.750-m string, is whirled around in ay.1 7 w d)t7k6pki4h(qiy)6 kpwwhjtn smooth level table. If the maximum tension.pjy 17i t)wth wkdh qw4y)(7 knk6i6p 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 mas3ipp72 +csnxk5 5 gqum32 uwyrd +rrb5s 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 5m5wrdkg iyxrsr+2b3 u 2p7cn3 q+5 pu4.3 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 wizh(zf::p lo; eldkr1n o/e j0(th 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 au5l:ywtj-8q3m dnki:0 ud 2sw constant angular 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 rg00z uedcs-3lqq hw( 9otate after starting from rest and accelerating at a constanz0ud hq0- c g3wleq(s9t angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerationy s0p:e+2ugyq uevt )2 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 accee :)g3caar; wgd0q)gwleration 0waqwgcg; :a3g er))dof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 ravjv5 pyvt(66 md/s while turning through 2.0 revolutions. What is the average angular 6p t6vj yvvm(5acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows js :w0hka0 lfro9u* /tnkc4+bdown uniformly from 8.40 m/s to rest over a distance of 115 m. What is t+u9 4/krlwnc*j0sak oh:0bf t he total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/sibzcxw0 7b 2yb-b5u(jm s(+lu l t3h5m to rest over a distance of 115 m. What is the ambiul(+x bt (3 0wz2bulj y-57hsbc5mngular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.48d*by: zlc 9r1hmv9m d0 m/s to rest over a dc19lhdymr*z mb9: 8v distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a 0t :juhe +( jmfp6)tuyrotational speed of 3600 rev/min. When swi+fut ej: hmup( 0jt)y6tched off, 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 tightening to a torque of 90 Nm. If a 30 cxur v;a kgzy7- vk+/7rm long wrench is used, what is the magnitude of the force required when the force is perpendicular to th +-z/xay;vrru7k7gkv e wrench?

  The bolts on a car wheel require tighpyi qfxrz- 3;pxpa1 :9tening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitudeq1yp-;p:x 9f 3xzpar i of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerh ab6v6eajq2(j83oo* e jl5nc tia $3.00 \; kgm^{2}$ 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 origb*gpuuf :s(j3;6 c+bcv.ti gsin, mass 2m is at x = a, cusjsbf +ib;u63.t:cgv p(*gand, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a-z6nkk*+ ze vc3ps(g*st;wgq frictionless axis thought the center O. ;g* 3szcgv(wsen+pkq zt *6k- 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?

  A solid cylinder of mass 10 kg is pivotedd:jk/xr3mdfegvj1(7 (m3ae, vt4eo o 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 axtdevkedmojm3e f17, (g (o3 rj: va4/round 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 hinged at one end. The rod is initially h6+s6k3ar-kh)kmw ih m eld in the horizontal position, and then released as the k sh)mh66k-iw+3akm rfree 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 z z7p6ue; ,hsba ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 7 hzs6;pzueb, 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 rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu 2h+8gaurx- r q 45mrraxa(ut3lley of mass 7.07 kg and radius q8 a(hr-r 5+32amua tgrru4xx66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disp2*kcwf ti ii r*g7b84k pulley of mass 7.07 kg and radius 66.0 cm. What is the accelerationpg2*iibtc *4 rw 8if7k of the mass?

  A rotating flywheel can be used to store ene( vug*r rau u.j5uk8i)rgy. 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 :67tvwgzuyd5lt);f *v ao9e-bxz h z9 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 rol(8dz woq( yz)9 s,nk.sta,zhols without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of thezws,(q9 h)d.ootsz8 , ynz(ka inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010+ u1rqg4 m;h lmt9e0wc6xdvfqh 3 *u2i m rolls with a speed of 10 m/s. How high up an inclined plane can it climb id6te mhh+q1lw30 2 rmu*vgx4c9 f; qubefore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releavq8kj6r/3*7l etj ,elvjz 6lpsed from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance oz l trjp87kqj66j*lv v ee3,/lf 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dmfsrf.sp5 +z ejonr9+:,,0ky. r+w (j rvobvo own a 35e incline that is 7.0 m long. Assume it started +z+(e.frr5 ky+ osvf0 wb.vnoo,ps:jr9 jm, r 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 chanu63.2,c ut an d-hkwmpges 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 inn)e( nsfnz08x ertia 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 m pm0dqn 8rd.:9vg3m8lng yp eyu305tioment of inertia of y93v3m0eup d0mnldnig :8.g58qtr py
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?