Question

9. A disc is rotating about a axis through the center at a constant angular velocity oo. Two ants of equal mass suddenly drop onto the edge the disc and gets stuck to the rotating disc. Does the Moment of Inertia of the system increase or decrease? Explain a. b. Does the angular velocity increase or decrease? Explain 01 c. Now suppose the two ants start moving toward the center at a constant speed. i.Does the moment of inertia increase or decrease? Explain 01 ii.Does the angular velocity increase or decrease? Explain

Answer 1

The moment of inertia of a disk about an axis through its center and perpendicular to its plane is 911 ет 64 г disk ? My mass of disc RJ Radius of disc Let with initially this disk is rotating anguear velocity Woo now the stuck suppose two ants drols on to edge of the disc and gets to the rotating disco

ant. Let my mass of each RR so ants two were start rotating about axis xx, Distance of ants from axis of rotation - R (2) = R so Net moment of inertia of system become [ disk + ants] I = I diss t Tant t Iant Net Inet - I MR + mp + me?

२ २ @ > Iver - LMR't pmp Net - partia from equation ① and ® we can say that moment of inertia of system increases. Because moment of inertia of of ants gets added to moment of imertia of disk. partib 1 As the met torque on - system is zero. so using conservation of angular momentum L; = Lf [: L-IW]

L; Le initial angular momentum final angular momentum * I; Wp = If Wf I; = I disk = 1 MR? W; = Wo If = 2 ? MRT amR Tea

* = me) as = (4 meu amor) ay W41 (***)ws 1907 MR? +2mR?

. We <Wo 50 to angular velocity will decrease conserve angular momentum. 2 Partic (6) If ants start moving toward center at constant speed, their distance from axis of rotation decreases. Hence their moment of inertia , I = mi will also decrease. (ii) Now it moment of inertia of system decreases, due to conservation of angular momentum

I W = constant wa angular Velocity will increase.