A disc of mass 4 ~kg and radius 0.4 ~m is rotating with angular velocity 30 rad s ⁻¹ . When two point-masses, each 0.25 ~kg are attached on the periphery of the disc, at diametrically opposite points, its angular velocity becomes

Step-by-step solution

Given, mass of disc, M=4 ~kg Radius of disc, R=0.4 ~m Initial angular velocity of disc, ₁=30 rad s ⁻¹ Mass of point-masses, m=0.25 ~kg Now, moment of inertia of disc, I₁= 1 2 M R^2 Moment of inertia of disc and two point mass system, I₂= 1 2 M R^2+2 m R^2 Let ₂ be the final angular velocity. According to conservation of angular momentum, I₁ ₁=I₂ ₂ ₂=I₁ ₁ / I₂ Substituting the values, we get ₂= 1 2 M R^2(30) ( 1 2 M R^2+2 m R^2 ) = 1 2 4 (0.4)^2 30 1 2 4 (0.4)^2+2 0.25 (0.4)^2 ₂=24 rad / s Hence, the final angular v