A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. Find the magnitude of the angular momentum of the particle about the origin.

A uniform disc has mass M and radius R. How much tangential force should be applied to the rim of the disc so that it rotates with an angular velocity ω in time t starting from rest?

From a uniform circular disc of mass 'M' and radius 'R', a circular hole of diameter 'R' is cut such that its rim passes through the center of the disc. The moment of inertia of the remaining part of the disc about a perpendicular axis passing through the center of the original disc is: