A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is ______. ( g is acceleration due to gravity)

Step-by-step solution

From the given figure, the axis of rotation is a horizontal line passing through the point A on the edge of the disc. The circular arrow around the axis indicates that the disc oscillates out of its plane, meaning the axis of rotation is a tangent to the disc in its own plane. The moment of inertia of a uniform disc about its diameter is I_ cm = 1 4 MR^2 . Using the parallel axis theorem, the moment of inertia of the disc about the given axis of rotation is: I = I_ cm + MR^2 = 1 4 MR^2 + MR^2 = 5 4 MR^2 The distanc