Subjected to a constant torque of 0.10 N-m , a uniform square plate of mass 2.0 kg and edge 10 cm rotates about one of its diagonals. Determine the angular momentum and the kinetic energy of the plate at the end of the fifth second after starting.

Step-by-step solution

The moment of inertia of a uniform square plate of mass m and side length a about its diagonal is given by: I = ma^2 12 Substituting the given values, m = 2.0 kg and a = 10 cm = 0.1 m : I = 2.0 (0.1)^2 12 = 0.02 12 = 1 600 kg-m ^2 The angular momentum L after time t = 5 s under a constant torque = 0.10 N-m starting from rest is: L = t = 0.10 5 = 0.5 kg-m ^2/ s The kinetic energy K of the plate is given by: K = L^2 2I Substituting the values of L and I : K = (0.5)^2 2 ( 1 600 ) = 0.25 1 300 = 0.25 300 = 75 J