A uniform rod having a mass of 300 g and a length of 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through one end. Compute the kinetic energy of the rod.

Step-by-step solution

Mass of the rod, m = 300 g = 0.3 kg Length of the rod, l = 50 cm = 0.5 m Angular speed, = 2 rad/s The moment of inertia of a uniform rod about an axis passing through one end and perpendicular to its length is: I = m l^2 3 Substituting the given values: I = 0.3 (0.5)^2 3 = 0.1 0.25 = 0.025 kg m ^2 The rotational kinetic energy of the rod is given by: K = 1 2 I ^2 Substituting the values of I and : K = 1 2 0.025 (2)^2 K = 0.025 2 = 0.05 J