A CD is a solid disk of mass of 0.0140 kg and a radius 0.0600 m. It rotates at 31.4 rad/s. What is its ROTATIONAL KE?

Answer 1

Rotational kinetic energy is analogous to motional kinetic energy. Ke= 1/2 mv², in which mass is the resistance to motion -- the more mass an object has, the more kinetic energy is required to accelerate it to a desired speed. Similarly, for rotation, Ke=1/2 Iω², in which I is the moment of inertia of the object and ω is its angular velocity. The moment of inertia is an object's resistance to rotation, similar to how mass is an object's resistance to acceleration.

To calculate the kinetic energy required to rotate the solid disk at 31.4 rad/s, we must first gauge its moment of inertia. For a solid disk spun about its central axis perpendicular to the surface (i.e, the axis coming out of the center of the disk), the moment of inertia is equal to 1/2 mr².

Hence, plugging in to the initial equation, Ke = 1/2 (1/2 mr²)(ω²) = (1/4)(mr²ω²).

Plugging in the variables, Ke = 1/4 * 0.0140 kg * (0.06 m)² * (31.4 rad/s)².

Ke = 0.01242 J is the rotational kinetic energy of the given disk.