# Question Video: Calculating the Rotational Kinetic Energy of a Disk

A solid metal disk is rotating with an angular velocity of 15 rad/s. The disk has a moment of inertia of 4.0 kg.m² around its axis of rotation. What is the rotational kinetic energy of the disk?

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### Video Transcript

A solid metal disk is rotating with an angular velocity of 15 radians per second. The disk has a moment of inertia of 4.0 kilogram meter squared around its axis of rotation. What is the rotational kinetic energy of the disk?

In the problem, we are given angular velocity, moment of inertia, and asked to find the rotational kinetic energy. To solve the problem, we therefore need an equation that relates these three variables together. The rotational kinetic energy, 𝑘, of an object is equal to one-half 𝐼, the moment of inertia of the object, times 𝜔 squared, where 𝜔 is the angular velocity of the object. The question asked us to solve for the rotational kinetic energy of the disk. We therefore do not need to rearrange our formula to solve for our unknown variable.

Plugging in the values given to us in our problem, we have 4.0 kilogram meter squared for our moment of inertia and 15 radians per second for our 𝜔. When multiplying out our values, we have to be careful to make sure that we square our 15 radians per second before multiplying it by 4.0 kilograms meter squared and one-half. Multiplying out our values, we get a rotational kinetic energy of 450 joules. The rotational kinetic energy of the disk is 450 joules.