Rotational Inertia of a centrifuge?

Question

A centrifuge has a rotational inertia of 6.66 X10^ -3 kg·m^2. How much energy must be supplied to bring it from rest to 458 rad/s?

Answer 1

The Kinetic Energy of a rotating body is given as,
KE = 1/2 I * ω^2
Where I is the rotational inertial of the body, and ω (Greek letter, lowercase, Omega) is the angular velocity the object.
In order to increase an object’s angular velocity, work must be done. The amount of work which must be done is equal to the change in rotational kinetic energy of the object.

In the question you are explicitly told what the value of the rotational inertia is as well as what the final angular speed of the object is, you can therefore plug those values into the formula and find the energy which must be spend in order to achieve this.

KE = 1/2 6.66 X10^ -3 kg•m^2 * (458 rad/s)^2
KE = 698.5 Joules