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.