Suppose a disk with constant angular velocity has rotational kinetic energy 1250 J. If its angular velocity is 24 rad/s, then what is its moment of inertia?
To find the moment of inertia of a disk, we can use the formula:
Rotational kinetic energy = (1/2) * moment of inertia * angular velocity^2
Using the given values:
Rotational kinetic energy = 1250 J
Angular velocity = 24 rad/s
Substituting the values into the formula, we get:
1250 J = (1/2) * moment of inertia * (24 rad/s)^2
To find the moment of inertia, we need to rearrange the formula. Divide both sides of the equation by (1/2) * (24 rad/s)^2:
moment of inertia = 1250 J / [(1/2) * (24 rad/s)^2]
Simplifying the denominator:
moment of inertia = 1250 J / [(1/2) * 576 rad^2/s^2]
moment of inertia = 1250 J / (288 rad^2/s^2)
moment of inertia = 4.34 kg·m^2
Therefore, the moment of inertia of the disk is 4.34 kg·m^2.