Calculate the rotational inertia of a wheel that has a kinetic energy of 41.6 kJ when rotating at 264 rev/min.
To calculate the rotational inertia of a wheel, you can use the formula:
Rotational Inertia (I) = (Kinetic Energy (K) * 60^2) / (2 * π * n^2)
where K is the kinetic energy in joules, n is the rotational speed in revolutions per minute (RPM), π is a mathematical constant approximately equal to 3.14159, and 60^2 is used to convert RPM to seconds.
Let's plug in the values given:
K = 41.6 kJ = 41.6 * 1000 J
n = 264 RPM
Substituting these values into the formula:
I = (41.6 * 1000 J * 60^2) / (2 * π * 264^2 RPM^2)
Now, we can simplify and evaluate this equation to find the rotational inertia of the wheel.