Kinetic energy of a rotating bar with varying speed along its length

[swechan02]

What would be the kenetic energy, it the bar is rotating? But it has different speed along it's mass. Need to use calculas?

 

[Tide]

The short answer is "yes." You can roll it all up into a single package if you know (or can calculate) the moment of inertia about the axis of rotation in which case the rotational energy is $\frac {1}{2} I \omega^2$