We have already shown that the KE of a body is
given by mv2/2.
What if the object is spinning?
Spinning is moving, so there must be such a thing
as rotational KE. (KErot).
Remember that v=rw
Replace "v" with "rw". and arrive at KErot= mr2w2/2
Strange thing... different objects behave differently. It seems to depend on how the mass is distributed in the object; a dumbbell takes a different amount of energy to spin than a solid sphere, even if their masses and radii are the same.
So we have to modify the equation above. Since KErot depends on the mass and radius of the object, the "mr2" term can be different for differently shaped objects. Also, mr2 is referred to as the "moment of inertia" and is abbreviated I.
Our new equation is...KErot= Iw2/2
The moment of inertia for
several shapes are given below...
| SHAPE | I |
| dumbbell | mr2 |
| hoop/ring | mr2 |
| disc | mr2/2 |
| sphere | 2mr2/5 |
| rod (with axis perpendicular to rod Length) | mL2/12 |