Hey JayDilla, I get 1/3. Here's how:
Kinetic energy due to linear motion is:
where
giving
The rotational part requires the moment of inertia of a solid cylinder
Then the rotational kinetic energy is
Adding the two types of energy and factoring out common terms gives
Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part. Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.
Kinetic energy due to linear motion is:
where
giving
The rotational part requires the moment of inertia of a solid cylinder
Then the rotational kinetic energy is
Adding the two types of energy and factoring out common terms gives
Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part. Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.