I got a test back and the teacher marked my entire answer wrong because to get the kinetic energy, I used the moment of inertia which included the parallel axis theorum to account for where it's rotating. The teacher says rotational energy is not affected by where the centre of rotation is (meaning the parallel axis theorum should not be used), yet I think he's wrong and intend to prove it. Since I can't use any energies which are based on "I", I made 2 examples where I calculate the instantaneous kinetic energy of a rotating bar based on (1/2)mv^2 where v = wr. Please have a look at my work and tell me what you think. small letters imply variables in an equation, capital letters mean substituted values. For example, the formula may ask for m, but if the value for m is half the mass, the subbed in value will be M/2. For the first case, I based the mass at the centre of mass. For the second question, I broke the piece into 2 separate pieces, which is why there are 2 centres of mass and the formula is multiplied by 2. http://myfiles.dyndns.org/math/rotation_kinetic1.jpg I tend to skip a lot of steps so if you don't understand why something was done, please ask. http://myfiles.dyndns.org/math/rotation_kinetic2.jpg On this one I calculated the different I values. One of them is just Ic, one of them includes the parallel axis theorum. For the examples, the one with the parallel axis of rotation has 4x as much energy. That same example has an I value 4x as big. Coincidence? HA! So what do you think? Am I wrong or is my teacher wrong?