Why is rotational kinetic energy included in total energy of a rolling ball?

[mikefitz]

http://img207.imageshack.us/img207/5524/untitledll1.png

what I'm looking for is 1. the total energy of the sphere, and 2. the height of the ball after it has traveled up the incline.

i have some questions however. First, i understand that total energy = KE+PE. looking at the solution, KE=1/2mv^2. why does PE=1/1*Iw^2? this is the first time I've ever seen PE defined as such an equation.

in the second part of the solution, they use mgh - why isn't mgh used in the first solution? thanks

 

[radou]

i have some questions however. First, i understand that total energy = KE+PE. looking at the solution, KE=1/2mv^2. why does PE=1/1*Iw^2? this is the first time I've ever seen PE defined as such an equation.

The term 'PE=1/1*Iw^2' you were referring to was supposed to be the rotational kinetic energy of the sphere, which equals 1/2 I w^2, so I assume it was a mistype. You're right - total energy is defined as the sum of potential and kinetic energy - but, since you have a rolling sphere, the kinetic energy is the sum of rotational and translational kinetic energy.