Need help understanding KE rotation

[kurosaki69]

i used the formula for KE rotation KE=(1/2)Iw^2 and i translated it to (1/2) v^2/r^2, but i wanted to know what does the v in the equation stand for. is it initial velocity or velocity of center of mass. if its is the velocity of center of mass can u tell me how to solve for it

 

[Doc Al]

Whether you know it or not, you made use of the relation $v = \omega r$, where v is the tangential velocity of some point on the rotating body and r is its distance from the axis.

 

[kurosaki69]

ok thanks a lot my other question is what if the rotating object was rolling down a incline and it started at rest. would the velocity be the velocity of center mass of the object that is being rolled.

 

[Doc Al]

Let's take an example: A wheel, with radius r, rolls without slipping along some surface. The speed of its center with respect to the surface will be equal to the tangential speed of its rim with respect to its center.