- #1

- 1,170

- 3

Consider a rotating body with an angular acceleration α. There must be a tangential force component if it is rotating:

For a general point on the body we can write:

Ftan = mi * ai = mi * ri * α (1)

Multiply by ri and sum up you get:

Ʃτ = Iα (2)

I just don't understand why you multiply by ri and thus force yourself to work with "torques" rather than just forces:

Why don't you just sum the equation for a single point (1). Then you get:

ƩFtan = Ʃmiri * α

Then you could call Ʃmiri whatever you like, not the center of mass though since the ri are not vectors.

But then doing that must be wrong. Because then it seems like you lose that part in (2), which says that the acceleration is bigger the further away from the centre of rotation you apply your force. So what is wrong with my version, i.e. equation (3)?

Also I have now struggled alot with rotating bodies, but one question always pops into my mind: Can you prove that rotation exists mathematically, or does all these mathematical derivations for rotating bodies just assume that you physically can observe rotations in nature. hmm.. maybe this last question doesn't make sense for you, and so if not, don't bother answering it.

Cheers :)