Newton's Laws of Motion: Translation & Angular Forms, Assumptions & Equivalence

[Lil Frank]

please write down the three Newton's laws of motion in both translation and angular forms, including their "equivalent" expressions of Newton's second law. what are the assumptions for their application in classic mechanics? are those "equivalent" forms really equivalent? why?

this is from my mid-term. i don't know how to answer this though it seems simple. in fact, i don't really understand what the question is about. especially the ""equivalent" part.
can anyone please help me with it? Thank you.

 

[olgranpappy]

I think they mean that they want you to explain why there is an angular "equivalent" of
$$F=ma$$

which looks like

$$T=I\alpha$$

 

[Senjai]

theirs also
$$I = F \Delta t$$

in relation to momentum and

$$E_k = \frac{1}{2}mv^2$$

as it derives from F = ma, so it would be 2nd law in terms of energy.