Angular displacement times r = |Linear displacement| (Intuitively I understand this but i can't put it into words, I know r*theata = L and if L = 0 then L after t seconds is the size of linear displacement t seconds after the object is released from the centripetal force)

Angular displacement over time = |Linear velocity| (as the size of the velocity is constant and acceleration only changes the direction of the object)

v = r*w, I would like to know what this means, when looking at a situation, what is the significance of it, can I express angular velocity in terms of angular velocity?

Is, that the tangential velocity of an orbiting object is equal todistancetraveled by the object over the time taken?

One more thing, I learned that tangential acceleration is related to angular acceleration in the following way.

a = r*alpha

I'm not sure what this means as I thought that linear (tangential) velocity had to be constant for v = r*w to be true, so how can tangential acceleration (which would break the current circular path)

Also expressing centripetal acceleration in terms of angular speed, I know how to do it, but i don't know what it means, it's significance.

Also this looks quite close to the derivation of Kepler's third law, i just did this while messing around with equations, it probably means nothing, who knows.

a_{c }= v^{2}/r

w = v/r (linear - angular velocity rearranged)

a_{c}= (v/r)^{2}/r

a_{c}= v^{2}/r^{3 TBH i don't think this last derivation is logical. Sorry about the previous font size.}