Thread: Angular displacement, Angular velocity

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 to distance traveled 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 = v²/r
w = v/r (linear - angular velocity rearranged)
a_c= (v/r)²/r
a_c= v²/r<sup>3

TBH i don't think this last derivation is logical.

Sorry about the previous font size.</sup>

Originally Posted by Subliminal

^{Sorry about the previous font size.}

The previous font size? What about the current size? Just use the regular font size. As it is, it's unreadably large on my screen.

Originally Posted by MagiMaster

Originally Posted by Subliminal

^{Sorry about the previous font size.}

The previous font size? What about the current size? Just use the regular font size. As it is, it's unreadably large on my screen.

Oh sorry, how about now?

Thanks. That's much more readable. Unfortunately, I can't comment too much on the content of your post as it looks like you haven't defined some of your variables (though those might be standard variables I'm just not familiar with).

oh sorry.

R is radius, alpha is angular acceleration, ac is centripetal acceleration, w is angular velocity.

v = r*w would then be a way of converting instantaneous angular velocity (in radians per second) to instantaneous linear velocity. So if you keep the angular velocity the same and increase the radius, the object will cover more distance in the same time. The equation is valid at any one instant, so it's also valid if all of those numbers are kept constant.

You've defined both a and alpha as angular acceleration, so there's some confusion there.