# Rotational motion (confused about the variables)

we have many accelerations in rotational motion ,and I don't know the difference between them. first the linear acceleration which as I understand is the vector acceleration which has the same direction as the change of velocity and it affects the speed and direction then it's two components are centripetal acceleration which changes the angle and is towards the center and it doesnt change the magnitue of the velocity. Then there is the tangential acceleration which is perpendicular to the centripetal acceleration and it increases the magnitude of the velocity.
First is my understanding of the acceleration correct ? second I also see that we have the angular acceleration and it changes the the the angular velocity but this confuses me what is the difference between it and the centripetal acceleration? they both change the angle.

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Doc Al
Mentor
Here's how I'd put it. Something moving in a circle has a linear (or translational) acceleration. That acceleration has two components: a centripetal component and a tangential component.

What is usually called the angular acceleration is the rate of change of angular speed. The angular speed relates to the tangential speed via: ω = r*vt. In turn, the angular acceleration relates to the tangential acceleration via: α = r*at.

Does that help?

but what I don't understand is whether the centripetal acceleration and the angular acceleration are measuring the same thing or not? I mean they all affect the change of the direction of the velocity right?

Doc Al
Mentor
but what I don't understand is whether the centripetal acceleration and the angular acceleration are measuring the same thing or not?
No. Centripetal acceleration is the rate of change in linear velocity (for constant speed). Angular acceleration is the rate of change of the angular speed. For something moving with constant speed, there will be a non-zero centripetal acceleration while the angular acceleration will be zero.

No. Centripetal acceleration is the rate of change in linear velocity (for constant speed). Angular acceleration is the rate of change of the angular speed. For something moving with constant speed, there will be a non-zero centripetal acceleration while the angular acceleration will be zero.
oh thanks I see it now but if angular acceleration is the rate of change of angular speed then what is the rate of change of angular velocity?

Doc Al
Mentor
oh thanks I see it now but if angular acceleration is the rate of change of angular speed then what is the rate of change of angular velocity?
As long as the axis of rotation doesn't change, as when you stick to two dimensions, angular speed and velocity are the same (for practical purposes). When you deal in three dimensions, and the axis of rotation can change, things get complicated fast. Angular velocity is a vector (pseudovector, really) whose magnitude is the angular speed and whose direction is along the axis of rotation. See: http://en.wikipedia.org/wiki/Angular_velocity" [Broken]

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but isnt the rotation negative if it is clockwise?

Doc Al
Mentor
but isnt the rotation negative if it is clockwise?
That's the convention, sure.