Angular Position, Velocity, Acceleration

The angular position of a point object provides the rotational location of the point object around a given axis of rotation. Now, the linear position is measured in a linear method(as suggested) kind of like an x-axis or number line. However, the angular position is measured by the location on a given circle of rotation. Because of this, we measure angular position in radians(or degrees).

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Angular displacement is the change in an object's angular position, given by Δϴ(the final angle - the initial position). Angular displacement is a vector and is measured in radians or degrees. The relation between angular displacement and linear displacement is given by:

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Keep in mind that this minds the angle in radians only. If you want to convert radians to revolutions, you just divide radians by 2π.

Angular velocity is defined as the rate of change of an object's angular position with respect to time, also seen as the derivative of angular position with respect to time. The most intuitive definition of angular velocity is, of course, known as rotation rate. It's also a vector which means it has rotational direction and magnitude.

Above are the mathematical definitions for the angular velocity of an object. ​

If you take this arc length formula and divide it by the change in time, you get the relation below between linear and angular velocity.

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In practice, however, angular velocity is independent of radius. If we take a rotating wooden disk and track the angular velocity of an object close to the center and the angular velocity of an object on the edge, they're both the same. They both rotate the same amount of radians so just because one is closer than the other doesn't mean it's rotating faster.

Angular acceleration is the derivative of angular velocity with respect to time. It is related to the tangential acceleration(linear acceleration) in the same way that angular velocity and position are related to their linear cousins.

​This is pretty much all there is to position, velocity, and acceleration in terms of rotational motion. One thing to keep in mind is that these relations are all approximated to circular paths as calculus would be required if the radial vectors were variant.