Fundamentals of Biomechanics by Nihat Özkaya

Author:Nihat Özkaya
Language: eng
Format: epub
Publisher: Springer International Publishing

Recall from Eq. (9.3) that . For a circular motion, radius r is constant and Eq. (9.9) can be evaluated as follows:

By definition, time rate of change of angular displacement is angular velocity. Therefore:

(9.15)

Equation (9.15) states that the magnitude of the linear velocity of a point in a body that is undergoing a rotational motion about a fixed axis is equal to the distance of that point from the center of rotation multiplied by the angular velocity of the body. Notice that at a given instant, every point on the body has the same angular velocity but may have different linear velocities. The magnitude of the linear velocity increases with increasing radial distance, or as one moves outward from the center of rotation toward the rim.

Using the relationship given in Eq. (9.15), Eq. (9.10) can be evaluated for a motion in a circular path as follows:

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