Angular Acceleration

Angular acceleration is a vector, having both magnitude and direction. How do we denote its magnitude and direction? Illustrate with an example.

Solution

The magnitude of angular acceleration is $\alpha$ and its most common units are $\mathrm{rad} / \mathrm{s}^{2}$. The direction of angular acceleration along a fixed axis is denoted by $\mathrm{a}+$ or $\mathrm{a}$ - sign, just as the direction of linear acceleration in one dimension is denoted by a + or a - sign. For example, consider a gymnast doing a forward flip. Her angular momentum would be parallel to the mat and to her left. The magnitude of her angular acceleration would be proportional to her angular velocity (spin rate) and her moment of inertia about her spin axis.