Calculating Tangential Acceleration on a Curve
In physics, tangential acceleration is a measure of how the tangential velocity of a point at a certain radius changes with time. Tangential acceleration is just like linear acceleration, but it’s specific to the tangential direction, which is relevant to circular motion. You start with the magnitude of the angular acceleration,
which tells you how the speed of the object in the tangential direction is changing.
For example, when you start a lawn mower, a point on the tip of one of its blades starts at a tangential velocity of zero and ends up with a tangential velocity with a pretty large magnitude. So how do you determine the point’s tangential acceleration? You can start with the following equation, which relates velocity to acceleration
Tangential velocity, v, equals
so you can plug in this information in the previous equation to relate the tangential acceleration to the change in angular velocity:
Because the radius is constant here, the equation becomes
the angular acceleration, so the equation becomes
Translated into layman’s terms, this says tangential acceleration equals angular acceleration multiplied by the radius.