How is tangential acceleration calculated in circular motion?

Tangential acceleration in circular motion is calculated using the formula a = rα, where r is the radius and α is the angular acceleration.

Circular motion is the movement of an object along a circular path. Tangential acceleration is the acceleration of an object along the tangent to the circular path. It is caused by a change in the object's speed or direction. The magnitude of tangential acceleration can be calculated using the formula a = rα, where r is the radius of the circular path and α is the angular acceleration.

Angular acceleration is the rate of change of angular velocity. It is given by the formula α = Δω/Δt, where Δω is the change in angular velocity and Δt is the time taken for the change to occur. Angular velocity is the rate of change of angle with respect to time. It is given by the formula ω = Δθ/Δt, where Δθ is the change in angle and Δt is the time taken for the change to occur.

To calculate tangential acceleration, we need to know the radius of the circular path and the angular acceleration. Once we have these values, we can substitute them into the formula a = rα and calculate the tangential acceleration. For example, if the radius of the circular path is 2 metres and the angular acceleration is 3 radians per second squared, then the tangential acceleration is:

a = rα
a = 2 x 3
a = 6 metres per second squared

Therefore, the tangential acceleration in circular motion is 6 metres per second squared.