# Tangential Acceleration Formula

Tangential acceleration concept is applied to measure how the tangential velocity of a point at a certain radius changes with time. Tangential acceleration is similar to linear acceleration but specific to the tangential direction which relates to circular motion.

In other words, the rate of change of tangential velocity of a particle in a circular orbit is known as Tangential acceleration. It directs towards tangent to the path of the body.

Tangential acceleration formula is expressed as

$a_{t}=\frac{d\mid&space;v\mid&space;}{dt}$

Where

at = tangential acceleration,

dv = change in angular velocity,

dt = change in time.

Tangential acceleration in terms of distance is given by,

$a_{t}=\frac{d^{2}&space;s&space;}{dt^{2}}$

Or

$a_{t}=v\frac{dv&space;}{ds}$

Where,

v = linear velocity,

s = distance covered,

t = time taken

Tangential acceleration formula is applied to calculate the tangential acceleration and the parameters related to it.

It is expressed in meter per sec square (m/s2).

Example 1: A body accelerates uniformly on a circular path with a speed of 30 m/s to 70m/s in 20s. Calculate its tangential acceleration.

Solution:

Given:

Initial velocity vi = 30 m/s,

Final velocity vf = 70 m/s,

Change in velocity dv = vf – vi = 70 – 30 = 40 m/s

Time taken dt = tf – ti = 20 – 0 = 20s

The tangential acceleration is given by at = dv / dt

= 40 / 20

= 2 m/s2.

Example2:

A runner starts from rest and accelerates at a uniform rate 10m/s in the time interval of 5s, running on a circular track of radius 50m. Determine the tangential acceleration.

Solution:

Given:

Initial velocity vi = 0,

Final velocity vf = 10 m/s,

Change in velocity dv = vf – vi = 10 – 0 = 10 m/s

Time taken dt = 5s

The tangential acceleration is given by at = dv / dt

= 10 / 5

= 2m/s.