Tangential Acceleration Formula

We shall apply the concept of tangential acceleration in measuring the change of the tangential velocity of a point with a given radius as a function of time. The linear and tangential accelerations are equal but in the tangential direction, results in circular motion .

Definition

Tangential acceleration is defined as the rate of change of velocity of a particle moving in a circular path, changing tangentially. Acceleration is tangential to the circle at the point where the particle is moving.

Formula

Tangential Acceleration Formulas in Terms of Distance

Notations Used in the Formula

• at is the tangential acceleration

• Δv is the variation of the angular velocity

• Δt is the variation of time

• v is the linear velocity

• s is the distance covered

• t is the time taken

The formula of tangential acceleration is used to determine the tangential acceleration along with other related parameters and the unit is m/s2.

Linear Acceleration Formula

Linear acceleration can be defined as the uniform acceleration caused by a moving body in a straight line. There are three equations that are crucial in linear acceleration depending upon the parameters like initial and final velocity, displacement, time and acceleration .

Following is the table that explain all the three equations which are used in the linear acceleration:

First equation of motion

v=u+at

Second equation of motion

The third equation of motion

Notations Used In The Formula

• u is the initial velocity

• a is the acceleration

• t is the time taken

• v is the final velocity

• s is the acceleration

Solved Example

Example 1: A body has uniform acceleration in a circular path with a velocity of 20 m / s to 80 m/s in 30s. Calculate the acceleration is tangential to it.

Solution:

Given,

vi = 20 m/s

vf = 80 m/s

dv = vf – vi

    = 80 – 20 

    = 60 m/s

dt= tf – ti 

   = 30 – 0 

   = 30sec 

Tangential acceleration formula          

 at=dv/dt          

 at=60/30      

 at=2m/s2