In a circular motion, we usually associate the term “acceleration” with radial and tangential acceleration. This type of acceleration measures how quickly a tangential velocity changes. It acts in a perpendicular direction to the centripetal acceleration of a rotating object. Tangential acceleration is defined as the rate of change in the tangential velocity of the matter in the circular path. In this article, we derive the formula for tangential acceleration.
Tangential acceleration definition
Tangential acceleration can be defined as the change in velocity taking place tangentially in a circular motion.
Tangential acceleration formula
It is represented mathematically as,
at = v2 – v1 / t2-t1 ——————-(1)
Where a is given as the tangential component
t = t2-t1 is the time period
and v1 and v2 are the respective velocities of two objects
The unit is represented as ms-2
Other forms of the formula for tangential acceleration
Using the basic formula of physics, we can convert equation (1) in terms of distance as:
Again, using the formula speed = distance by time:
Tangential acceleration formula in terms of velocity and distance.
Numerical problems on Tangential acceleration
A boy is running at a speed of 10 km/h in a uniform circular path, and he tries to accelerate to a speed of 20 km/h(double his current speed). Calculate the tangential acceleration required to achieve this in 30 seconds.
at = v2 – v1 / t2-t1 (Formula for tangential acceleration)
Here, the change in velocity is 10 km/h(2.77m/s), and the time taken is 30 seconds. Using the formula for tangential acceleration we have:
at = 2.77/30 = 0.092 m/s
So, the tangential acceleration for a velocity change of 10 km/h in 30 s is 0.092 m/s.
A cow moving in a uniform circular path has a tangential acceleration of 1 m/s. Find the velocity change it can achieve in 1 minute.
Again using the formula for tangential acceleration (at = v2 – v1 / t2-t1) we have :
1 = v2 – v1 / 60.
Therefore the change in velocity that can be achieved by the cow is 60 m/s or 216 km/h(which is practically impossible! :))
