Solved Examples on Tangential Acceleration

Example 1: Calculate the tangential acceleration if an object is undergoing circular motion for radius 5 m and angular acceleration 2 rad/s². 

Solution:

We have,

r = 5

α = 2

Using the formula we get,

 a_t = r α

= 5 (2)

= 10 m/s²

Example 2: Calculate the tangential acceleration if an object is undergoing circular motion for a radius of 12 m and angular acceleration of 0.5 rad/s².

Solution:

We have,

r = 12

α = 0.5

Using the formula we get,

a_t = r α

= 12 (0.5)

= 6 m/s²

Example 3: Calculate the angular acceleration if an object is undergoing circular motion for radius 20 m and tangential acceleration 40 m/s².

Solution:

We have,

r = 20

a_t = 40

Using the formula we get,

a_t = r α

α = a_t/r

= 40/20

= 2 rad/s²

Example 4: Calculate the angular acceleration if an object is undergoing circular motion for radius 2 m and tangential acceleration 20 m/s².

Solution:

We have,

r = 2

a_t = 20

Using the formula we get,

a_t = r α

 α = a_t/r

= 20/2

= 10 rad/s²

Example 5: Calculate the radius if an object is undergoing circular motion for an angular acceleration of 4 rad/s² and tangential acceleration of 20 m/s².

Solution:

We have,

α = 4

a_t = 20

Using the formula we get,

a_t = r α

r = a_t/α

= 20/4

= 5 m 

Tangential acceleration is the rate at which a tangential velocity varies in the rotational motion of any object. It acts in the direction of a tangent at the point of motion for an object. The tangential velocity also acts in the same direction for an object undergoing circular motion. Tangential acceleration only exists when an object travels in a circular path. It is positive if the body is rotating at a faster velocity, negative when the body is decelerating, and zero when the body is moving uniformly in the orbit.