Angular Acceleration Formula with Solved Examples

Angular Acceleration Formula

Angular acceleration is the acceleration with a certain angle, and acceleration is the rate of change of velocity concerning time.

Angular acceleration for any object adopting circular motion can be defined as the change in the rate of the angular velocity over time.  Another name for Angular acceleration can be given as rotational acceleration. Angular acceleration is the vector quantity, which means it has both magnitude and ion.

Some specific symbols denote Angular acceleration, that is, α, and it is expressed as the units equal to rad/s2 or, in terms, radians per second square.

Formula:

Expression of Angular acceleration can be written as  below,

α = Δω / Δt

Where, α = Angular acceleration

             ω = Angular Velocity

And also, twice the differentiation of angular displacement is equal to angular acceleration.

Derivation:

The rate at which angular velocity changes to the time is known as angular acceleration, or it can be written as, 

α= dω/dt 

Here, α is called angular acceleration, which we have to calculate in terms of the rad/s2, ω is called angular velocity, which is given in terms of rad/s, and t is said to be the time taken that is expressed in terms of seconds.

The expression of angular velocity can be written as:

ω = v/r

Here, ω is called angular velocity and expressed in terms of rad/s, v is the linear velocity, and r is the radius of the path.

The change of angular displacement concerning the time is known as angular velocity, as below.

ω = θ/t

 Where θ is said to be the angular rotation of any object and t is the total time taken.

Using the formula above, angular acceleration α can be written as

α = d2θ / dt2

Solved Examples

1. An animal is sitting at the edge of a rotating circular disc. Its angular velocity changes at the rate of 50 rad/s for 5 seconds. Calculate its angular acceleration during this time?

Given: The change in angular velocity is equal to dω = 50 rad/s. The time for this change to occur is equal to t = 5s.

Using the formula for the angular acceleration also substituting the values above given, we get,

 α = dω/dt = 50/5 = 10 rad/s2

1. The rear wheel of a motorcycle has an angular acceleration of 10 rad/s2 in a second. What can be said about its angular velocity?

Given: The angular acceleration of the wheel is equal to α = 10 rad/ s2

 Time is taken t = 1 s, 

According to the formula for angular acceleration,

α = dω/dt

Upon substituting the values, we get,

Angular velocity d is

dω = αdt

dω =10×1 = 10 rad/s