## Angular Acceleration Definition

Angular acceleration is the rate of change of angular velocity with time of an object in motion. Acceleration is the change in velocity of moving object in respect to time. If the object moves on a circular direction than its velocity is called as angular velocity.

The angular acceleration is also known as rotational acceleration. It is a quantitative expression of the change in angular velocity per unit time. The acceleration vector, magnitude or the length is directly proportional to the rate of change in angular velocity.

## Units of Angular Acceleration

The angular acceleration vector direction is perpendicular to the plane where the rotation takes place. Increase in angular velocity clockwise, then the angular acceleration velocity points away from the observer. If the increase in angular velocity counterclockwise, then the vector of angular acceleration points toward the viewer.

The amount of angle covered per square of time is measured in radians per second squared. The angular acceleration unit is degrees/square of time like s^{2}, min^{2}, hr^{2}.

In SI units, it is measured in radians per second squared (rad/s^{2}), and is usually denoted by the alpha (α).

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The angular acceleration can also be defined as either:

\(\large \alpha = \frac{d \omega }{dt} = \frac{d^{2}\theta }{dt^{2}}\)

Or

\(\large \alpha = \frac{a_{T}}{r}\)

Where,

ω = Angular Velocity

a_{T} = Linear Tangential Acceleration

r = Radius of Circular Path

## Angular Acceleration Formula

The rate of change of angular velocity regarding time is angular acceleration, which is a vector quantity. It is denoted by α. The angular acceleration formula is given by,

\(\large \omega = \frac{\theta }{t}\)

Where,

ω = Angular Velocity

θ = Angle Rotated

t = Time Taken

When the angular velocity is constant, the angular acceleration is 0. If the velocity is not constant, then the constant angular acceleration α is defined as:

\(\large \alpha = \frac{\omega }{t} = \frac{\theta }{t^{2}}\)

If the angular acceleration is not constant and differs time to time, then:

\(\large \alpha _{av} = \frac{\left ( \omega _{2}-\omega _{1} \right )}{\left ( t_{2}-t_{1} \right )}\)

And

\(\large \alpha _{i} = \frac{d\omega }{dt} = \frac{d^{2}\theta }{dt^{2}}\)

The Earth takes 23 hours and 56 minutes to complete one revolution, and rotates at angular velocity of 7.2921159 × 10^{–}^{5}radians/second.

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