Angular Acceleration Formula

Angular Acceleration Formula

Angular acceleration is defined as the rate at which angular velocity changes over time. It is a pseudovector in three dimensions. The SI unit of measurement is radians/second squared (rad/s2). Moreover, we commonly represent it by the Greek letter alpha α. Learn about the angular acceleration formula here.

What is Angular Acceleration?

The angular velocity of an object in circular motion varies with time, and this variation in angular velocity is known as angular acceleration. It is a vector quantity with magnitude and direction, commonly known as rotational acceleration. It may be defined as the temporal rate of change in angular velocity.

Angular Acceleration is usually expressed in radians per second whole square. Thus,

α = dω / dt

α is the angular acceleration
ω is the angular velocity
t is the time taken by the object

If angular displacement θ is given then the angular acceleration is calculated as,

α = d2θ/dt2

Angular Acceleration Types

There are mainly two types of Angular Acceleration-

  • Spin Angular Acceleration.
  • Orbital angular acceleration

These two indicate the temporal rate of change in spin angular velocity and orbital angular velocity, respectively. Unlike linear acceleration, rotational acceleration does not have to be generated by the following external torque. A figure skater, for example, can quickly speed up his or her spin (and so acquire angular acceleration) by squeezing his or her arms inwards, with no personal torque required.

Angular Acceleration Formula Derivation

Suppose an object is doing circular motion with a linear velocity v, angular velocity ω on a circular path of radius r in time t. Now, we know the angular acceleration of an object is the first derivative of its angular velocity with respect to time. So we get,

α = dω/dt   ……. (1)

Also we know that the angular velocity of an object is the first derivative of its radius with respect to time.

ω = dθ/dt   ……. (2)

Substituting (2) in (1) we get,

α = d(dθ/dt)/dt

α = d2θ/dt2

This derives the formula for angular acceleration.

Angular Acceleration Solved Examples

Example 1: Find the angular acceleration of an object if its angular velocity changes at the rate of 100 rad/s for 10 seconds.

Solution: dω = 100

dt = 10

Using the formula we have,

   = 100/10
= 10 rad/s2

Example 2: Calculate the angular acceleration of an object if its angular velocity changes at the rate of 124 rad/s for 4 seconds.

Solution: dω = 124

dt = 4

Using the formula we have,

α = dω/dt
= 124/4
= 31 rad/s2

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Momentum Formula Average Force Formula
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Torque Formula Deceleration Formula
Displacement Formula Drag Force Formula
Kinetic Energy Formula Elastic Collision Formula
Potential Energy Formula Electrical Resistance Formula

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