Angular Acceleration Calculator

This calculator finds the angular acceleration of a spinning object, which is the rate of change of it's angular velocity with respect to time. The angular acceleration is commonly calculated when a torque is applied to an object. 
CalculationInputs﻿﻿T
:20.00N m​
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﻿﻿I
:2.00kg/m2​
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Output﻿﻿α
:10rad/s^2​
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α=TIα = \dfrac{T}{I}α=IT​
Where:
﻿﻿T
 is the total torque, which is the rotational or twisting force required to rotate an object about an axis, pivot, or fulcrum ﻿(Nm)
﻿
﻿﻿I
 is the moment of inertia, which is a geometric property of an object that tells us how well it can resist angular acceleration. This is based on how far the object's mass particles are distributed from the axis of rotation ﻿(kg/m2)
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﻿﻿α
 is the angular acceleration, which is the rate of change of an object's angular velocity with respect to time ﻿(rad/s)
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ExplanationAngular acceleration of a spinning object is the rate of change of it's angular velocity with respect to time. It is commonly calculated when a torque is applied to an object. 
Torque, ﻿T
 is a twisting force that causes an object to rotate. Torque is a vector quantity that requires both magnitude and direction to define it. The magnitude is given by ﻿T=Frsinθ
 where ﻿F
 is an applied force and ﻿r
 is the radius from the axis of rotation. The direction is determined using the right-hand rule as per the below figure: curl the four fingers of your right hand in the direction of rotation and your thumb is pointing in the direction of ﻿T
.
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Right-hand rule to determine the torque vector direction.
When the torque of an object is constant its angular acceleration is also constant. The constant angular acceleration, ﻿α
 can be calculated by the ratio of the total torque of the object, ﻿T
 to its moment of inertia, ﻿I
 and is given by:
﻿
α=TIα = \dfrac{T}{I}α=IT​
The figure below shows the direction of the angular acceleration and torque due to an applied force, creating a counterclockwise angular acceleration about the rotational axis and a positive torque.
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Direction of angular acceleration with respect to an applied force and the torque.
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Related ResourcesAcceleration vs. Velocity equations
Angular Velocity Calculator
Centripetal Force Calculator
Force Due To Acceleration
Rotational Kinetic Energy Calculator
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