Average Angular Acceleration Calculator

This calculator determines the average angular acceleration over a specific period based on a specified initial and final angular velocity. Angular acceleration tells us the rate at which the angular velocity of a spinning object changes over time. 
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CalculationInputs﻿﻿ω1
:137,509.87 rpd​
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﻿﻿ω2
:68,754.94 rpd​
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﻿﻿Δt
:2.00 s​
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Output﻿﻿α
:-2.50 rad / s^2​
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α=ω2−ω1Δtα = \dfrac{\omega_2-\omega_1}{\Delta t}α=Δtω2​−ω1​​
Where:
﻿﻿α
 is the angular acceleration (﻿rad/s2
)
﻿﻿ω1​
 is the initial angular velocity ﻿(rad/s)﻿
﻿
﻿﻿ω2​
 is the final angular velocity ﻿(rad/s)﻿
﻿
﻿﻿Δt
 is the time period in seconds, over which the average angular acceleration is calculated ﻿(s)
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ExplanationAngular acceleration, ﻿α
 is a foundational concept in rotational motion that explains how quickly an object's angular velocity, ﻿ω
 changes with time, due to external forces. Angular velocity denotes the speed at which an object rotates around a fixed axis. When an object rotates, it experiences changes in its angular velocity, either speeding up or slowing down. Angular acceleration measures the rate of this change and provides critical insights into the dynamics of rotational motion.
Positive ﻿(+)
 angular acceleration means the object's rotation is accelerating, while negative ﻿(−)
 angular acceleration means it's decelerating. In the figure below, the left image shows positive angular acceleration while the right image shows negative angular acceleration.
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Rotational acceleration (left) and rotation deceleration (right).
Mathematically, we can define angular acceleration as the ratio of the change in angular velocity to the change in time. This is expressed as: 
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α=ΔωΔt=ω2−ω1t1−t2α= \dfrac{Δω}{Δt}= \dfrac{\omega_2-\omega_1}{t_1-t_2}α=ΔtΔω​=t1​−t2​ω2​−ω1​​
Where:
﻿﻿Δω
 is the change in angular velocity measured in radians per second (﻿rad/s
)
﻿﻿Δt
 is the change in time measured in seconds ﻿(s)
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ApplicationsAngular acceleration is crucial in real-world applications such as engineering and physics, where it helps analyse the motion of rotating machinery, celestial bodies and gyroscopes. Angular acceleration provides a quantitative measure of how an object's angular velocity changes, enabling scientists and engineers to understand and predict the behaviour of rotating objects in various contexts.
A lathe is one of many applications in the real world that may involve calculations of angular acceleration. The image below shows a lathe at high speed to bore a hole.
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A lathe used to bore a hole in cylindrical metal component (Source: MobilSpaw)
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Related ResourcesAngular Velocity Calculator
Centripetal Force Calculator
Mass moment of Inertia Calculator
Rotational Kinetic Energy Calculator
Check out our full library of CalcTree templates here!
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