Angular Acceleration Calculator
What is Angular Acceleration?
Angular acceleration (denoted by the Greek letter alpha, α) represents how quickly an object’s rotational speed changes. Just as a car accelerating increases its speed in meters per second, a spinning wheel accelerating increases its rotation speed in radians per second.
How to Calculate It
Our calculator supports the three most common physics scenarios:
- By Velocity: If you know how fast it started spinning, how fast it ended, and the time it took.
Formula: α = (ω₂ – ω₁) / t - By Dynamics: If you know the force (Torque) twisting the object and the object’s resistance to motion (Inertia).
Formula: α = τ / I (Newton’s Second Law for Rotation) - By Geometry: If you know the linear acceleration at the edge of the circle and the radius.
Formula: α = aₜ / r
Common Units
The standard SI unit is radians per second squared (rad/s²). However, engineers often work in RPM/s (Revolutions Per Minute per second). This tool automatically converts your inputs (like RPM or Degrees) into standard units for calculation.
Junaid Ahmed
A high school teacher with ten years of experience and a lifelong love for physics. Holds a Bachelor of Engineering in computer science and enjoys making scientific ideas simple, clear, and engaging. Quiet by nature, but fully expressive when exploring motion, energy, and the wonders of the physical world.
Overview
This visualization provides a simplified explanation of the concept of angular momentum. Angular momentum is a fundamental concept in physics, representing the rotational equivalent of linear momentum. Essentially, it quantifies the amount of rotation an object has, considering its mass, shape, and speed of rotation.
Rotating Object
At the top, a simple diagram illustrates the concept with a red sphere. This sphere is shown rotating around a vertical axis, indicated by the straight line passing through it. The curved arrow around the sphere represents the direction of its rotation.
Direction of Angular Momentum
The straight arrow pointing downwards along the axis of rotation represents the direction of the angular momentum vector. According to the right-hand rule, if you curl the fingers of your right hand in the direction of the object’s rotation, your thumb will point in the direction of the angular momentum vector. In this case, the sphere’s rotation is such that the angular momentum vector points downward.
Angular Momentum Formula
Below the diagram is the mathematical formula for angular momentum. It is expressed as L = I × ω, where L represents the angular momentum vector, I is the moment of inertia, and ω is the angular velocity vector. This equation is a fundamental relationship in rotational dynamics.
Angular Velocity
The first term defined is ω, which stands for angular velocity. Angular velocity is a vector quantity that describes how fast an object is rotating or revolving relative to a point, along with the direction of the rotation. The magnitude of the angular velocity is the angular speed.
Moment of Inertia
The second term, I, represents the moment of inertia. The moment of inertia is a measure of an object’s resistance to changes in its rotational motion. It is the rotational analog of mass for linear motion and depends on the object’s mass and how that mass is distributed relative to the axis of rotation.