Angular acceleration is a fundamental concept describing the rate at which the angular velocity of an object changes over time. Angular acceleration is denoted by the symbol “α” (alpha) and is mathematically defined as the change in angular velocity divided by the change in time. It is expressed in units of radians per second squared (rad/s²).

Angular Acceleration Formula :

The Formula for angular acceleration is :

Angular Acceleration = (Final Angular Velocity – Initial Angular Velocity) / Time

Angular velocity represents the rate at which an object rotates and is measured in radians per second (rad/s). To understand angular acceleration using velocity and time, it’s essential to recognize that changes in angular velocity occur due to external torques applied to the rotating object.

If an object’s angular velocity increases over time, the angular acceleration is positive, indicating that the object is experiencing a net torque causing it to rotate faster. Conversely, if the angular velocity decreases, the angular acceleration is negative, signifying a torque opposing the rotation.

Angular Acceleration Units:

Angular acceleration is typically measured in units of radians per second squared (rad/s²). The unit “radian” represents the angle subtended when the length of an arc equals the radius of the circle. Therefore, when angular acceleration is expressed in radians per second squared, it signifies the change in angular velocity per unit time, specifically in terms of radians.

The formula for angular acceleration is :

Angular Acceleration = (Final Angular Velocity – Initial Angular Velocity) / Time

If the units of angular velocity are in radians per second (rad/s), and the units of time are in seconds (s), then the units of angular acceleration will be: (rad/s²)

This unit represents the rate of change of angular velocity per unit time and is widely used in physics and engineering when dealing with rotational motion. It provides a standardized measure for quantifying how quickly the rotational speed of an object is changing.

Angular Acceleration Using Moment of Inertia and Torque :

Certainly, angular acceleration can also be determined using the moment of inertia and torque acting on a rotating object. The relationship between these quantities is described by Newton’s second law for rotational motion:

Torque = Moment of Inertia x Angular Acceleration

So rearranging the formula to solve for angular acceleration, we get:

Angular Acceleration = Torque / Moment of Inertia

Angular Acceleration Calculator with Moment of Inertia and Torque

How an Angular Acceleration Calculator Works: A Step-by-Step Example

Question:

A rotating object has an initial angular velocity of 32 rad/sec. Over a period of 42 seconds, it undergoes a change in angular velocity, reaching a final angular velocity of 422 rad/sec. Determine the angular acceleration experienced by the object during this time interval.

Answer:
Given:
  • Initial Angular Velocity : 32 (rad/sec)
  • Final Angular Velocity : 422 (rad/sec)
  • Time : 42 (sec)
Calculate angular acceleration using the formula:

Angular Acceleration = (Final Angular Velocity – Initial Angular Velocity) / Time
Angular Acceleration = (422 – 32) / 42
Angular Acceleration = 9.285714 rad/s²
Result :
The angular acceleration of the rotating object during this time interval is approximately 9.2857 rad/sec².

Why to use our Angular Acceleration Calculator?

Our Angular Acceleration Calculator Using Velocity and Time provides a quick and efficient way to determine angular acceleration based on the given velocity and time parameters. This tool is invaluable for engineers, physicists, students, and enthusiasts working with rotational motion and dynamics.

Our calculator simplifies complex calculations, saving valuable time and effort while ensuring accuracy. It promotes productivity and facilitates precise decision-making in designing, analyzing, and optimizing systems involving rotational motion. Whether for academic, professional, or practical purposes, our Angular Acceleration Calculator Using Velocity and Time is an essential tool for anyone dealing with rotational dynamics.