Define Angular Acceleration:

Angular acceleration is a measure of how quickly the angular velocity of an object changes over time. It is influenced by both the moment of inertia and the torque applied to an object.

Moment of Inertia : Moment of inertia is a property of an object that describes its resistance to changes in rotation. It depends on both the mass distribution and shape of the object. The higher the moment of inertia, the more difficult it is to change the object’s angular velocity.

Torque : Torque is the rotational equivalent of force and is responsible for causing changes in angular motion. It can be determined by multiplying the force released and the distance from the rotational axis.

The relationship between angular acceleration, moment of inertia , and torque is given by Newton’s second law for rotational motion:

Torque = Moment of Inertia * Angular Acceleration

The above equation states that the torque applied to an object is equal to the product of its moment of inertia and angular acceleration. In practical terms, increasing the torque or reducing the moment of inertia will result in a higher angular acceleration, indicating a faster change in rotational motion.

Certainly! The angular acceleration of an object can be calculated using the moment of inertia and the applied torque :

Angular Acceleration Formula :

Angular Acceleration = Torque / Moment of Inertia

The above angular acceleration formula expresses the relationship between torque, moment of inertia, and angular acceleration. In simple terms, the angular acceleration of an object is directly proportional to the torque applied to it and inversely proportional to its moment of inertia. If you apply a greater torque or reduce the moment of inertia, the angular acceleration will increase, indicating a faster change in the object’s rotational motion.

Units in Angular Acceleration Calculator :

Angular Acceleration :
  • Unit: Radians per second squared (rad/s²).
  • Explanation: Angular acceleration represents the rate at which the angular velocity of an object changes over time. The unit reflects the change in radians of angular velocity per second squared.
Torque :
  • Unit: Newton-meters (N·m).
  • Explanation: Torque is the rotational equivalent of force. It is the result of multiplying the force by the perpendicular distance from the rotational axis. The unit is derived from the force unit (Newtons) multiplied by the distance unit (meters).
Moment of Inertia :
  • Unit: Kilogram-square meters (kg·m²).
  • Explanation: Moment of inertia is a measure of an object’s resistance to changes in its rotational motion. The unit is derived from the mass unit (kilograms) multiplied by the square of the distance unit (meters), reflecting the distribution of mass around the axis of rotation.

Angular Acceleration Using Velocity and Time :

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 :

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

Explore Further: Angular Acceleration Calculator with Velocity and Time

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

Question:

Suppose you have a wheel with a moment of inertia of 0.2 kg·m². A torque of 10 N·m is applied to the wheel. Calculate the angular acceleration .

Solution :

Calculate angular acceleration using the formula:

Angular Acceleration = Torque / Moment of Inertia

Angular Acceleration = 10 / 0.2

Angular Acceleration = 50.000000 rad/s²

Therefore, the angular acceleration of the wheel is 50 radians per second squared. This means that the wheel’s angular velocity is increasing at a rate of 50 radians per second for each second.