Equation For Angular Force

Torque Formula:

\[ \tau = I \times \alpha \]

Torque (τ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Torque Equation?

Definition: This equation calculates the rotational force (torque) based on an object's moment of inertia and its angular acceleration.

Purpose: It helps engineers and physicists determine the rotational force needed to achieve a certain angular acceleration for a given object.

2. How Does the Equation Work?

The equation is:

\[ \tau = I \times \alpha \]

Where:

\( \tau \) — Torque (Newton meters, N m)
\( I \) — Moment of inertia (kilogram square meters, kg m²)
\( \alpha \) — Angular acceleration (radians per second squared, rad/s²)

Explanation: The torque required to rotate an object increases with both its resistance to rotation (moment of inertia) and the desired angular acceleration.

3. Importance of Torque Calculation

Details: Proper torque calculation is essential for designing rotating machinery, vehicle drivetrains, robotics, and understanding rotational dynamics.

4. Using the Calculator

Tips: Enter the moment of inertia (I) and angular acceleration (α). Both values must be > 0. The calculator will compute the required torque (τ).

5. Frequently Asked Questions (FAQ)

Q1: What is moment of inertia?
A: It's a measure of an object's resistance to changes in its rotational motion, depending on mass distribution relative to the rotation axis.

Q2: How is angular acceleration different from linear acceleration?
A: Angular acceleration refers to the rate of change of angular velocity (rotational speed), measured in radians per second squared.

Q3: What are some real-world applications of this equation?
A: Used in designing engines, calculating required motor torque, analyzing rotational systems, and understanding celestial mechanics.

Q4: How do I find the moment of inertia for complex objects?
A: For standard shapes, use formulas (e.g., I = ½MR² for solid cylinder). For complex objects, use CAD software or experimental methods.

Q5: What's the relationship between torque and power?
A: Power (P) is torque (τ) multiplied by angular velocity (ω): P = τ × ω. More torque at the same RPM means more power.