The Gravitational Torque Calculator helps you find the turning effect caused by the force of gravity on an object. Torque is what makes objects rotate around a pivot point when a force is applied at a distance. This calculator is commonly used in physics, engineering, and mechanics to understand how weight creates rotational motion. By entering simple values like mass, lever arm length, and angle, the calculator instantly shows the torque. It saves time, reduces errors, and helps in solving real-world problems involving balance, levers, and mechanical systems.
Formula
The primary formula to calculate gravitational torque is:
τ = r * F * sin(θ)
Where:
- τ is the gravitational torque
- r is the lever arm length (distance from pivot to where force is applied)
- F is the gravitational force (weight)
- θ is the angle between the lever arm and force
Supporting Formula
To find the gravitational force, you can use:
F = m * g
Where:
- F is the force of gravity
- m is the object’s mass
- g is the acceleration due to gravity (9.81 m/s² or 32.2 ft/s² on Earth)
Combined Formula
By substituting the gravity formula into the torque formula, we get:
τ = r * m * g * sin(θ)
This combined formula is the most practical for calculating torque because it uses mass directly.
Common Reference Table
Here is a helpful table that gives approximate torque values for different common cases, assuming the angle θ = 90° (where sin(θ) = 1, giving maximum torque).
| Mass (kg) | Lever Arm Length (m) | Torque (N·m) |
|---|---|---|
| 1 | 1 | 9.81 |
| 2 | 1 | 19.62 |
| 5 | 0.5 | 24.53 |
| 10 | 0.2 | 19.62 |
| 20 | 1 | 196.2 |
This table helps users quickly estimate torque without doing step-by-step calculations.
Example
Let’s calculate the torque for a 5 kg object placed 0.4 meters away from the pivot at an angle of 60°.
Step 1: Find the gravitational force.
F = m * g = 5 * 9.81 = 49.05 N
Step 2: Apply the torque formula.
τ = r * F * sin(θ)
τ = 0.4 * 49.05 * sin(60°)
τ = 0.4 * 49.05 * 0.866
τ ≈ 16.98 N·m
So, the torque in this case is about 16.98 Newton-meters.
Most Common FAQs
It belongs to the Physics and Engineering calculators category. It is useful for mechanical design, structural analysis, and education.
Torque depends on the angle because the force’s effectiveness changes based on direction. Maximum torque occurs at 90° because the force acts fully perpendicular to the lever arm.
Yes, the same principle applies to levers, gears, and rotating systems. However, in real machines, additional factors like friction and material strength should also be considered.