Enter the mass and angle of the gyration into the calculator to determine the gyroscopic force.

Gyroscopic Force Formula

The following equation is used to calculate the Gyroscopic Force.

Fg = m*g*sin(a)
  • Where Fg is the gyroscopic force (N)
  • m is the mass of the gyroscope (kg)
  • g is the acceleration due to gravity (9.81 m/s^2)
  • a is the angle of the gyration from vertical (degrees)

To calculate the gyroscopic force, multiply the mass and acceleration by the sine of the angle of gyration.

What is a Gyroscopic Force?


Gyroscopic force, also known as gyroscopic inertia, is an inertial force explained by the law of conservation of angular momentum. This law states that the angular momentum remains constant unless acted upon by an external torque.

A gyroscope is a device consisting of a rapidly spinning wheel mounted on a base that allows it to tilt freely in any direction. The gyroscopic force plays a significant role in the operation of the gyroscope.

How to Calculate Gyroscopic Force?

Example Problem:

The following example outlines the steps and information needed to calculate Gyroscopic Force.

First, determine the mass of the gyroscope. In this example, the mass is determined to be 12.5 kg.

Next, determine the angle of the gyration relative to vertical. In this case, the angle is found to be 25 degrees.

Finally, calculate the gyroscopic force using the formula above:

Fg = m*g*sin(a)

Fg = 12.5*9.81*sin(25deg)

Fg = 51.82 N


What is the significance of the angle of gyration in calculating gyroscopic force?
The angle of gyration is crucial because it determines the component of gravitational force that contributes to the gyroscopic effect. A larger angle means a greater component of gravity affects the gyroscope, thereby increasing the gyroscopic force. This angle directly influences the sine value used in the calculation, affecting the overall result.

How does the mass of the gyroscope affect its gyroscopic force?
The mass of the gyroscope directly influences the gyroscopic force. A heavier gyroscope (with more mass) will experience a greater gyroscopic force for the same angle of gyration and acceleration due to gravity. This is because the force is directly proportional to the mass, as shown in the formula Fg = m*g*sin(a).

Can gyroscopic force be negative, and what would that indicate?
Gyroscopic force itself is a vector quantity, which means it has both magnitude and direction. In the context of the formula Fg = m*g*sin(a), the force can’t be negative because mass, gravitational acceleration, and the sine of an angle (within the physical constraints of a gyroscope’s operation) are all positive. However, if considering direction, a negative value could theoretically indicate a force acting in the opposite direction of what might be conventionally expected, but this would depend on the coordinate system being used rather than the physical properties of the gyroscopic force.