Dimensions Formula of Moment of Force

The moment of force is also known as torque, which is a vector quantity that measures the tendency of a force to rotate an object about an axis or pivot. The formula for moment of force is given by:

Moment of Force = Force x Perpendicular Distance from the Axis of Rotation

The dimensions of moment of force can be determined using the method of dimensions, which is a technique used to determine the dimensions of physical quantities.

Dimensions of Force

The dimension of force is given by:

Force = Mass x Acceleration

The dimension of mass is [M] and the dimension of acceleration is [LT^-2]. Therefore, the dimension of force can be written as:

Force = [M][LT^-2]

Dimensions of Perpendicular Distance

The perpendicular distance is the shortest distance from the axis of rotation to the line of action of the force. The dimension of distance is [L]. Therefore, the dimension of perpendicular distance can be written as:

Perpendicular Distance = [L]

Dimensions of Moment of Force

Using the formula for moment of force, we can write:

Moment of Force = Force x Perpendicular Distance

Substituting the dimensions of force and perpendicular distance, we get:

Moment of Force = [M][LT^-2][L]

Simplifying the above expression, we get:

Moment of Force = [ML^2T^-2]

Therefore, the dimensions of moment of force are [ML^2T^-2], which means that moment of force is a derived unit that is composed of the dimensions of mass, length, and time.