Moment of a Force

The magnitude of a moment of a force acting about a point is proportional to the magnitude of the acting force and the distance between this point and the vector line of the force producing the moment. The moment arm is the distance between the force’s vector line and a chosen point. This article will discuss the moment of a force in detail, with some examples. Thus, if one wants to learn about it in detail, keep reading.

Newton-metre is the SI unit for a force’s moment (Nm). It’s a quantity with a vector.

The right-hand grip rule, which is perpendicular to the plane of the force and has a pivot point parallel to the axis of rotation, determines its direction.

Moment of force formula

One can also use the vector equation to describe the moment of a force around an arbitrary moment centre ‘O’.

= r F

Where r refers to the position vector from the moment centre to any given point along the line of action of the force vector F, by first aligning the force and the position vectors tail to tail, then curling the right hand’s four fingers from r to F, with the thumb pointing in the moment vector’s direction, you can find the directional sense of the moment. The moment vector’s axis is perpendicular to the plane containing F and r, which passes through the moment centre. The moment’s magnitude is expressed in units of force per unit of length (for example, lb-in or N-m).

To use the vector approach to calculate the moment of a force, we must know:

• Vector of force
• The moment’s centre’s location
• Vector of position (measured from the moment centre to any point along the force vector’s line of action)

The vector approach’s calculation of moment is demonstrated in the following example.

Example:

Notably, the position vector r can be calculated from the moment centre to any point along the line of action r. In all cases, the resulting cross-products will be equal. 

= rOA F= rOB F= rOCF

Because all cross products in the above equation yield the same result,

= F (rsin) = Fd

and

rOA sin1 = rOB sin2 = rOC sin3 = d 

where the angle formed Where the tails of r and F are θ. 

Thus, the force vector along its line of action, its moment concerning an arbitrary point or moment centre, remains unchanged due to the principle of transmissibility.

Sign Convention Used for Moment of Force:

• It is positive if the force applied to the body rotates the body in an anticlockwise direction.
• It is deemed negative if the force exerted to the body turns the body in a clockwise direction.
• The right-hand rule determines the direction of the moment of force (torque). “Encircle the axis of rotation with right-hand fingers pointing in the direction the body wants to rotate, then point the thumb in the direction of torque or moment of the force vector,” it says.

Principle of Moments:

• The sum of the anticlockwise moments equals the sum of the clockwise moments if a body is in rotational equilibrium.
• The algebraic sum of the moments about any location is zero if a body is in rotational equilibrium.

Applications of the Principle of Moments:

• Calculate the mass of an object
• Machine with levers (Simple)

Dimension of Moment of force

For torque, the SI units are N m and the dimensions of a moment of a force are [ML2T-2]

Moment of inertia dimensional formula

dimensional formula of moment of inertia can be described as an M1 L2 T0. 

Conclusion:

The magnitude of a moment of a force acting about a point is proportional to the magnitude of the acting force and the distance between this point and the vector line of the force producing the moment. The moment of a force has been clarified through examples. We have also mentioned examples for easy understanding. Moreover, we have discussed moments direction, gravity centre, the dimensional formula of the moment of inertia and more.