A Moment of a Force

The moment of a force about a point in simple words can be defined as the measure of the ability of a body to rotate around a specific point or axis. This is different from the tendency of a body to move along the direction of the force. Moment of force is developed only when the applied force does not align on the same line with the centroid of the body. It is because a force passing through the centroid of a body does not tend to rotate it along any axis. Hence it can be inferred that Moment is due to a force not having an equal and opposite force along its line of action.

Since the force that we apply here is made to rotate different bodies, we name it differently called Torque. Torque can also be considered equivalent to force in linear dynamics(linear motion).

As torque is equivalent to force in linear motion, it also plays the same role that force plays in linear motion.

Torque can be defined as a measure of how much a force acting on a particle can cause it to rotate about an axis called the pivot.

Greater the force, the greater the rotational motion of the object.

Torque is a vector quantity, which means it has magnitude as well as a defined direction. It is represented by ‘tau’ in the Greek alphabet.

Torque can also be defined as a product of the force and the perpendicular distance between the line of action of force and the point of rotation.

[Torque=Force x Perpendicular distance between the axis of rotation and point of application of force]

[From this formula we can understand that torque is the cross product of the force and the perpendicular distance.]

Therefore,

=rf

=rfSin

[Here is the angle between the force and the perpendicular distance]

Three cases can be developed here,

Case 1: When θ is 0° torque is equal to zero as Sin0 has a value of zero.

Case 2: When θ is 180° torque is again equal to zero as Sin180 has a value of zero

Case 3: When θ is 90° then torque is maximum, because sin 90=1, hence which is equal to the product of F and D.

i.e. =fd

The SI unit of torque is Newton metre (Nm).

By using the right-hand rule, we can find the direction of the torque vector. If we put our fingers in the direction of r(Distance of point of rotation and point of application of force) and curl them to the direction of Force, then the thumb points in the direction of the torque vector.

In rotational equilibrium, the sum of all the torques acting on a body is equal to zero, which simply means that there is no net torque on the object.

∑=0

Torque depends upon two factors:

1. The magnitude of the force applied on the object.
2. The perpendicular distance of the line of action of the force from the axis of rotation which is also called the lever arm.

Hence it can be inferred that the greater the magnitude of the force and the perpendicular distance between the line of action of force, the greater will be the moment of force, greater will be its turning effect.

It can also be written that force applied and distance are directly proportional to the moment of force.

Moment of Inertia:

It is a physical quantity that expresses a body’s tendency to resist angular acceleration. It can also be defined as the sum of the product of the mass of the particle with the square of the distance between the axis of rotation and the position of the particle.

Relation between the moment of inertia and torque.

According to Newton’s first law of motion, the body remains at rest until and unless an external force acts on it.

For example, fans, washing machines, and AC only work when we switch on them. That means they remain at rest until we switch on the power button. We can see that all the rotating electrical appliances remain at rest, and when the torque is offered, each particle in the system having its rotational masses(moment of inertia) starts rotating about their axis of rotation. This is how we can understand the relation between them by Newton’s first law of motion.

Parallel axis theorem:- 

It states that the moment of inertia of a rigid body about its axis is equal to the moment of inertia about a parallel axis passing through its centre of mass and the product of the mass of the body and the square of perpendicular distance between two axes collectively

Perpendicular axis theorem:- 

It states that moment of inertia of a plane about an axis perpendicular to its plane is equal to the sum of moment of inertia about any two mutually perpendicular axes in its plane and intersecting each other at a point where the perpendicular axis pass through it.

IMPORTANT POINT:[The moment of force is taken positive if the force tends to turn a body in an anticlockwise direction and negative if it tends to turn the object in a clockwise direction.]

Conclusion:

A moment of force is the tendency of an object to cause circular movement about a fixed point. It tells us about the force generated to cause the rotational movement which is called the turning effect. If an object is fixed at a hinge and we apply a force then this produces a torque which results in a change in the rotational state of motion of the object. We come across torque in our daily life, while opening a door, on a see-saw, and much more.