Moment Formula

The word moment refers to a very short period of time. If we consider a see-saw, putting weights on both sides and making it be in a balanced moment. If we put extra weight or less weight on one side, the see-saw is no more balanced. Hence this is known as the unbalanced moment. Here this measure of turning effect is called torque. In this topic, we will discuss the moment formula with suitable examples. Let us learn the concept!

Moment Formula

What is the Moment of Force?

In the area of physics, the moment of force or simply moment is a measure of the tendency to cause a body to rotate about a given specific fixes point or axis.

In this concept, the moment arm is defined as the distance from the axis of rotation. This distance plays an important role. The lever, pulley, gear, and most other simple machines create a mechanical advantage by changing the distance i.e. the moment arm.

The Principle of Moment says that when a system is in equilibrium the sum of its CLOCKWISE MOMENTS will be equal to the sum of its ANTICLOCKWISE MOMENTS.

Some examples where moments i.e. turning effects are applicable will involve levers, like seesaws, opening and closing doors, nutcrackers, can openers, and crowbars.

As we know that a lever is a simple machine in which one force which is known as the effort is used to overcome another force which is known as a load. Therefore, in physics, a moment is a combination of a physical quantity and a distance.

The unit for a moment in SI is the newton meter (kgm² per s²). Also, we express the moment of force in Nm.

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The Moment Formula

The moment formula is as follows:

M= F × d

Where,

F	force applied
d	distance from the fixed axis
M	Moment of force

Moment of force formula is applicable to calculate the moment of force for balanced as well as unbalanced forces.

Solved Examples on Moment Formula

Q.1: A meter-rule of length 200 cm, is pivoted at the middle point. If the weight of 10 N is hanged from the 30 cm mark. Another weight of 20 N is hanged from its 60 cm mark. Then find out whether the meter rule will remain balanced over its pivot or not.

Solution:

According to the principle of moments, for rotational balance, we will have

Total anticlockwise moments = Total clockwise moments

So, we will compute both side moments and then compare their values.

Total anticlockwise moments will be,

Length of lever arm \( d_1 \)= (50 – 30)

\(d_1\) = 20 cm

\(d_1 \)= 0.20 m

Amount of balanced force applied,

\(F_1\)= 10 N.

So, Anticlockwise moment will be,

= \(F_1 × d_1\)

= 10 × 0.20

= 2 Nm

Now, total clockwise moment will be,

Length of lever arm \(d_2 = (60 – 50) \)

\(d_2 = 10 cm \)

\(d_2 = 0.10 m\)

Amount of balanced Force applied, \(F_2= 20 N\)

So, the clockwise moment will be,

= \(F_2 \times d_2 \)

= 20 × 0.10

= 2 Nm

It is obvious that,

total anticlockwise moment = total clockwise moment

Therefore, according to the principle of moments, there will be a rotational equilibrium.