# What is the principle of moments and how to use it to solve numerical problems?

Last updated on April 14th, 2021 at 04:37 pm

Here we will state the ** principle of moments** first and then will see how to use it to solve numerical physics problems related to equilibrium.

**What is the principle of moment**s?

The **Principle of Moments** states that the *rotational equilibrium* of a body is possible only when the sum of

*clockwise moments*is equal to the sum of

*anti-clockwise moments*acting on that body.

## How to **Solve numerical problems on ***rotational equilibrium* **with the principle of moments**?

*rotational equilibrium*

**Let’s solve one numerical problem by applying the principle of moments.**

1 ] The beam shown in the figure is 2 m long and has a weight of 20 N. It is pivoted as shown. Two forces of 20 N and 10 N are acting on it as shown in the figure. What force F must be applied downwards at the other end (see the figure for force F) to balance the beam? The pivot point is shown as the **red** triangle.

**Solution:**

Both 20 N and 10N forces are creating clockwise moments. And the sum of clockwise moments is = (10×1.5 + 20×0.5) Nm = (15 + 10) Nm = 25 Nm…. (1)

And the anticlockwise moment created by the force F Newton = F x 0.5 Nm …(2)

For equilibrium, clockwise moment must be equal to anticlockwise moment.

Hence, as per principle of moments, from equation (1) and (2):

**F x 0.5 = 25 => F = 25/0.5 N = 50 N**

**Answer: 50 N**