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Moment Formula

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Last updated date: 23rd May 2024
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Moment Formulas - Definitions, Equation & Examples



The turning effect of a force is known as the moment. It is the product of the force multiplied by the perpendicular distance from the line of action of the force to the pivot or point where the object will turn.

The SI unit of moment of a force is Newton-metre (Nm). It is a vector quantity.

Its direction is given by the right-hand grip rule perpendicular to the plane of the force and pivot point which is parallel to the axis of rotation.

 

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𝝉=\[ F \times d \]

where 𝝉 is the moment of force/torque

F is the force

d is the perpendicular distance from the line of action of the force to the pivot

 

Example:

The moment of force of 10 N about a point is 3 Nm. The distance of the point of application of the force from the point is

Moment of force = force × distance

⇒ 3 Nm = 10 \[ N \times r \]

⇒ r = 0.3 m

Question:

If a uniform bar of mass 8 Kg is pivoted at one end, What is the net moment of force on the bar?

FAQs on Moment Formula

1. How can we describe the moment of force?

Moment of force can be described as the measure of the force that can rotate a body about a definite axis or point. The moment arm is an important factor that refers to the distance of force from the axis of rotation. The concept of the moment arm is used for the functioning of the lever, gear, pulley, and other simple machines. According to the principle of the moment, the sum of clockwise moments and anticlockwise moments are equal, if the system is in equilibrium.

2. How can we calculate the moment?

The moment of force is calculated using a simple formula and is one of the easiest methods and can be calculated using only two parameters, that is, force applied and the distance from the fixed axis. The moment of force can be calculated as the product of the force applied and the distance from the axis. The moment of force can be calculated for both balanced as well as unbalanced forces. The SI unit of moment and moment of force is the newton meter.  

3. A meter rule is fixed at the middle and has a length of 200cm. The weight of 10N is changed from the 30cm mark of the meter rule and another weight of 20N is changed from the 60cm mark. Then interpret if the meter rule is balanced or not using the moment formula.

To test if the meter rule is balanced or not, we need to check the principle of momentum. Therefore, according to the principle of momentum, the total anticlockwise moments are equal to the total clockwise moments. In such questions, we need to calculate the momentum of both sides and then compare their values. For total anticlockwise moments, the distance will be (50 - 30), which is equal to 20cm or 0.20m. 

The force applied is 10N and therefore, the anticlockwise moment will be the product of 10N and 0.20m, that is, 2Nm. The distance for the total clockwise moment will be 60 - 50, that is, 10cm or 0.10m, and the force applied in this case is 20N. Therefore, the clockwise moment will be the product of 20N and 0.10m, that is, 2 Nm. now, since anticlockwise moment and clockwise moment are the same, therefore, according to the principle of moments, the meter scale will be in a state of rotational equilibrium.

4. What will be a real-life example of a moment of force?

The best example of a moment of force in our day-to-day life will be a see-saw that we swing in a park. In a see-saw, when we put weight on both sides to balance the moment of the see-saw, but if we add extra weight to any side of the see-saw, then the swing doesn't stay in a balanced position. Thus, this is known as an unbalanced moment. This turning effect is measured in terms of torque. There are even more examples in our day-to-day life that work on the concept of moment of force.

5. Using the moment formula, how can I calculate the weight required to be applied at the 80cm mark of a 500cm meter rule to keep it in a balanced position if a weight of 2N is changed from the 20cm mark of the same rule?

Based on the principle of moments, the sum of anticlockwise moments and the sum of clockwise moments should be equal so that an object is in rotational equilibrium. Therefore, if we want the 500m rule to be in rotational equilibrium, then the force exerted on the 80cm mark must exert a moment that is equal to the moment exerted on the 20cm mark by weight of 2N. For the anticlockwise moment, the length of the lever arm will be 50 - 20, which is equal to 30cm or 0.30m and the force applied is 2N. Thus, the anticlockwise moment will be the product of 0.30m and 2N, that is, 0.6Nm. Therefore, the clockwise moment should also be equal to 0.6Nm. The length of the lever arm will be calculated as 80 - 50, that is, 30cm or 0.30m. Thus, the force required to be hanged at the 80cm mark will be 0.6 divided by 0.30, which is equal to 2N.