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Moment Formula: Definition, Equations, Principle, Application and Solved Examples

Kasturi Talukdar

Updated on 07th June, 2023 , 7 min read

Moment Formula Overview

Moment, in physics, refers to the combination of a physical quantity and its position or arrangement, expressed by the product of a distance and the physical quantity. Typically, moments are described with reference to a specific point, involving physical quantities located at a particular distance from that point. The moment of force, on the other hand, is the product of a force applied to an object and the distance between the object and the point of application of the force. The turning effect produced by a force is measured by torque, and the force responsible for this effect is referred to as the moment of force. In this article, we will discuss the moment formula, its significance, and its application in mechanics.

Define Moment

The term "moment" does not actually refer to a short interval of time. Instead, it describes the product of a physical quantity and its position or arrangement. Consider a see-saw, for example, which can be balanced by placing weights on both sides. If we add more weight to one side, the see-saw becomes unbalanced, resulting in an imbalanced moment. The measure of this turning effect is referred to as torque.

Turning forces are necessary in various common scenarios and are essential for the proper functioning of machinery. Levers and gears utilize these rotating forces to create mechanical advantages. An object can rotate around a pivot point when subjected to a force, and the turning effect of this force is known as the moment of force. Moments can cause clockwise or counterclockwise rotation around a pivot.

What is Moment Formula?

Moment formula is used to calculate the torque or rotational force applied to an object. It is given by the product of the force applied and the distance between the point of application of the force and the point of rotation. The moment formula is as follows:

Moment of force (M)= F x d 

where,

  • Moment is the rotational force or torque (measured in newton-meters, Nm or pound-feet, lb-ft)
  • Force is the perpendicular force applied to an object (measured in newtons, N or pounds, lbs)
  • Distance is the distance between the point of application of the force and the point of rotation (measured in meters, m or feet, ft)

The moment formula is based on the concept of lever arm, where the force is applied at a distance from the point of rotation. The lever arm is the perpendicular distance between the point of rotation and the point of application of the force.

moment formula

Significance of Moment Formula

The moment formula is an important concept in mechanics because it helps in understanding the rotational motion of objects. Moment is an essential parameter that is used in the analysis and design of many mechanical systems, such as engines, gearboxes, and machines.

The moment formula is also used to calculate the bending moment in beams. A bending moment is the torque or rotational force that is applied to a beam, causing it to bend. By calculating the bending moment, engineers can determine the maximum stress and deflection in a beam, which is important in the design of structures.

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Moment Formula: Application

The moment formula has a wide range of applications in various fields, including physics, engineering, and construction. Some common applications of the moment formula are:

  1. Calculation of engine torque: The moment formula is used to calculate the torque produced by an engine. The torque is an important parameter that determines the engine's power output and its ability to perform work.
  2. Design of gearboxes: The moment formula is used in the design of gearboxes to determine the required torque and gear ratios. This helps optimize the performance and efficiency of the gearbox.
  3. Analysis of structures: The moment formula is used in the analysis of structures such as bridges, buildings, and dams. By calculating the bending moment, engineers can determine the structural integrity and safety of these structures.
  4. Construction of machines: The moment formula is used in the construction of machines such as cranes, excavators, and bulldozers. By calculating the required torque, engineers can design the machine's powertrain and hydraulic systems to provide the necessary force and speed.

Moment Formula: Principle

  • The principle of moment is a fundamental concept in mechanics that describes the equilibrium of a body or system under the action of forces and moments.
  • For an object to be in equilibrium, the sum of the clockwise moments around any point must be equal to the sum of the counterclockwise moments around that same point.
  • Moments are calculated by multiplying the force applied to an object by the perpendicular distance between the force and the point of rotation or pivot.
  • The principle of moment can be applied to various scenarios, such as analyzing the balance of a seesaw or determining the stability of a structure.
  • By applying the principle of moment, engineers can design structures and machines that are stable, safe, and efficient.
  • The principle of moment is closely related to the concept of torque, which is the measure of a force's ability to cause rotational motion around a pivot point.
  • In summary, the principle of moment is a powerful tool that helps scientists and engineers to analyze and understand the behavior of physical systems and design more efficient and reliable mechanical systems and structures.

Moment Formula: Things to Remember

  1. The moment formula, also known as the torque formula, relates the torque produced by a force to the force's magnitude and its distance from the pivot point.
  2. The formula can be written as:
    torque = force x distance x sin (angle),
    where torque is measured in newton-meters (N*m), force is measured in newtons (N), distance is measured in meters (m), and angle is measured in radians.
  3. The direction of the torque depends on the direction of the force and the direction of the lever arm (perpendicular distance between the force and the pivot point).
  4. The moment formula is used to analyze and optimize the performance of machines and mechanical systems, such as engines, gears, and turbines.
  5. It is also used to calculate the bending moment in structural members, such as beams, which is important in designing safe and reliable structures.
  6. When solving problems using the moment formula, it is important to use the correct units and pay attention to the sign conventions to ensure that the direction of the torque is correctly determined.
  7. The moment formula is closely related to the principle of moment, which states that for a body to be in equilibrium, the sum of the clockwise moments around any point must be equal to the sum of the counterclockwise moments around that same point.

Moment Formula: Solved Examples

A force of 50 N is applied perpendicularly to a lever arm of 0.5 m from the point of rotation. Calculate the moment.

Solution: Using the moment formula, we can calculate the moment as follows:

Moment = Force x Distance

Moment = 50 N x 0.5 m

Moment = 25 Nm

Therefore, the moment produced by the force of 50 N at a distance of 0.5 m from the point of rotation is 25 Nm.

A beam of length 6 m is supported at its ends and a force of 500 N is applied at a distance of 2 m from one end. Calculate the bending moment at the point of application of the force.

Solution:To calculate the bending moment, we need to first determine the reaction forces at the supports. Since the beam is symmetrically supported at its ends, each support will carry half of the beam's weight, which is:

Weight of beam = density x volume x acceleration due to gravity

= 7850 kg/m^3 x (6 m x 0.1 m x 0.2 m) x 9.81 m/s^2

= 926.1 N

Reaction force at each support = 0.5 x 926.1 N = 463.05 N

Now, we can calculate the bending moment at the point of application of the force using the moment formula as follows:

Moment = Force x Distance

Moment = 500 N x 4 m

Moment = 2000 Nm

Therefore, the bending moment at the point of application of the force is 2000 Nm.

If a 10N force acts at a perpendicular distance of 0.50m from the turning point, calculate the moment of the force?

Solution:As we know, 

Moment = Force x Distance

Moment = 10 x 0.50

Moment = 5.0 Nm

Therefore, the moment of force will be 5.0 Nm.

The central point at 70cm of a 500 cm rule is pivoted. Calculate the amount of weight that must be placed at the 100 cm mark to keep the weight in a balanced position if a 2 N weight is hung from the 40 cm point.

Solution: To keep an item in rotational balance, the total of anticlockwise and clockwise moments operating should be equal, according to the principle of moments. As a result, the weight to be hung from the 80 cm mark must be capable of producing a clockwise moment equivalent to the anticlockwise moment produced by the weight hung from the meter rule's left side.

Moment of anticlockwise rotation:

Lever arm length = (70 – 40)

=30 centimeters

= 0.30 meter

The distance from the mid-point of the lever arm, where it is balanced, is the length of the lever arm.

2 N force applied.

Lever arm x applied force equals anticlockwise moment

= 0.30 x 2 N

=0.6 Nm

Moment in time (clockwise):

Lever arm length = (100 – 70)

=30 centimeters

= 0.30 meter

because the distance between the lever arm and the force exerted equals the length of the lever arm.

Let it be the letter 'F.'

As a result, the clockwise moment equals F x 0.30

= 0.30 FNm

Moment in the clockwise direction equals moment in the anticlockwise direction

0.6 x 0.30 F

2 N = F

To maintain the meter rule balanced, a weight of 2 N must be hung from a 100 cm point.

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