Moment of Force

Topic: Moment of Force

What is a Moment?

The Moment of a force is a measure of its tendency to cause a body to rotate about a specific point or axis. This is different from the tendency for a body to move, or translate, in the direction of the force. In order for a moment to develop, the force must act upon the body in such a manner that the body would begin to twist. This occurs every time a force is applied so that it does not pass through the centroid of the body. A moment is due to a force not having an equal and opposite force directly along it's line of action.

The magnitude of the moment of a force acting about a point or axis is directly proportinoal to the distance of the force from the point or axis. It is defined as the product of the force (F) and the moment arm (d). The moment arm or lever arm is the perpendicular distance between the line of action of the force and the center of moments.

Moment = Force x Distance or M = (F)x(d)

Unit: newton-meters (Nm)

Conditions for Equilibrium

The general conditions for equilibrium are as follows:

(i) The total force must be zero.

(ii) The total turning effect of force about any axis must be zero.

Equilibrant:

If a resultant force acts on a body, then that body can be brought into equilibrium by applying an

additional force that exactly balances this resultant. Such a force is called equilibrant and is equal in

magnitude but opposite in direction to the original resultant force acting on the body.

Couple

• A couple is a pair of equal parallel forces pointing in opposite directions.

• The only thing a couple can do is cause or prevent a body from turning.

• The amount of one of the forces is multiplied by the perpendicular distance between their action lines to calculate the turning effect, or moment.

Application of Couple in Physics

You can know different types of applications for couples. Some of them are given hereunder:

• Steering wheel applied by the car driver

• Opening and closing of a water tap

• Winding the spring of an alarm clock

• Unlocking the locker by using a key

• Opening and closing of a cap of a water bottle, or jug.

• Turning of a screwdriver

Principle of moment.

According to the principle of the moment, if the body is balanced, the total clockwise moment about a point is equal to the total anticlockwise moment about the same point. The moment is given by the product of force and the perpendicular distance from the applied force to the object.

Moment = Force x perpendicular distance

In equilibrium : Total Counter Clockwise Moment = Total Clockwise Moment

The appliances that work on the principle of the moment are

• Beam balance

• Seesaw

1. Two forces each of 20 N is applied to a car steering wheel that has a diameter of 40 cm. If the two forces act tangentially to the steering wheel and in anti-parallel directions calculate the torque applied.

2. Explain the term ‘equilibrant’.

3. Why is it easier to open a door by holding it from its edge?

4. A father with a weight of 80 N is seated on the left side of a see-saw which is 3 m away from the pivot and her son with a weight of 40N is seated at a distance of 4m on the right. Where should the sister of 10 N be seated to balance the see-saw?

5. Write the units for following quantity.

• torque

• force

6. What is resultant force? Explain with examples for forces in opposite direction and same direction.

7. What are the general conditions for equilibrium

8. Explain the term equilibrium with example.

9. Explain the term equilibrant with an example.

10. Explain parallelogram law of vector addition with example.

11. Find the resultant of vectors 7 N and 12 N inclined at an angle of 600 with each other.

12. What is a couple? Give examples.

13. Explain moment of couple.

14. Explain moment of force.

15. What does principle om moment states? Give example and the mathematical expression.