Two forces each of magnitude 2 N act vertically upward and downward respectively .on two ends of a uniform rod of length 1m, freely pivoted at its center. determine the resultant moment of forces about the midpoint of the rod.

Definition of Moment of a couple:

Moment of the couple: The tendency of a force is to rotate a body. It is measured by the moment of the force. The product of one of the forces of a Couple and the perpendicular distance between their lines of action (called the arm of the Couple) is called the Moment of the Couple.

moment of couple( τ ) = F × d

Solution:

given,

Force=2N

rod length = 1m

The figure shows a rod AB of length 1 m is pivoted at center C.

At A, 2N force acting upward, and at B 2N force acting downward.

If we take a moment of the forces about C,

both moments are clockwise moments.

Moment of force at A = 2N × 0.5 m = 1 N

Moment of force at B = 2N × 0.5 m = 1 N

Resultant moment = 2 N-m

Conclusion

Therefore the resultant momentum of force about the midpoint is equal to 2 N-m