Moment of a Force Topics Definition of Moment

Moment of a Force

Topics • Definition of Moment • Sum of Moments • Conditions for Equilibrium • Centre of Gravity • Couple

Consider this… Rotation • What happens to the wood when a force is applied at one end from the hinge?

Moment of a Force • Rotational effect of a force • Product of force and its perpendicular distance from the pivot • M = F x d • Units: Nm

Moment of a Force pivot Perpendicular distance from the pivot

Moment of a Force 1 N 2 N • Which of these forces will cause greater rotation at the hinge?

Moment of a Force 1 N 1 N • Which of these forces will cause greater rotation at the hinge?

Moment of a Force 0. 8 m 0. 5 m 1 N 1 N • What is the magnitude of the moment of each of these forces?

Moment of a Force • Vector Quantity • Direction – Clockwise – Anticlockwise

Sum of Moments 10 N 0. 4 m 0. 5 m 10 N • In which direction will the beam rotate?

Sum of Moments 20 N 0. 4 m 0. 5 m 10 N • What is the net moment for this beam?

Sum of Moments 10 N 0. 5 m 10 N • What is the net moment for this beam? • What will happen to the beam?

Conditions for Equilibrium • Sum of the forces is zero in all directions • Sum of the moments is zero at any point

Conditions for Equilibrium • Sum of the forces in one direction is equal to the sum of the forces in the opposite directions • Sum of the clockwise moments is equal to the sum of the anticlockwise moments at any point

Conditions for Equilibrium 10 N 0. 5 m 30 N 10 N

Sample Problem 1 10 N 0. 5 m 0. 3 m W • What magnitude of weight will balance the seesaw?

Sample Problem 2 10 N 0. 5 m x 30 N • Where should the 30 -N force be to balance the seesaw?

Sample Problem 3 30 kg 40 cm 30 cm m • Two boys played on a seesaw. What is the mass of the other kid?

Centre of Gravity

What is meant by centre of gravity?

Centre of Gravity A point where the whole weight of the object may be considered to act

If an object is supported at its centre of gravity, it is balanced.

Regularly-shaped objects The centre of gravity is at its geometric centre.

The centre of gravity does not have to be on the body of the object.

If an object is hanged at one point, the string hangs such that the line passes through its centre of gravity.

Sample Problem 4 • A beam is hanged between two spring balances as shown. S 1 S 2 80 cm

• If Spring balance 1 reads 1 N and Spring balance 2 reads 1 N, what is the weight of the beam? S 1 S 2 80 cm

Sample Problem 5 • A beam is hanged between two spring balances as shown. And an orange is placed at the position shown. S 1 S 2 20 cm 80 cm

• If spring balance 1 reads 2. 0 N and spring balance 2 reads 1. 0 N, what is the weight of the orange? S 1 S 2 20 cm 80 cm

• What is the weight of the beam? S 1 S 2 20 cm 80 cm

Couple

What is meant by a couple?

Couple A pair of forces That have equal magnitudes but opposite in direction And have a turning effect about a pivot located midway between them

Couple is composed of 2 forces equal magnitudes opposite in direction same distance from pivot ΣF = 0 but ΣM ≠ 0

Exercises