When a force is applied to an object connected to a pivot, it can cause the object to turn about that pivot. This process is referred to as the turning effect or moment of a force. From doors to steering wheels, the turning effect of forces helps to drive all sorts of simple and sophisticated technology that we take for granted today.

To fully comprehend the intricacies of this turning effect of forces, we have to explore the underlying concepts and calculations involved. Let’s start with the most fundamental definitions of moments themselves.

Moments

The moment of a force is a vector quantity that measures the tendency of a body to rotate about a pivot or axis. Moments can act in a clockwise or anti-clockwise direction and can cause the object to spin in the corresponding direction.

Consider the see-saw above. There are four forces acting on it, each with a different moment and direction. How then can we determine the overall turning effect? Here’s when the mathematical definition of moments comes in:

• Formula: Moment of a force = Force (N) x Perpendicular distance between the pivot and the line of action of the force (m)
• Simplified formula: Moment = F x d
• SI Unit: Newton metre (Nm)

Using this formula, we can easily deduce the magnitude and direction of each moment. From left to right, they are:

1. 7N x (2+4)m = 42Nm, Clockwise
2. 8N x 4m = 32Nm, Anti-clockwise
3. 9N x 5m = 45Nm, Clockwise
4. 10N x (3+5)m = 80Nm, Anti-clockwise

The overall turning effect can be deduced by adding up all the moments acting on the see-saw. Taking the anti-clockwise direction to be the ‘positive’ direction, the overall turning effect is 80+32-45-42 = 25Nm, Anti-clockwise.

Do note that the direction in which a force is applied can change the moment significantly, even if there is no change in the force’s magnitude.

The moment of the force in the left figure is 4N x 8m = 32Nm, Clockwise. However, the moment of the force in the right figure is reduced, at 4N x 5m = 20Nm, Clockwise. This is because the line of action is now directed at an angle towards the pivot. This, in turn, lowers the perpendicular distance between the pivot and line of action.

Equilibrium & Stability

Stability refers to how well an object or system can return to its original state after being displaced. The concept of stability can be explained in terms of equilibria. An object is said to be in equilibrium when two conditions have been fulfilled.

1. The resultant external forces acting on the object adds up to zero.
2. The resultant moment around the pivot is zero.

The second criterion is in line with the Principle of Moments, which states that an object is in equilibrium when the sum of clockwise moments is equal to that of the anti-clockwise moments about the same pivot.

There are three main types of equilibria in physics:

1. Stable: As the name suggests, this ranks the highest in stability. When displaced, the system experiences a net force in the opposite direction of the displacement. (e.g. a ping-pong ball at the bottom of a cup)
2. Unstable: When displaced even slightly, the system moves even further away from its equilibrium position. (e.g. a ball balanced on the tip of your finger)
3. Neutral: When displaced, the system remains in its new state. (e.g. a pencil placed lengthwise on a table)

Centre of gravity

The centre of gravity of an object is an imaginary point on an object, from which the full weight of the object is considered to act. One can also think of it as the point in an object which mass or weight is evenly distributed around.

The concept of the centre of gravity comes in handy when designing infrastructure and equipment. There are two simple ways to increase the stability of an object:

1. Lowering the object’s centre of gravity.
2. Increasing the object’s base area.

The turning effect of forces can be a tricky topic to grasp at first, especially given the diverse and numerous concepts that surround it. However, with a strong foundational understanding and enough practice, you will be a master in moments.

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