Force Energy

What is energy?

Energy is the ability to do work, while work is equal to the force being applied to move an object a certain distance in the direction determined by that force. So, energy is how much of the work is applied to the object by that force. The unique thing about energy is that it can be transformed.

Conservation of energy

The conservation of energy states that energy is only transferred from one state to another so that the total energy of a closed system is conserved.

For example, when an object falls, its potential energy is converted to kinetic energy, but the total sum of both energies (the mechanical energy of the system) is the same at every instant during the fall.

What is a moment?

The turning effect or a force produced around a pivot is called the moment of a force or torque. Examples of pivots are the hinges of an opening door or a nut turned by a spanner. Loosening a tight nut and a door opening around a fixed hinge both involve a moment.

While this is a rotatory motion around a fixed pivot, there are also other types of turning effects.

What are the types of moments of a force?

Apart from the rotatory aspect, we also need to note the direction in which the object moves. For instance, in the case of an analogue clock, all its hands rotate in the same direction around a fixed pivot located in its centre. The direction, in this case, is a clockwise one.

Clockwise moment

When a moment or a turning effect of a force about a point produces a clockwise movement, that moment is clockwise. In calculations, we take a clockwise moment as negative.

Anticlockwise moment

Similarly, when a moment or a turning effect of a force about a point produces an anticlockwise movement, that moment is anticlockwise. In calculations, we take an anticlockwise moment as positive.

How do we calculate a moment of a force?

The turning effect of a force, also known as torque, can be calculated by the formula:

\[T = r \cdot F \sin(\theta)\]

1. T = torque.
2. r = distance from the applied force.
3. F = applied force.
4. 𝜭 = Angle between F and the lever arm.

In this diagram, two forces are acting: F₁ and F₂. If we want to find the moment of force F₁ around pivot point 2 (where force F₂ acts), this can be calculated by multiplying F₁ by the distance from point 1 to point 2:

\[\text{Moment of force} = F_1 \cdot D\]

However, to calculate the moment of force F₂ around pivot point 1 (where force F₁ acts), we have to improvise a little. Have a look at Figure 6 below.

F₂ is not perpendicular to the rod. We, therefore, need to find the component of the force F₂ that is perpendicular to the line of action of this force.

In this case, the formula becomes F₂ sin𝜭 (where 𝜭 is the angle between F₂ and the horizontal). So, the formula to calculate the torque around the force F₂ is:

\[\text{Moment of force} = F_2 \cdot \sin(\theta) \cdot D\]

The principle of moment

The principle of moment states that when a body is balanced around a pivotal point, the sum of the clockwise moment equals the sum of the anticlockwise moment. We say that the object is in equilibrium and will not move unless either one of the forces changes or the distance from the pivot of either of the forces changes. See the illustration below:

What is a couple?

In physics, a moment of a couple is two equal parallel forces, which are in opposite directions from each other and at the same distance from the pivot point, acting on an object and producing a turning effect. An example would be a driver turning the steering wheel of their car with both hands.

The defining feature of a couple is that, although there is a turning effect, the resultant force adds up to zero. Hence, there is no translational but only rotational movement.

To calculate the moment of a couple, we need to multiply either one of the forces by the distance between them. In the case of our example above, the calculation is:

\[\text{Moment of a couple} = F \cdot S\]

What is the unit of moment of a force?

As the unit of a force is Newton and the unit of the distance metres, the unit of moment becomes Newton per metre (Nm). A torque, therefore, is a vector quantity as it has a magnitude and a direction.