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Sir Isaac Newton's third law of motion is a fundamental principle that helps us understand the relationship between forces and interaction. It states that for every action, there is an equal and opposite reaction. This means that whenever an object exerts a force on a second object, the second object exerts a force of equal magnitude but in the opposite direction on the first object.

Imagine playing tug of war. When you pull on the rope, the opposing team is pulling back with an equal force. If we apply this to the coffee cup you are holding, as you exert a normal force upwards to support the cup, the cup pushes downward with the same amount of force. This interaction is ongoing and keeps the cup balanced in your hand, so long as the forces remain equal.

Gravity is a natural phenomenon by which all things with mass or energy are brought toward one another. On Earth, this force gives weight to physical objects and causes the ocean tides. The force of gravity near the Earth's surface is what pulls objects toward the center of the Earth, and its strength is proportional to the object's mass.

In our case with the cup of coffee, gravity exerts a downward force on the cup. If the cup has a mass of, say, 200 grams, the force of gravity on it could be calculated using the formula \( F = m \times g \) where \( m \) is the mass, and \( g \) is the acceleration due to gravity (\( g \) is \(9.81\,\text{m/s}^2\) on Earth's surface). This is why you need to hold the cup firmly to prevent it from falling.

The normal force is the force exerted by a surface to support the weight of an object resting on it. It is a contact force perpendicular to the surface. If we revisit the coffee cup, when you hold the cup in your hand, your hand provides a supporting force that prevents the cup from falling through your hand due to gravity. This is the normal force.

What's essential to note is that the normal force is not always equal to the weight of the object. If you were to carry the cup in an elevator that accelerates upwards or downwards, the normal force would increase or decrease accordingly, because the effective weight of the object changes with the acceleration.

Air resistance, also known as drag, is a force that opposes the relative motion of an object through the air. Imagine you're walking against a strong wind. The force you feel pushing you back is air resistance. For the coffee cup scenario, if the cup were in motion — perhaps you're walking with it — it would experience a force opposing its motion due to air resistance.

However, in most everyday situations where the cup is simply held in the hand without significant motion, the force of air resistance is negligible compared to the force of gravity and the normal force exerted by your hand. Air resistance becomes more relevant at higher speeds or if the object has a large surface area relative to its weight.