Forces and their interactions

Because a vector has direction, one direction is treated as positive and the opposite direction as negative — so vectors (unlike most scalars) can be negative. For example, if a ball is thrown upward off a cliff, its displacement is 0 at the height it was thrown from, positive above that point, and negative below it.

Speed only becomes velocity once a direction is given: '10 m/s' is a speed, but '10 m/s at 30° above the horizontal' is a velocity.

Vectors are often represented in diagrams by arrows: the arrow's length represents the vector's magnitude, and the arrow's direction represents the vector's direction.

When two objects interact, they always exert a force on each other — this pair of forces is equal in size and opposite in direction (see Newton's Third Law, 4.5.6.2).

Every object with mass has a gravitational field around it, which attracts all other masses towards it. The larger the mass, the stronger its gravitational field, and the greater the force of attraction it exerts on other objects.

On Earth, gravitational field strength g ≈ 9.8 N/kg (often rounded to 10 N/kg in calculations). Weight is measured directly using a calibrated spring-balance (a newton-meter); a normal weighing scale actually measures the force you exert on it and divides by g to display your mass.

An object falling freely under gravity (with no other forces acting) accelerates at g, i.e. about 9.8 m/s² near the Earth's surface.

For forces acting along the same straight line, add forces acting in the same direction, and subtract forces acting in opposite directions, to find the resultant.

A free body diagram shows all the forces acting on an object as labelled arrows, without showing the other objects involved. For a skydiver falling, the two forces are weight (constant, acting downwards) and air resistance (acting upwards, increasing with speed):

1. 1Just after jumping: air resistance is very small, so the resultant force is close to the full weight, acting downward — the skydiver accelerates rapidly.
2. 2As speed increases, air resistance increases, reducing the resultant downward force — the skydiver still accelerates, but less quickly.
3. 3Eventually air resistance grows to equal the weight — the resultant force is zero.
4. 4With zero resultant force there is no acceleration: the skydiver falls at a constant speed, called terminal velocity.

Resolving a force (HT only): a single force F acting at an angle θ to a surface can be split into two component forces at right angles to each other — one parallel to the surface (F cos θ) and one perpendicular to it (F sin θ) — which together have exactly the same effect as the original force F.