Newton's second law links force to acceleration
Definition
Resultant force
The resultant force is the vector sum of all forces on the body. If it is not zero, the body accelerates in that direction.
- Acceleration is proportional to the resultant force: F = m × a.
- It is inversely proportional to mass — the same force gives a heavier body less acceleration.
- Acceleration always has the same direction as the resultant force.
Note
- If the resultant force is zero, the body is at rest or moves at constant speed.
- The unit of force is the newton: 1 N = 1 kg·m/s².
Weight is a force. Mass is not.
Common mistake
- Mass is measured in kilograms and weight in newtons — not the same thing.
- Mass does not change with place. Weight changes when g changes.
Analogy
Push an empty cart and a full cart with the same force: the full cart accelerates less because its mass is larger.
Check yourself
- What happens to acceleration if we double the force and keep mass fixed?
- Why can a body at rest still have forces on it and not move?
