Newton’s Second Law of Motion

Newton’s Second Law explains how forces change motion. It links three ideas: resultant force, mass, and acceleration.

Key Idea

When a resultant force acts on an object, it accelerates in the same direction as that force. The size of the acceleration depends on the force and the mass.

The equation is:

$$F_{\text{resultant}} = m a$$

• F is the resultant force in newtons (N)
• m is mass in kilograms (kg)
• a is acceleration in metres per second squared (m/s²)

Direction: acceleration points in the same direction as the resultant force, not always the same as the velocity.

Resultant Force

The resultant force is the single force that has the same effect as all the forces combined. Add forces in the same line, remembering their directions. If the resultant force is zero, acceleration is zero and the object stays at rest or moves at constant speed in a straight line.

What the Law Tells Us

• For a fixed mass, bigger force → bigger acceleration (directly proportional).
• For a fixed force, bigger mass → smaller acceleration (inversely proportional).
• A negative acceleration (deceleration) means acceleration opposite to the motion.

Real-World Connections

• Pushing an empty shopping trolley (small mass) gives a large acceleration; a full trolley (large mass) accelerates less with the same push.
• Cycling: pushing harder on the pedals (greater force) increases acceleration.

Common Misconceptions

• “A force is needed to keep something moving.” In fact, if the resultant force is zero, it keeps moving at constant speed.
• “Force and velocity are always in the same direction.” Force and acceleration share direction; velocity may differ.
• Confusing mass and weight: mass is the amount of matter (kg); weight is a force due to gravity (N), with $W = mg$.