Newton’s Second Law: Force, Mass, and Acceleration

Manual: General · Subject: Newtonian Mechanics

Learn the central law of dynamics and how to solve basic force problems.

The Main Equation of Motion

Newton’s second law

The net force on an object equals mass times acceleration: $\sum \vec{F} = m\vec{a}$ . This is the most important equation in basic mechanics.

What it means

If the net force gets bigger, acceleration gets bigger. If mass gets bigger, the same force produces less acceleration. Force and acceleration point in the same direction.

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How to think about it

A force does not directly determine velocity; it determines acceleration, which then changes velocity over time.

Units check

Since $F = ma$ , the unit of force is $kg\cdot m/s^2$ , which is defined as one newton, $1\,N = 1\,kg\cdot m/s^2$ .

If the same force acts on a larger mass, the acceleration is:

Larger Smaller Unchanged Always zero

Write Newton’s second law in symbols.

Solving with the second law

1

Step 1: Draw all forces on the object.
2

Step 2: Choose coordinate axes.
3

Step 3: Add forces in each direction to get the net force.
4

Step 4: Use $\sum F = ma$ to find the unknown.

Common force situations

Net force	Acceleration
Zero	Zero
Constant nonzero	Constant nonzero
Changing with time	Changing with time

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