Newton's Laws of Motion

• What inertia is and why it explains the seatbelt
• How to relate force, mass, and acceleration with F = ma
• Why action–reaction pairs don't cancel each other out
• How to apply Newton's laws to everyday and exam problems

Newton's First Law — The Law of Inertia An object at rest stays at rest, and an object in motion continues in a straight line at constant speed, unless acted upon by a net external force.

This property — resistance to change in state of motion — is called inertia. Heavier objects have more inertia than lighter ones. The seatbelt example: when a car brakes suddenly, the car decelerates rapidly but your body tends to keep moving forward (inertia). Without a seatbelt, you would continue at the car's original speed and hit the dashboard. The seatbelt applies a backward force on you, bringing you to rest along with the car.

Other examples of inertia: a tablecloth pulled quickly from under dishes (dishes stay due to inertia); dust falling off a carpet when beaten (carpet moves but dust's inertia keeps it momentarily still).

Newton's Second Law — F = ma The net force acting on an object equals the product of its mass and acceleration:

F_net = m × a

Units: Force is in Newtons (N). 1 N = 1 kg·m/s². Acceleration is in m/s².

Key consequences:

• For the same force, a larger mass accelerates less (a = F/m).
• For the same mass, a larger force produces greater acceleration.
• The acceleration is always in the same direction as the net force.
• If the net force is zero, acceleration is zero (object moves at constant velocity or stays at rest — consistent with First Law).

Newton's Third Law — Action and Reaction For every action force, there is an equal and opposite reaction force. These forces always act on different objects.

When you push a wall with 50 N (action), the wall pushes back on you with 50 N (reaction). When a rocket expels gas backward (action), the gas pushes the rocket forward (reaction). When you walk, your foot pushes the ground backward; the ground pushes your foot forward — that reaction is what propels you.

Critical point: action and reaction pairs never cancel each other because they act on different objects. They would only cancel if both forces acted on the same object.

Problem: A 1000 kg car accelerates uniformly from rest to 20 m/s in 10 seconds. What net force does the engine exert on the car?

Solution:

Step 1 — Find acceleration: a = (v - u) / t = (20 - 0) / 10 = 2 m/s²

Step 2 — Apply Newton's Second Law: F = ma = 1000 kg × 2 m/s² = 2000 N

The engine must provide a net force of 2000 N to achieve this acceleration. In reality the engine produces more force, with part of it overcoming air resistance and friction.

Bonus — Third Law in this situation: The road pushes the car forward (reaction to the tyres pushing back on the road). The car pushes the road backward with 2000 N; the road pushes the car forward with 2000 N.

• Thinking the Third Law pairs cancel. They act on different objects — action is on object A, reaction is on object B. They cannot cancel because cancellation requires forces on the same object.
• Using total force instead of net force in F = ma. If friction opposes the applied force, F_net = F_applied − F_friction.
• Ignoring direction. Force and acceleration are vectors. Always establish a positive direction and assign signs accordingly.
• Confusing mass and weight. Mass (kg) is used in F = ma. Weight (N) = mg is itself a force, not the m in F = ma.

1. A 5 kg ball is pushed with 20 N on a frictionless surface. What is its acceleration?
2. You push a friend on a skateboard with 30 N. What force does your friend exert back on you?
3. Why does a rocket accelerate in the vacuum of space where there is no air to push against?