Newton's First and Second Laws

This lesson covers inertia, the equation F = ma, and balanced and unbalanced forces, as required by the Edexcel GCSE Combined Science specification (1SC0). Newton's laws are the foundation for understanding how forces affect motion.

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Newton's First Law

Newton's First Law states: An object at rest will remain at rest, and an object in motion will continue to move at a constant velocity, unless acted upon by a resultant force.

In simpler terms:

• If the resultant force on an object is zero, it stays still or keeps moving at the same speed in the same direction.
• If the resultant force is not zero, the object will accelerate (change velocity).

Examples

A book on a table: The weight of the book acts downward and the normal contact force acts upward. These forces are balanced (resultant = 0 N), so the book stays at rest.

A car at constant speed on a straight road: The driving force equals friction plus air resistance. The resultant force is zero, so the car continues at constant velocity.

A ball kicked along grass: Friction acts backward on the ball, creating an unbalanced force. The ball decelerates and eventually stops.

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Inertia

Inertia is the tendency of an object to resist a change in its state of motion. It is related to the object's mass.

• An object with a large mass has greater inertia — it is harder to start moving, stop, or change direction.
• An object with a small mass has less inertia — it is easier to change its motion.

Examples

• A bowling ball is harder to push than a tennis ball because it has more mass and therefore more inertia.
• When a bus brakes suddenly, passengers lurch forward because their bodies have inertia — they tend to keep moving at the same velocity.

Exam Tip: Inertia is not a force. It is a property of mass. Objects do not "have inertia force" — they have inertia because they have mass.

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Newton's Second Law

Newton's Second Law states: The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.

$F = ma$F=ma

where:

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s²)

This can be rearranged:

$a = \frac{F}{m}$a=mF​

$m = \frac{F}{a}$m=aF​

What This Means

• A larger force produces a larger acceleration (for the same mass).
• A larger mass produces a smaller acceleration (for the same force).
• The acceleration is always in the same direction as the resultant force.

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Worked Examples

Example 1: A resultant force of 600 N acts on a car of mass 1200 kg. What is the acceleration?

$a = \frac{F}{m} = \frac{600}{1200} = 0.5 \text{ m/s}^2$a=mF​=1200600​=0.5 m/s2

Example 2: A 0.15 kg ball accelerates at 20 m/s². What is the resultant force?

$F = ma = 0.15 \times 20 = 3.0 \text{ N}$F=ma=0.15×20=3.0 N

Example 3: A force of 50 N accelerates an object at 2 m/s². What is the mass?

$m = \frac{F}{a} = \frac{50}{2} = 25 \text{ kg}$m=aF​=250​=25 kg

Example 4: A car of mass 1500 kg has a driving force of 4500 N and friction of 1500 N. Find the acceleration.

First find the resultant force: $F_{resultant} = 4500 - 1500 = 3000 \text{ N}$Fresultant​=4500−1500=3000 N

Then apply F = ma: $a = \frac{3000}{1500} = 2.0 \text{ m/s}^2$a=15003000​=2.0 m/s2

Exam Tip: Always use the resultant force in F = ma, not just the driving force. Subtract friction and air resistance first, then calculate the acceleration.

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Relating Newton's Laws

Law	Key Idea	Mathematical Expression
First Law	No resultant force → no change in motion	If F = 0, then a = 0
Second Law	Resultant force → acceleration proportional to F, inversely proportional to m	F = ma

Newton's First Law is actually a special case of the Second Law: when F = 0, a = 0, so the object maintains constant velocity (or stays at rest).

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Balanced and Unbalanced Forces Revisited

Balanced Forces (Resultant = 0 N)

graph LR
    A["500 N ←"] --- Object["Object at constant velocity"] --- B["500 N →"]

• Resultant force = 0 N
• Acceleration = 0 m/s²
• Object is stationary or moves at constant velocity

Unbalanced Forces (Resultant ≠ 0 N)

graph LR
    A["300 N ←"] --- Object["Object accelerating →"] --- B["800 N →"]

• Resultant force = 800 − 300 = 500 N to the right
• Object accelerates to the right

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Terminal Velocity (Falling Objects)

When an object falls through a fluid (such as air):

1. Initially, weight >> air resistance, so there is a large resultant downward force and the object accelerates.
2. As speed increases, air resistance increases.
3. Eventually, air resistance = weight, the resultant force = 0 N, and the object reaches terminal velocity — it falls at constant speed.

Worked Example

A skydiver of mass 80 kg reaches terminal velocity. What is the air resistance at this point?

At terminal velocity, resultant force = 0, so: $\text{Air resistance} = \text{Weight} = mg = 80 \times 9.8 = 784 \text{ N}$Air resistance=Weight=mg=80×9.8=784 N

Exam Tip: At terminal velocity, forces are balanced — weight equals air resistance. The object is NOT stationary; it is moving at constant velocity.

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Summary

• Newton's First Law: no resultant force → no change in velocity (object stays still or moves at constant velocity).
• Inertia is the resistance to change in motion; it depends on mass.
• Newton's Second Law: $F = ma$F=ma. Acceleration is proportional to force and inversely proportional to mass.
• Always use the resultant force in F = ma calculations.
• Balanced forces (F = 0) → constant velocity or at rest. Unbalanced forces → acceleration.
• Terminal velocity occurs when air resistance equals weight, giving zero resultant force.