Newton's Laws of Motion

Newton's laws describe inertia when net force is zero, the link F = ma between net force and acceleration, and equal-and-opposite action-reaction on different objects. Your body lurching forward when a bus brakes, or a wall pushing back when you push it, are everyday examples. In F = ma the F is the net force, and larger mass means less acceleration for the same force. Slide mass and force here to see how acceleration changes.

Intuition for the Three Laws

🍎 Newton's Three Laws at a Glance

①Law 1 (Inertia): without force, motion does not change — why your body lurches forward when a bus brakes

②Law 2 (Acceleration): F = ma — bigger force or smaller mass means more acceleration

③Law 3 (Action-Reaction): when I push a wall, the wall pushes me with equal force

Visualizing F = ma

Mass m5 kg

Force F20 N

💡 Observation Points

①Larger F → proportionally larger a

②Larger m → smaller a for the same force

③Mass = resistance to motion change = magnitude of inertia

Newton's Second Law Formula

Newton's Second Law

F = ma

Force (N) = mass (kg) × acceleration (m/s²)

Acceleration Form

a = Fm

Acceleration is proportional to force, inversely proportional to mass

Unit: Newton (N)

1 N = 1 kg · m/s²

Force needed to accelerate 1 kg at 1 m/s²

Action and Reaction

🤝 Law 3: Action and Reaction

①When I press a desk, the desk pushes me up with equal force

②A rocket pushes gas backward, gas pushes the rocket forward

③Action and reaction act on different objects → they do NOT cancel out!

Worked Examples

Example 1

A net force of 12 N acts on a 4 kg object. What is its acceleration?

From Newton's second law F = ma, a = F/m.

a = Fm

Substitute F = 12 N, m = 4 kg.

a = 124 = 3 m/s²

▸ 3 m/s²

F = ma rearranges to a = F/m. The larger the force and the smaller the mass, the larger the acceleration.

Example 2

A 10 N force is applied to a 2 kg object, but 4 N of friction acts in the opposite direction. What is the acceleration?

The F in F = ma is the net force, so subtract friction first.

F_net = 10 − 4 = 6 N

Compute a = F_net/m.

a = 62 = 3 m/s²

▸ 3 m/s²

The F in F = ma is always the net force. Subtract opposing forces (like friction) before substituting.

Summary

Newton's Laws Core

F_net = ma (net force = mass × acceleration)

Law 1: F=0→constant/at rest, Law 2: F=ma, Law 3: F₁₂=-F₂₁

CSAT-style

On a frictionless floor, a 3 kg and a 2 kg object are connected by a string and pulled with 10 N. What is their acceleration?

①1 m/s²

②2 m/s²

③3 m/s²

④4 m/s²

⑤5 m/s²

▸ ② 2 m/s²

Treat the two connected objects as one system and find the total mass.

m_total = 3 + 2 = 5 kg

Apply F = ma to the whole system.

a = 105 = 2 m/s²

🎯 Exam Points

①F in F = ma is the net (resultant) force — vector sum of all forces

②Larger mass = more inertia (harder to change motion)

③Action-reaction is between two different objects

④Object on horizontal: vertical N=mg, horizontal F=ma

⑤Always draw a free-body diagram (FBD) before solving

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Uniformly Accelerated Motion

Momentum and Impulse

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