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Newton's laws of motion

Inertia, F = ma, and action–reaction pairs applied to real situations.

  • Define and explain Newton's laws of motion in your own words
  • Use key terms such as Friction accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Newton's laws of motion: inertia, F = ma, and action–reaction pairs applied to real situations.

Definition: Newton's laws of motion

Inertia, F = ma, and action–reaction pairs applied to real situations.

Key ideas

Newton's second law

The resultant force on a particle equals mass times acceleration (F = ma). Draw a force diagram, resolve along the direction of motion, and equate; mass in kg, acceleration in m/s² gives force in newtons.

Projectile motion

Horizontal and vertical motion are independent: horizontal velocity stays constant (no air resistance), while vertical motion accelerates at g = 9.8 m/s² downwards. Resolve the initial velocity into components, then treat each direction with SUVAT.

Key term — Friction: A force opposing relative motion between surfaces, modelled as F ≤ μR where μ is the coefficient of friction and R the normal reaction.

Worked example: Newton's laws of motion

A box on rough ground has normal reaction 50 N and μ = 0.4. Find the maximum friction.

F_max = 0.4 × 50 = 20 N.

Answer: F_max = 0.4 × 50 = 20 N.

Common mistakes
  • Forgetting g = 9.8 m/s² in vertical projectile motion Vertical motion always accelerates downwards at g; a sign error here flips the whole trajectory.
  • Confusing speed with velocity, or distance with displacement SUVAT uses vectors: fix a positive direction at the start and keep signs consistent, or the equations give nonsense.

Practice

A particle starts from rest and accelerates at 3 m/s² for 5 s. Find its final velocity.
v = u + at.

v = 0 + 3 × 5 = 15 m/s.

Find the distance travelled in the previous question.
s = ut + ½at².

s = 0 + ½ × 3 × 25 = 37.5 m.

A 2 kg mass experiences a resultant force of 10 N. Find its acceleration.
F = ma.

a = 10/2 = 5 m/s².

A ball is dropped from rest. How far does it fall in 2 s? (g = 9.8 m/s²)
s = ut + ½gt² with u = 0.

s = ½ × 9.8 × 4 = 19.6 m.

Quick check

Newton's laws of motion — quick check

Which of these best defines "Friction"?

A force opposing relative motion between surfaces, modelled as F ≤ μR where μ is the coefficient of friction and R the normal reaction.

A projectile is launched horizontally at 20 m/s from a 45 m cliff. How long until it hits the sea? (g = 9.8 m/s²)

t² = 90/9.8 ≈ 9.18; t ≈ 3.03 s.
Key takeaways
  • Newton's laws of motion: inertia, F = ma, and action–reaction pairs applied to real situations.
  • Newton's second law: The resultant force on a particle equals mass times acceleration (F = ma).
  • Force: A push or pull measured in newtons (N); a resultant force causes acceleration via F = ma.
  • Watch out for: forgetting g = 9.8 m/s² in vertical projectile motion
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