Mini-Lesson

Forces & Momentum

This mini-lesson covers Theme A.2 — Forces and momentum: Newton's three laws, drawing free-body diagrams, using F = ma, and the powerful ideas of impulse and conservation of momentum.

Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.

A.2 · Newton I & II

Newton's first two laws

Forces are pushes and pulls (vectors, in newtons). The first two laws:

First law: an object stays at rest or moves at constant velocity unless a resultant (net) force acts. Constant velocity ⇒ zero resultant force (equilibrium).
Second law: the resultant force equals rate of change of momentum; for constant mass this is F = ma.

F = maresultant force (N) = mass (kg) × acceleration (m s⁻²)

Weight is the gravitational force on a mass: W = mg. A 6 kg bag weighs 6 × 9.81 = 58.9 N. Mass (kg) is not weight (N).

Quick check

?A car drives along a straight, level road at a constant 25 m s⁻¹. What is the resultant force on it?

Calculate

#A 1200 kg car accelerates at 2.5 m s⁻². Find the resultant force driving it.

N

Hint: F = ma = 1200 × 2.5.

Calculate

#Find the weight of a 6.0 kg mass on Earth (g = 9.81 m s⁻²).

N

Hint: W = mg = 6.0 × 9.81.

A.2 · Newton III

Newton's third law

Third law: if body A exerts a force on body B, then B exerts an equal and opposite force on A. The pair acts on two different bodies and is the same type of force.

Classic trap: the weight of a book and the table's normal force on it are not a third-law pair — they act on the same body. The third-law partner of the book's weight is the book's gravitational pull on the Earth.

Quick check

?A rifle fires a bullet forwards and recoils backwards. Which statement uses Newton's third law correctly?

A.2 · momentum & impulse

Momentum and impulse

Linear momentum p = mv is a vector (kg m s⁻¹). Newton's second law is really: resultant force = rate of change of momentum.

p = mv · impulse = FΔt = Δpimpulse (N s) equals the change in momentum

On a force–time graph, the area under the curve is the impulse — handy when a force varies during a short collision.

Worked example — a struck ball

A 0.058 kg tennis ball is served from rest to 50 m s⁻¹ during a 5.0 ms contact.

Δp = mΔv = 0.058 × 50 = 2.9 kg m s⁻¹

F = Δp ÷ Δt = 2.9 ÷ 0.005 = 580 N

Calculate

#A 0.15 kg cricket ball travels at 40 m s⁻¹. Find its momentum.

kg m s⁻¹

Hint: p = mv = 0.15 × 40.

Calculate

#A 0.058 kg ball is accelerated from rest to 50 m s⁻¹ in a contact time of 5.0 ms (0.005 s). Find the average force.

N

Hint: F = Δp ÷ Δt = (0.058 × 50) ÷ 0.005.

Sort it

Which of Newton's laws?

Tap an item, then tap the group it belongs to.

① First law

② Second law

③ Third law

A.2 · conservation

Conservation of momentum

When no external resultant force acts, total momentum is conserved: total p before = total p after. This governs collisions and explosions.

Elastic collision: kinetic energy is also conserved.
Inelastic collision: momentum is conserved but some KE becomes heat/sound; if the bodies stick together it is perfectly inelastic.

Worked example — a sticky collision

A 2.0 kg trolley at 3.0 m s⁻¹ hits a stationary 1.0 kg trolley and they couple.

p before = 2.0×3.0 + 0 = 6.0 kg m s⁻¹

v after = 6.0 ÷ (2.0+1.0) = 2.0 m s⁻¹

Calculate

#A 2.0 kg trolley moving at 3.0 m s⁻¹ collides with and sticks to a stationary 1.0 kg trolley. Find their common velocity afterwards.

m s⁻¹

Hint: momentum conserved — v = (2.0×3.0) ÷ (2.0+1.0).

Match it

Match term to meaning

Tap a statement on the left, then its match on the right.

Statement

Answer

Recap

The big ideas to know

Newton I: no resultant force ⇒ rest or constant velocity (equilibrium)

Newton II: resultant F = ma = rate of change of momentum

Newton III: equal, opposite forces on two different bodies

Momentum & impulse: p = mv; impulse = FΔt = Δp = area under a force–time graph

Conservation: isolated system: total momentum before = after; KE extra-conserved only if elastic

That completes Forces & Momentum for IB Diploma Physics SL. Press Finish to see your score.

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