Edexcel A-level Physics (9PH0) · Topic 6: Further Mechanics
Mini-Lesson
Further Mechanics
Topic 6 has two halves: momentum and impulse (collisions, explosions, force–time graphs) and circular motion (angular velocity, centripetal acceleration and force).
p = mv · impulse = FΔt = Δp · a = v²/r = ω²r · F = mv²/rmomentum is a vector — direction and sign matter in every collision question
The rule that never fails: in a closed system, momentum is always conserved — in every collision and every explosion. Kinetic energy is only conserved in a perfectly elastic collision. Get those two straight and half the topic is done.
Work through each screen, answer the questions as you go (several are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.
Topic 6 · momentum
Momentum and Newton's second law
p = mv · F = Δp / Δtmomentum in kg m s⁻¹ (or equivalently N s) — and it is a VECTOR
Newton's second law in its full form is: the resultant force equals the rate of change of momentum. Only when mass is constant does this simplify to F = ma.
Take one direction as positive. A body moving the other way has negative momentum.
In two dimensions, momentum is conserved independently in each perpendicular direction.
The principle of conservation of linear momentum: for a system with no external resultant force, total momentum before = total momentum after.
Where it comes from: Newton's third law says the forces on two colliding bodies are equal and opposite, and they act for the same time. So the impulses are equal and opposite, so the momentum changes are equal and opposite — and the total is unchanged.
Calculate
Your turn — a sticky collision
1A trolley of mass 2.0 kg moving at 6.0 m s⁻¹ collides with a stationary trolley of mass 4.0 kg. They stick together. Calculate their common velocity after the collision, in m s⁻¹.
m s⁻¹
Hint: Momentum before = 2.0 × 6.0 + 4.0 × 0 = 12 kg m s⁻¹. After, the combined mass is 6.0 kg. So v = 12 ÷ 6.0.
Calculate
Your turn — kinetic energy lost
2For that same collision, calculate the kinetic energy lost. Give your answer in J.
J
Hint: KE before = ½ × 2.0 × 6.0² = 36 J. KE after = ½ × 6.0 × 2.0² = 12 J. Lost = 36 − 12.
Quick check
What is conserved?
?Two cars crash and crumple, ending up as a single wreck. Which quantity or quantities are conserved?
Topic 6 · impulse
Impulse and the force–time graph
impulse = FΔt = Δp = mv − muunit: N s, which is identical to kg m s⁻¹
The impulse of a force is the change of momentum it produces. On a force–time graph, impulse is the area under the curve — which is how you handle a force that varies during an impact.
Rearranged, F = Δp/Δt says: for a fixed change in momentum, extending the contact time reduces the force. That single idea explains:
Crumple zones and airbags — extend Δt, so the force on the passenger falls.
Bending your knees when you land, and catching a ball by drawing your hands back.
Rocket propulsion — the rocket expels gas backwards; the gas gains backward momentum, so the rocket gains an equal forward momentum.
Calculate
Your turn — impulse
3A constant force of 12 N acts on a body for 0.25 s. Calculate the impulse delivered. Give your answer in N s.
N s
Hint: Impulse = FΔt = 12 × 0.25.
Quick check
Reading the graph
?A ball bounces off a wall. The force on it varies with time during the contact. What does the area under the force–time graph represent?
Sort it
Elastic, inelastic, or explosion?
Tap a statement, then tap the type of interaction it describes. Momentum is conserved in all three.
⚡ Elastic collision
💥 Inelastic collision
🚀 Explosion
Topic 6 · circular motion
Angular velocity and centripetal acceleration
ω = 2π/T = 2πf · v = rωω = angular velocity in rad s⁻¹ · v = linear (tangential) speed in m s⁻¹
An object moving in a circle at constant speed is still accelerating, because its velocity — a vector — is constantly changing direction. That acceleration points towards the centre:
a = v²/r = ω²r · F = mv²/r = mω²rcentripetal acceleration and centripetal force — both directed to the CENTRE
Centripetal force is not a new force. It is the name for whatever existing force is doing the job: tension in a string, friction on tyres, gravity on a satellite, the normal contact force on a wall of death.
It acts perpendicular to the velocity, so it does no work and the speed never changes.
Remove it and the object flies off along a tangent — it does not fly radially outwards.
There is no centrifugal force. The outward push you feel on a roundabout is your inertia: your body tries to keep going in a straight line while the seat pushes you inwards.
Calculate
Your turn — angular velocity
4A wheel completes one revolution every 0.50 s. Calculate its angular velocity. Give your answer in rad s⁻¹ to 3 significant figures.
rad s⁻¹
Hint: ω = 2π ÷ T = 2π ÷ 0.50 = 4π.
Calculate
Your turn — centripetal force
5A ball of mass 0.20 kg is whirled on a string of radius 0.80 m at a constant speed of 4.0 m s⁻¹. Calculate the centripetal force. Give your answer in N.