8 What actually comes up

Three years of real questions, part by part, with the grade band each part sat at according to that year's marking schedule. Start with the pattern table — it is the fastest way to decide what to revise.

Across 3 years

9 questions · 36 parts 9 Achieved 27 Merit 18 Excellence

The pattern — what to prepare

Topic	Appears in	Grade level	What to practise
Show that / "show that" calculations (CM, ω, α, speed)	Every year	Achieved–Merit	Set the equation out with substitution and unrounded working; "show that" expects an explicit chain.
Centre of mass and momentum vectors	2025	Achieved–Merit	Vector addition; components at a right angle to each other = Pythagoras.
Gravitation / circular orbit (T from gravity = centripetal; why astronauts float)	2025	Merit–Excellence	GMm/r² = mω²r, then T = 2π/ω. Weightless = free fall with no reaction force, not "no gravity".
Banked curves (no sideways friction)	2023	Achieved–Merit	The net force is horizontal, towards the centre; tan θ = v²/(rg).
Vertical circles, loops and bumps: the forces at the top and bottom	2023, 2024	Merit–Excellence	Which way is the centre? F_c = F_R − F_g at the bottom of a loop or dip; at the top of a loop F_c = F_R + F_g, over a bump F_c = F_g − F_R. N = 0 gives √(gr).
Energy: GPE → E_k(lin) + E_k(rot)	2023, 2024	Achieved–Excellence	Rolling without slipping: v = rω links the two kinetic energies.
Rotational dynamics (α, τ = Iα, revolutions)	2023, 2024, 2025	Achieved–Excellence	Torque from accelerating mass; ω² = ωᵢ² + 2αθ for revolutions.
Conservation of angular momentum (arms in / jump on)	2023, 2025	Merit–Excellence	L = Iω stays constant; I changes with mass distribution.
Conditions for SHM & reference-circle time problems	Every year	Achieved–Excellence	a ∝ −x; phasor angle → time, sin vs cos (cos for a release from max displacement).
Mass-spring / pendulum period and "show that" derivations	2023, 2025	Achieved–Merit	T = 2π√(m/k) and T = 2π√(L/g); drive from F = −kx.
Damping	2023, 2024	Merit–Excellence	Energy lost to friction → amplitude decays, period unchanged.
Resonance from a driving force (force + energy)	2025	Merit–Excellence	Driving at the natural frequency pumps energy in faster than damping removes it.

not tried got it to review 2025 three questions 12 parts

The 2025 paper ↗ Marking schedule ↗

Question 1 — momentum & circular motion

Titan is the largest of Saturn's moons. Ignore every other body, and assume Titan is in a perfectly circular orbit.

M Saturn = 5.68×10²⁶ kg
r Saturn = 5.82×10⁷ m
M Titan = 1.35×10²³ kg
centre-to-centre = 1.22×10⁹ m

Not tried yet: a Show (Saturn + Titan) has its centre of mass 2.90×10⁵ m from Saturn's centre.Worked solution → Achieved
Not tried yet: b Two ice particles around Saturn collide and stick together without losing mass. A (2.45 kg) moves at 8.00 m s⁻¹ to the right on the diagram; B (3.20 kg) moves at 15.0 m s⁻¹ downwards, at right angles to A. Calculate the size and direction of their combined momentum, relative to A's initial velocity.Worked solution → Merit
Not tried yet: c Calculate the time for Titan to complete one orbit of Saturn. You could start with Titan's orbital velocity.Worked solution → Merit to Excellence
Not tried yet: d Astronauts on the International Space Station appear weightless, even though Earth's gravity is still acting on them. Explain why astronauts appear weightless yet can stay in orbit.Worked solution → Merit to Excellence

Question 2 — rotational motion

Rīhari and Jane are on a playground roundabout of radius 1.30 m. Rīhari stands on it while Jane pushes; from rest she steadily accelerates it so it takes 12.0 s to make 4.00 rotations.

r = 1.30 m
4.00 rotations in 12.0 s
I (roundabout + Rīhari) = 430 kg m²

Not tried yet: a Show that the roundabout's angular velocity after the 12.0 s is 4.19 rad s⁻¹.Worked solution → Achieved
Not tried yet: b Rīhari then drags his foot along the ground, bringing the roundabout to a stop over 19.2 s. Calculate the average torque that slows it, if the roundabout and Rīhari have a rotational inertia of 430 kg m².Worked solution → Merit
Not tried yet: c Jane (52.0 kg) runs at 6.39 m s⁻¹ and jumps onto the STATIONARY roundabout, landing 1.20 m from the axis. On the diagram her velocity is at right angles to that radius. The roundabout and Rīhari have I = 430 kg m²; for a point mass, I = mr². Calculate the angular velocity of the roundabout after she has jumped on.Worked solution → Merit to Excellence
Not tried yet: d Later, Rīhari and Jane both stand on the edge while the roundabout turns at a constant angular velocity. Rīhari moves inwards, towards the centre. Explain the effect this has on the rotational energy of the system.Worked solution → Merit to Excellence

Question 3 — simple harmonic motion

Rīhari swings a ball on a string as a pendulum. It is 1.20 m from the fixed point to the ball's centre of mass, and the ball is released 5.60° from the vertical. The string's mass is insignificant.

L = 1.20 m
θ = 5.60°

Not tried yet: a Show that the maximum displacement of the ball is 0.117 m.Worked solution → Achieved
Not tried yet: b Show that the angular frequency of the ball's motion is 2.86 rad s⁻¹.Worked solution → Merit
Not tried yet: c After the ball is released from the starting position, calculate the time it takes to reach a point 3.30 cm before its next stationary position. A reference circle may help.Worked solution → Merit to Excellence
Not tried yet: d Rīhari holds the end of the string between his fingers and moves his hand from side to side. At a certain frequency of movement, the ball swings with a very large amplitude. Explain why this happens, using both forces and energy.Worked solution → Merit to Excellence

2024 three questions 12 parts

The 2024 paper ↗ Marking schedule ↗

Question 1 — circular motion of a ball bearing

A solid steel ball bearing is released from different heights on a steel track. It rolls down and travels over a series of bumps and dips, each of radius 35.0 mm. Point X is the bottom of the first dip; Point Y is the top of a bump. As a solid sphere, I = ⅖mr².

r ball = 7.00 mm
m = 11.2 g
bump/dip radius = 35.0 mm

Not tried yet: a In one trial the ball reaches the bottom of the first dip (Point X) at 0.850 m s⁻¹. Calculate its angular velocity there.Worked solution → Achieved
Not tried yet: b Show that the maximum speed is 0.586 m s⁻¹ for the ball to stay in contact with the track going over the bump at Point Y (radius 35.0 mm).Worked solution → Merit
Not tried yet: c Compare the forces acting at the top (Point Y) and bottom (Point X), and hence explain how the net force varies between them. Labelled force diagrams will help.Worked solution → Merit to Excellence
Not tried yet: d By considering energy changes, calculate the maximum height h above Point Y that the ball can be released from if it is to stay in contact with the track over the bumps (a solid sphere, I = ⅖mr²).Worked solution → Merit to Excellence

Question 2 — rotational motion (flywheel)

A golf ball is placed in a light cup attached to a flywheel of diameter 0.220 m, and begins to accelerate downwards at a constant 1.83 m s⁻².

m ball = 0.0460 kg
flywheel diameter = 0.220 m
a = 1.83 m s⁻²

Not tried yet: a Show the flywheel accelerating at 1.83 m s⁻² has angular acceleration 16.6 rad s⁻².Worked solution → Achieved
Not tried yet: b The ball and cup start from rest and fall 0.750 m. Calculate the flywheel's final angular velocity.Worked solution → Merit
Not tried yet: c Calculate the rotational inertia of the flywheel. Begin with the force that makes it accelerate: a free-body diagram helps you find the tension in the string.Worked solution → Merit to Excellence
Not tried yet: d Explain what happens to the final velocity of the ball and cup if the flywheel is replaced by a solid disc of the same radius and mass.Worked solution → Merit to Excellence

Question 3 — simple harmonic motion (watch glass)

A ball bearing is released on a watch glass — a shallow semi-circular glass bowl of radius of curvature R — and rolls back and forth with simple harmonic motion.

released 0.0400 m from equilibrium
T = 0.882 s

Not tried yet: a State the two conditions for a ball rolling on a watch glass to show SHM.Worked solution → Achieved
Not tried yet: b The ball is released 0.0400 m to the right of equilibrium and oscillates with a period of 0.882 s. Using reference circles or otherwise, calculate its displacement after 1.20 s.Worked solution → Merit to Excellence
Not tried yet: c Eventually the ball comes to rest. Draw a labelled displacement–time graph for five complete oscillations, with values for displacement and time.Worked solution → Merit
Not tried yet: d Name this phenomenon, and explain in detail why the ball eventually comes to rest. Support your answer with any relevant formulae.Worked solution → Merit to Excellence

2023 three questions 12 parts

The 2023 paper ↗ Marking schedule ↗

Question 1 — vertical circular motion

Tane has a toy car track: part is a horizontal banked curve of radius 0.750 m, part is a vertical loop of radius 0.250 m. The car has a mass of 0.120 kg. Assume sideways friction on the tyres is negligible.

m = 0.120 kg
banked curve r = 0.750 m at 1.55 m s⁻¹
loop r = 0.250 m

Not tried yet: a On a diagram of the car on the banked curve, draw a vector diagram to identify the net force that makes the car go in a horizontal circle. Label the net force.Worked solution → Achieved
Not tried yet: b The banked curve has a radius of 0.750 m. Calculate the angle of banking when there is no sideways friction on the wheels as the car goes round at 1.55 m s⁻¹.Worked solution → Merit
Not tried yet: c Explain why a person in a car on a real roller coaster feels heavier at the bottom of the loop than at the top. Begin by drawing labelled vectors for the forces on the car at the top AND at the bottom of the loop.Worked solution → Merit to Excellence
Not tried yet: d The 0.120 kg car approaches the vertical loop of radius 0.250 m. Calculate the speed it must have at the bottom of the loop to go round so that it seems weightless at the top.Worked solution → Merit to Excellence

Question 2 — rotational motion

Tane works weekends unloading barrels. He rolls an empty barrel of mass 5.50 kg and radius 0.280 m down a ramp 1.34 m high. The linear speed of the barrel at the bottom of the ramp is 3.40 m s⁻¹. Parts (c) and (d) move to Tane on a swivelling stool holding a full bottle of water in each hand: he spins more slowly with his arms outstretched than with his arms in.

m = 5.50 kg
r = 0.280 m
h = 1.34 m
v = 3.40 m s⁻¹

Not tried yet: a Describe the energy changes that take place as the barrel rolls down the ramp.Worked solution → Achieved
Not tried yet: b Calculate the rotational inertia of the barrel. Begin your answer by calculating the gravitational potential energy at the top and the angular velocity of the barrel as it reaches the bottom of the ramp. Assume no energy is lost due to friction.Worked solution → Merit to Excellence
Not tried yet: c Tane sits on a swivelling stool holding a full bottle of water in each hand. He spins more slowly with his arms outstretched than when he brings his arms in. Explain the reason for this observation.Worked solution → Merit
Not tried yet: d Tane spins with an angular velocity of 3.00 rad s⁻¹ with his arms outstretched. Bringing his arms in, he reaches 7.00 rad s⁻¹ in 4.50 s. Calculate his angular acceleration and the number of revolutions made in this time.Worked solution → Merit to Excellence

Question 3 — simple harmonic motion

Tanya studies a toy bouncing on a spring hanging from the ceiling. The spring constant is 24.6 N m⁻¹. She draws a graph of acceleration against displacement for the toy oscillating in simple harmonic motion.

k = 24.6 N m⁻¹
a plotted against y
T = 0.199 s

Not tried yet: a Given the simple harmonic motion equation a = −ω²y, describe how the gradient of the graph line relates to the frequency of oscillation.Worked solution → Achieved
Not tried yet: b By calculating the gradient of the graph, show that the period of oscillation is T = 0.199 s, and hence determine the mass of the toy hanging on the spring.Worked solution → Merit
Not tried yet: c Tanya pulls the spring (period T = 0.199 s) down 0.100 m from the equilibrium position and releases it so the toy bounces in simple harmonic motion. Using a reference circle or otherwise, calculate the time the toy would take to travel 0.140 m up from its release position.Worked solution → Merit to Excellence
Not tried yet: d Once set oscillating with amplitude 0.100 m and period T = 0.199 s, the amplitude gradually decreases and the toy eventually stops. State the name of this phenomenon and explain what causes the decrease in amplitude, then draw a graph of amplitude against time for three complete oscillations.Worked solution → Merit to Excellence

Read the last column as a to-do list. In all three papers every (a) is an Achieved calculation, often a "show that", and every (d) is marked at Merit and Excellence: the forces, energy or resonance behind the numbers. Most (c)s are too, so aiming for Excellence means finishing both.

Practice for this standard covers the whole topic — flashcards and quiz.