Physics of Traditional Māori Games
Physics of Traditional Māori Games · Years 10–12
Ngā Whāinga Akoranga · Learning Intentions
- Investigate a scientific concept or phenomenon using observation and evidence
- Apply scientific understanding to explain natural processes and systems
- Connect scientific knowledge to environmental decision-making and kaitiakitanga
- Evaluate how both mātauranga Māori and Western science contribute to understanding
Paearu Angitu · Success Criteria
- I can describe the key concept or phenomenon accurately using scientific vocabulary
- I can explain how evidence supports my scientific understanding
- I can connect scientific knowledge to at least one real-world environmental application
- I can identify where mātauranga Māori and Western science perspectives intersect or differ
Physics of Traditional Māori Games
🌀 Force, momentum, angular velocity, and friction — through taonga tākaroTaonga tākaro — traditional Māori games — were not random play. Tī rākau developed precise neuromuscular coordination, poi trained rotational mechanics, and kī-o-rahi used complex spatial strategy. In this handout you will apply Newton's laws, circular motion, momentum and friction to scenarios drawn from these games.
About the numbers on this sheet
Every quantity in the tables below is an illustrative scenario value chosen for calculation practice — a plausible set of figures to reason with. They are not measurements taken from real taonga tākaro practice, and no measurement study is being reported here. If your class measures its own poi or rākau, use your own numbers instead; the physics method is the point.
Descriptions of how these games were and are played, and what they meant, belong to the hapū and iwi who hold them. This sheet applies physics to a classroom scenario; it does not settle questions of tikanga or history. Seek local mana whenua authority for those.
Part 1 — Poi: Angular Velocity and Circular Motion
🌀 What is Poi?
Poi are weighted balls on a cord, swung in patterns around the body. They are used today in kapa haka and as a coordination, rhythm and timing practice. Poi also carry a longer history in te ao Māori that this physics handout does not attempt to summarise.
The fastest poi in the table below — the performance LED poi, 3.8 rev/s on a 0.55 m cord — is moving at about 13 m s⁻¹, roughly 47 km/h, at the ball. Don't take that on trust: it is the first thing you will calculate.
When a poi ball travels in a circle, it undergoes uniform circular motion. The physics:
| Poi Style | String Length (r) | Rotations per second | Mass of ball (m) |
|---|---|---|---|
| Traditional raupō | 0.35 m | 2.5 rev/s | 80 g |
| Performance LED | 0.55 m | 3.8 rev/s | 120 g |
| Fire poi | 0.48 m | 1.8 rev/s | 200 g |
- For the traditional raupō poi, calculate:
- The period T (hint: T = 1/frequency)
- The speed v at the tip
- The centripetal force F_c needed
- The fire poi have more than double the mass of raupō poi but spin slower. Calculate the centripetal force for fire poi and compare to raupō. Why might a performer choose different poi types for different contexts?
- Extension: A poi string exerts centripetal force on the ball. The ball exerts an equal and opposite force on the performer's wrist (Newton's 3rd Law). Calculate the force on the wrist for performance LED poi at maximum speed. Convert to kg-force and comment on the physical conditioning required.
Part 2 — Tī Rākau: Momentum and Catching
🪵 What is Tī Rākau?
Tī rākau are short rākau (sticks) tossed and caught in synchronised patterns between partners. The game develops timing, spatial reasoning, and rapid reflexes. In advanced versions, 4–6 players exchange sticks simultaneously while chanting.
When a rākau (stick) is thrown and caught, we apply:
| Measurement | Value | Notes |
|---|---|---|
| Rākau mass | 0.18 kg | Traditional hardwood |
| Throwing speed | 4.2 m/s | Scenario value for this calculation |
| Catch time | 0.08 s | Time from contact to full stop |
| Throw angle | 72° from horizontal | Scenario throw angle |
| Max height reached | 0.81 m above release | Used to verify with projectile motion |
- Calculate the momentum of the rākau at release. What force is applied by the catcher's hand to stop it in 0.08 seconds?
- Using projectile motion, verify that a rākau thrown at 4.2 m/s at 72° would reach 0.81 m:
h = (v_y)² / (2g) where v_y = v × sin(72°)
-
Friction and Grip: A rākau would slip if the static friction force is less than the
horizontal force needed to redirect its momentum during catching. If μ (coefficient of friction between hand
and wood) = 0.55 and Normal force = 8 N, what is the maximum friction force? Is the rākau likely to slip?
f = μN
Part 3 — Kī-o-rahi: Strategy, Angles, and Energy
🏐 What is Kī-o-rahi?
Kī-o-rahi is a fast-moving team sport played on a circular field of concentric zones — Te Ao (the outer ring), Te Roto, and Te Pawero — with a central tupu (target) and pou (posts) spaced around the perimeter. One team (Kīoma) score by touching the pou with the kī and then scoring; the other team (Taniwha) score by throwing the kī to hit the central tupu. In 2005, McDonald's Passport to Play programme chose kī-o-rahi to represent Aotearoa in 31,000 American schools (NZ Herald, 8 October 2005) — recognising its deep roots and athletic complexity.
- Field Geometry: A kī-o-rahi field is circular with radius 40 m. A Kīoma player runs from the edge at position A to retrieve the kī beside the central tupu at position O (the field centre), then out to position B on the opposite side. If A and B are 120° apart on the circumference, what is the total distance run? What is the displacement? (Use the cosine rule for displacement: c² = a² + b² − 2ab cos C)
- Energy Expenditure: A 65 kg player sprints at 7.2 m/s. Calculate their kinetic energy. If they must stop in 1.5 seconds (due to a Taniwha defender), calculate the average retarding force.
-
Cultural-Physical Analysis: Kī-o-rahi is said to be based on the pūrākau of
Rahi-tutaka-hina and the rescue of his wife Tiarakurapakewai (Otago Daily Times, 2012;
r2r.org.nz) — tūpuna storytelling encoded in the very shape of the game.
Write 4–5 sentences connecting the physics of the game (circular motion, energy, spatial strategy) with its narrative meaning. What does it mean to say the game "contains physics" and "contains story" at the same time?
🌀 Whakamutunga — The Body Knows Physics
Before Newton published his laws in 1687, Māori were already encoding physics into culture — poi demonstrates torque and centripetal force, tī rākau demonstrates impulse and momentum, kī-o-rahi demonstrates circular geometry and kinetic energy. These are not coincidences; they are evidence of a deep embodied understanding of the physical world expressed through taonga tākaro.
Final challenge: Design your own "physics measurement" experiment using poi or tī rākau. What variables would you measure? What physics concepts would you test?
🌿 Ngā Rauemi Hono — Related Resources
Hononga Marautanga · Curriculum Alignment
"Investigate physical phenomena (in the areas of mechanics, electricity, electromagnetism, light and waves, and atomic and nuclear physics) and produce qualitative and quantitative explanations for a variety of unfamiliar situations."
NZC 2007 Level 7, Science: Physical World.
Tuhia ōu whakaaro · Write Your Thoughts
Reflect on your learning. What was the most important idea? What question do you still have?
Aronga Mātauranga Māori
Traditional games and tools like poi, tī rākau and kī-o-rahi carry generations of careful physical refinement — timing, weight, grip and motion tuned against how they actually behaved in use. This handout takes a Western-physics lens on that same behaviour (motion, force, energy); it is one way of describing it, not the only one, and it does not attempt to speak for the fuller mātauranga Māori and tikanga behind these games and tools. Kaiako wanting to bring that fuller picture in are best placed to do so, ideally alongside kaiako Māori.
Ngā Rauemi Tautoko · Resources already provided
This handout is designed to be used alongside other resources in the same unit. Related materials are linked in the unit planner. All content is provided — no additional preparation is required to use this handout in your classroom.