What it shows
Objects of the same mass and radius roll down a slope at different speeds, because their mass is spread differently. The ball wins and the hollow ring comes last, and the rolling acceleration can be calculated from the moment of inertia.
The science
Energy at the top, m g h, becomes both movement of the centre and rotation: m g h = ½ m v² + ½ I ω². Writing I = k m r² and ω = v / r, the acceleration along a slope of angle θ is a = g sin θ / (1 + k). For a thin ring k = 1 so a = g sin θ / 2, for a solid cylinder k = 1/2 so a = g sin θ × 2/3, and for a solid sphere k = 2/5, so a = g sin θ × 5/7. The object with the smallest k, the sphere, accelerates most.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A long smooth plank about 1.2 m long, raised by books
- An empty steel can with its lid and base on (hollow cylinder)
- A solid wooden or plastic cylinder of about the same radius, or a can filled with plaster
- A solid ball such as a steel or rubber ball of about the same size
- A phone stopwatch or phone video
- A tape measure and a protractor or a ruler for the slope
- A flat block to make the start line
Safety
For this project: Keep fingers clear of the objects at the end of the slope and catch them in a box.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Raise one end of the plank by 15 to 20 cm to make a gentle slope and measure its length L and the angle θ.
Line up the three objects at the start line with a flat block behind them and lift the block to release all three together.
Watch which reaches the bottom first and note the order, and repeat several times.
Time each object separately over the length L from rest, three times each, and take the average.
Calculate the acceleration a = 2 L / t² for each object.
Compare the experimental accelerations with g sin θ / (1 + k) for the ring, cylinder and sphere.
Repeat with a different slope and see that the order of the race does not change.
What you should see
The ball finishes first, the solid cylinder second and the hollow can last, whatever the size or mass. The accelerations are in the ratio of about 0.5 : 0.67 : 0.71 times g sin θ.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Why does the ball roll fastest?
Its mass is closest to the centre, so its moment of inertia is smallest and less energy goes into spinning.
2Does the mass of the object change the race result?
No, m cancels out in the equation, so only the shape matters.
3What is moment of inertia?
The rotational equivalent of mass: how hard it is to change an object’s rotation.
4Why does a sliding block beat all the rolling objects on a smooth slope?
It uses all the energy for movement and none for rotation, so a = g sin θ.
Take it further
Fill a can with sand and a can with water and race them to see how a loose filling changes the result.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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