How to play Hanging Mobile
- Choose a mobile and read the ornaments' masses and positions on the card.
- Start at the bottom: a balanced lower mobile acts as one mass, its total, where its string is tied.
- Find the top rod's centre of mass, x_cm = Σm·x ÷ Σm, or the ornament that puts it at the knot, and press Let go.
- Watch the green mark: if it is right below the knot, the rod hangs level; otherwise it tilts toward it.
Why does a mobile hang level?
A rod hanging from a string turns until its centre of mass is right below the knot. If the knot is tied exactly at the centre of mass, x_cm = Σm·x ÷ Σm, nothing turns the rod and it hangs level. A mobile is a set of such rods, one hanging from another. The trick is to work from the bottom up: once a lower mobile is balanced, everything in it pulls on its string like a single mass equal to its total, at the point where the string is tied. For the rod above, the whole lower mobile is just one more mass. The same idea finds the centre of mass of any object made of parts: replace each part by its mass placed at its own centre of mass.
A focused learning model
Rods are light and rigid; ornaments are point masses hanging from their tie points, and a balanced lower mobile acts as its total mass at its knot. The knot holds the top rod level while its centre of mass is within 0.5 cm of it. Otherwise the rod turns from rest about the knot, θ = ½·α·t² with α = M·g·d ÷ I, and is drawn until it has tilted 20°, found exactly. Plays in real time.