Celtrix

Spin Celtrix the wrong way and she wobbles, rattles, and spins back the other way.

The Physics

A rattleback is a boat-shaped top whose mass axes are slightly twisted relative to its curved base (δ ≠ 0). Friction at the contact point couples wobbling to spinning, so in the unfavoured direction spin turns into rocking and then back into spin the other way. Angular momentum is not violated: the friction force at the contact exerts the torque.

dL/dt = r_c × F_c

• L: angular momentum (kg·m²/s)
• t: time (s)
• r_c: position of the contact point from the centre of mass (m)
• F_c: contact force from the table (N)
• δ: misalignment angle (rad)

G. T. Walker analysed it in 1896.

Honest caveat: Some celts reverse more than once; not every rattleback reverses in only one direction.

On the shirt

Front: Celtrix, the pixel-art character, with the title. Back: the torque equation, the misalignment angle, the friction explanation and Walker's 1896 paper. Printed on a unisex tee.