The Maxwell's Pendulum

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Slow, compared with the free fall, movement of the pendulum is caused by a considerable share of the rotation in the overall energy balance.

While the share of the rotation energy in the total kinetic energy of the full cylinder rolling down freely is 1/3, for a big cylinder with a radius R fixed on the axis with a radius r , the kinetic energy of the translation motion is ½mv² and the rotation energy is ¼mv²(R/r)². v is the velocity of the centre of mass (we recall that moment of inertia for a hollow cylinder is mr²and for the solid one it is ½mr²).

If R = 5 cm and r = 0.5 cm, as is the case with our pendulum, 50 times more energy is accumulated in rotation than in sliding motion.

The pendulum falls with a 'diluted' gravitational acceleration of 2g(r/R)², i.e. 1/50 of the "full" gravitational acceleration.