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All linear dimensions of the ring will increase by the same percentage. delta L = L * alpha * delta T where delta L = change in linear dimension, L = original value of linear dimension (at the reference temperature), alpha = coefficient of thermal expansion, dalta T = change of temperature...

Thanks Nick55 for pointing out the mistake in my derivation. Deak's formula is indeed correct.

If the pivot is fixed, it is effectively infinitely stiff. Then the rotational natural frequency about 2 is: f = sqrt[(k1.L12^2 + k3.L23^2)/(m1.L12^2 +m3.L23^2)] /2/pi where L12 = distance from 1 to 2 L23 = distance from 2 to 3 m1 = mass at 1 m3 = mass at 3 f = frequency masses in kg...

The formula is wrong (by a factor of 100) For a hydraulic, positive displacement motor or pump, torque is the same as work per radian and there are 2.pi radians in a revolution. Thus 2.pi.T = work done per rev, in joules per rev if T is in Nm. Work done by fluid/rev = P.v where P = pressure...

If you want to build up a sphere with equilateral triangles you can only use the tetrahedron. All the other regular solids use different face geometries. Clearly a 600mm sided triangle is not going to give a tetrahedron inscribed on a sphere of 11000mm diameter. If approximations are allowed...