Question

A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the centre. Calculate x if the wheel now rotates at 80 rpm.

Answer 1

Data : f₁ = 60 rpm = 60/60 rot/s = 1 rot/s, f₂ = 30 rpm = 30/60 rot/s =1/2 rot/s, ∆E = — 100 J

(i)

This gives the MI of the flywheel about the given axis.

(ii) Angular momentum, L = Iω = I(2πf) = 2πIf The change in angular momentum, ∆L

= L₂ – L₁ = 2πI(f₂ – f₁)

= 2 × 3.142 × 6.753(\(\cfrac{1}{2}\)– 1)

= -3.142 × 6.753 = -21.22 kg.m² /s