1. The problem statement, all variables and given/known data A uniform circular disc has mass M and diameter AB of length 4a. The disc rotates in a vertical plane about a fixed smooth axis perpendicular to the disc through the point D of AB where AD=a. The disc is released from rest with AB horizontal. (See attached diagram) (a) Calculate the component parallel to AB of the force on the axis when AB makes an angle θ with the downward vertical. (b) Calculate the component perpendicular to AB of the force on the axis when AB makes an angle θ with the downward vertical 2. Relevant equations KE = (1/2)Iω2 I of a disc about axis perpendicular to disc through centre is (1/2)mr2 Transverse component of acc. = r(dω/dt) Radial component of acc. = rω2 3. The attempt at a solution I have done (a) okay with no problems and got the correct answer. I used a similar approach for part (b) but got the incorrect answer. For part (b): The moment of inertia is (1/2)M(2a)2 + Ma2 = 3Ma2 (using the parallel axis theorem). Using conservation of energy: (1/2)(3Ma2)ω2 = Mgacosθ (3/2)aω2 = gcosθ Differentiating w.r.t. θ gives: 3aω(dω/dθ) = -gsinθ 3aω(dω/dt)(dt/dθ) = -gsinθ (dω/dt) = -(g/3a)sinθ * Resolving forces: Mgsinθ - Y = Ma(dω/dt) Substituting in *: Mgsinθ - Y = -(Mag/3a)sinθ Y = Mgsinθ + (1/3)Mgsinθ = (4/3)Mgsinθ The answer is supposed to be (2/3)Mgsinθ. I can't see what I have done wrong. Any help would be greatly appreciated!