physics kinematics

Question

The moment of inertia of a uniform circular disc about its diameter is 100 g cm². What is its
moment of inertia (i) about its tangent (ii) about an axis perpendicular to its plane ?

Answer 1

(i) By the theorem of parallel axes, moment of inertia about a tangent parallel to the diameter, 

I = Id+MR² = 1/4 MR²+MR²=5/4 MR² 

I = 5×100 = 500 gcm².

(ii) By theorem of perpendicular axes, moment of inertia of the disc about an axis perpendicular to its plane, 

I = Sum of the moments of inertia about two perpendicular diameters 

I = Id+Id=2×1/4×MR²=2×1000= 200 gcm².