Question
The moment of inertia of disc about an axis passing through centre and perpendicular to the plane of disc is1/2 MR2 , where M is mass and R is radius of disc. Find the moment of inertia about:
(i) diameter
(ii) tangent parallel to diameter.
Solution
(i) Moment of inertia of ring about diameter:
Disc is symmetric with respect to all of its diameters, therefore the moment of inertia of disc about all the diameters is same.
Let Id be the moment of inertia of ring about its diameter.
According to the theorem of perpendicular axis,
Disc is symmetric with respect to all of its diameters, therefore the moment of inertia of disc about all the diameters is same.
Let Id be the moment of inertia of ring about its diameter.
According to the theorem of perpendicular axis,
(ii) Moment of inertia of disc about tangent parallel to diameter:
Let A' B' be the tangent parallel to diameter AB. By using the theorem of parallel axis,
