Momentum (Linear and Angular)

Moment of Inertia: Momentum of inertia can be defined as:

r = distance of the body of mass, m from centre of asis.

• Very thin circular loop (ring): I=MR²

where, M = mass of the body

R = radius of the ring

I = moment of inertia

• Uniform circular loop 

• Uniform solid cylinder 

• Uniform solid sphere 

• Uniform thin rod

(AA’) moment of inertia about the centre and perpendicular axis to the rod moment of inertia about the one corner point and perpendicular (BB’) axis to the rod.

• Very thin spherical shell

• Thin circular sheet

• Thin rectangular sheet

• Uniform right cone

• Uniform cone as a disc

Suppose the given section is 1/n th part of the disc, then mass of disc will be nM.

Inertia of the disc, 

Inertia of the section,