Moment of inertia Parallel axis theorem The moment

Moment of inertia

Parallel axis theorem The moment of inertia of a body about a given axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of mass and the product of its mass and square of perpendicular distance between the two axes. r I=Ic+Mr 2 Ic

Perpendicular axis theorem The moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of moment of inertia about two mutually perpendicular axes in its plane and intersecting each other at the point where the perpendicular axis meet the lamina. Iz Iz=Ix+Iy

To find moment of inertia Consider a small element Ø Find its mass Ø Find the MI of that small element Ø Integrating with proper limit to get total MI Ø

Thin uniform rod Through one end of the rod and perpendicular to its length about an axis, passing through its centre and perpendicular to its length

About an axis, passing through its centre and perpendicular to its length x length l and mass M Thickness dx

Through one end of the rod and perpendicular to its length Ic I=Ic+Mr 2

Circular ring About any diameter Through its centre and perpendicular to its plane About any tangent parallel to the diamete

Through its centre and perpendicular to its plane

About any diameter z Iz=Ix+Iy Iz=2 Ix

About any tangent parallel to the diameter R

Circular disc

Through its centre and perpendicular to its plane

About any diameter

About any tangent parallel to the diameter

Solid cylinder

About the axis

Through the centre perpendicular to its own axis