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THEOREMS OF PERPENDICULAR AND PARALLEL AXES

Perpendicular axes theores

By the theorem of perpendicular axes for a disc,

Iz = Ix + Iy

X, Y and Z are mutually perpendicular axes

In the above equation, axes lie in the plane of the disc

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Moment of Inertia of a Rod

Question

p

L is the length of the rod, Iz is the MI about an axis through mid point and perpendicular to the rod

Moment of Inertia about an axis perpendicular to it through one end ?

Hint

Parallel axes theorem on MI , Iz′ = Iz + Ma2

a = L/2

 

Answers

m

m

m

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Examples - Theorems on M I

Question

ring

About the axis perpendicular to plane, at centre I = MR2

Answers

½MR2 Moment of Inertia about any diameter

³/²MR2  Moment of Inertia about any diameter

It = 3MR2 Moment of inertia of a ring about a tangent perpendicular to its plane 

It = 2MR2 Moment of inertia of a ring about a tangent perpendicular to its plane 

It = ³/² MR2 Moment of inertia of a ring about a tangent in its plane 

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