CBSE Class 11-science Answered
State the theorem of :(i) perpendicular axis (ii) parallel axis
Asked by Rizu | 05 Nov, 2019, 07:27: PM
Expert Answer
Figure shown above illustrates the perpendicular axis theorem. It states that the moment of inertia of a planar body (lamina)
about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent
with perpendicular axis and lying in the plane of the body.
The figure shows a planar body. An axis perpendicular to the body through a point O is taken as the z-axis.
Two mutually perpendicular axes lying in the plane of the body and concurrent with z-axis, i.e. passing through O,
are taken as the x and y-axes. The theorem states that
are taken as the x and y-axes. The theorem states that
Iz = Ix + Iy
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Parallel axis theorem is stated as follows:
The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing
through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.
The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing
through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.
As shown in the above Figure, z and z′ are two parallel axes separated by a distance a.
The z-axis passes through the centre of mass O of the rigid body. Then according to the theorem of parallel axes
Iz′ = Iz + Ma2
where Iz and Iz′ are the moments of inertia of the body about the z and z′ axes respectively, M is the total mass of the body
and a is the perpendicular distance between the two parallel axes.
Answered by Thiyagarajan K | 05 Nov, 2019, 11:00: PM
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