Question

An uniform rod of length 2L has mass per unit length m the moment of inertia after rod about an axis passing through its centre and perpendicular to its length is​

Answer 1

The moment of inertia of the rod is I = 2/3 m L^3.

Explanation:

Let the mass is dm, and the length is dx at a distance x from the given axis  then

• dm = mdx

The moment of inertia of this mass will be

• dI = dmx^2 = mx^2dx

Thus, the moment of inertia of the half rod of length L

I = ∫L - 0 mx^2dx

I = mx^3/3

I  = m L^3/ 3

The other half will also have this moment of inertia

Therefore, the moment of inertia of the rod

= 2 I

= 2 x m L^3/ 3 = 2/3 m L^3

Hence the moment of inertia of the rod is I = 2/3 m L^3.

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What is the moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end?

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Answer 2

Explanation:

Physics 11th Rotational motion