Question

Find the moment of inertia of a disc(m=2kg,r=0.5) about an axis passing through it’s edge and parallel to its plane

Answer 1

Answer:

The required moment of inertia is 5/8

Explanation:

Given :

mass of the disc, m = 2 kg

radius of the disc, r = 0.5 m

To find :

the moment of inertia about an axis passing through it’s edge and parallel to its plane

Solution :

By parallel axis theorem,

I = I꜀ + md²

where

I꜀ denotes the moment of inertia of the disc about an axis passing through center and parallel to its plane

d denotes the distance of point from the center

here, we have to find the moment of inertia about an axis passing through it’s edge and parallel to its plane  

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so, d = r

and moment of inertia of the disc about an axis passing through the center and parallel to its plane, I꜀ = mr²/4

Substitute the values,

I = mr²/4 + mr²

I = (mr² + 4mr²)/4

I = 5mr²/4

I = 5(2)(0.5)²/4

I = 10 × 0.25 × 1/4

I = 25/40

I = 5/8

Therefore, the moment of inertia of the given disc about an axis passing through it’s edge and parallel to its plane is 5/8