Question

Moment of intertia of a solid sphere about its diameter is 25 kg m². Calculate its moment of inertia about a tangent.

Answer 1

Given: `I_"diameter"` = 25 kg m²

For a solid sphere,

`I_"diameter" = 2/5 M R^2`

25 = `2/5 M R^2`

MR² = `(25 xx 5)/2`

 = `125/2`

= 62.5

The moment of inertia about a tangent is found using the parallel axis theorem:

∴ `I_"tangent" = I_"diameter" + MR^2`

= 25 + 62.5

= 87.5 kg.m²