Derivation of Moment of Inertia of Solid Sphere

Recall that in our derivation of this equation each piece of mass had the same magnitude of velocity which means the whole piece had to have a single distance r to the axis of rotation. Hence the relative density is a ratio which is a constant for a particular substance.

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Find the moment of inertia of the rod and solid sphere combination about the two axes as shown below.

. The rod has length 05 m and mass 20 kg. Generally it is used as a base for building the moment of inertia expression for different other shapes such as a cylinder or a sphere. The Buckingham π theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n m dimensionless parameters where m is the rank of the dimensional matrixFurthermore and most importantly it provides a method for computing these dimensionless parameters from the given variables.

They are as follows. An irregular solid when immersed in water displaces 3 litre of water. However for a disk we have to take it as a special character.

So the ratio of the density of body and density of water do not change. Meanwhile we can also find the moment of inertia of a circular disc with respect to different situations. Th 4 1 litre 1000 cm3 The mass of the displaced water 750 g.

The volume of the solid 750 cm3.

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