# Stresses in a bar due to rotation (Stress and Strain Part-2)

## Stress in a bar due to rotation

#### In the figure above consider a small strip dx at a distance x from the center. As the bar is rotating along axis Y-Y’ there will be a tensile force generated in the element AB or dx which will be given by the expression

##### Force on element AB (dx) = Centrifugal force Fc on the part BC.

First let us take some assumptions:

Mass of part BC = M

Area of Cross-section = Ac

Density of material = ρ

as shown in the figure distance of centre of  Mass BC from Y-Y’ axis = r

With these assumptions let’s proceed

#### Centrifugal force Fc on the part BC, Fc = ω²rM      ————–( 1 )

We all know that Mass = ρ x Volume

Now we will put the values of equation (2) , (3) in equation (1) , we get

This expression is very important because in exams if there is a question of rotating beams or bars,  you can directly use this expression to calculate stress at some general point.

#### Let us see some special cases, which might be asked in the exams.

We have already seen in figure that x is the distance from rotational axis.

## Stress = E* Strain

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