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Problem: A uniform, thin, solid door has height 2.20 m, width 0.870 m, and mass 23.0 kg. (a) Find its moment of inertia for rotation on its hinges. (b) Is any piece of data unnecessary?

FREE Expert Solution

We get the moment of inertia from the principle of summing up the moment of inertia of infinitesimal mass elements. 

Let the infinitesimal mass element be dm.

The moment of inertia of this mass element is dm•r2

Here, is the distance from the mass element to the axis about where we're considering the moment of inertia. 

Therefore, the moment of inertia of the door on its hinges is given by:

I=r2dm

The horizontal position with respect to the hinge can be taken to be x.

We can also define a linear density λ = m/L where m is the mass of the door and L is the width of the door.

We see that dm = λdx

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Problem Details

A uniform, thin, solid door has height 2.20 m, width 0.870 m, and mass 23.0 kg. 

(a) Find its moment of inertia for rotation on its hinges. 

(b) Is any piece of data unnecessary?

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Our data indicates that this problem or a close variation was asked in Physics for Scientists and Engineers - Serway Calc 9th Edition. You can also practice Physics for Scientists and Engineers - Serway Calc 9th Edition practice problems.