Question

In: Physics

You are handed a rod that is three times as dense on one end as it...

You are handed a rod that is three times as dense on one end as it is on the other end. Find the moment of inertia when the axis of rotation is about the heavy end, and find the moment of inertia when the axis of rotation is about the light end.

Expert Solution

the linear density may be changes from to 3

then ( x ) = ( 1 + 2x/L )

the moment of inertia of the lighter end is

I_Lighter = ( x ) x² dx

I_Lighter = 5 L³ / 6

the total mass is M = ( x ) dx

= 2 L

so

the moment of inertia when the axis of rotation is about the light end is I_Lighter = 5 M L² / 12

the moment of inertia of heavier end is

x = ( L - x )

so

I_heavier = ( L - x ) x² dx

so

the moment of inertia when the axis of rotation is about the heavy end is I_heavier = M L² / 4

genius_generous answered 47 minutes ago

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