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Chapter 10: Problem 25

Four equal masses \(m\) are located at the comers of a square of side L. connected by essentially massless rods. Find the rotational inertia of this system about an axis (a) that coincides with one side and (b) that bisects two opposite sides.

Short Answer

Expert verified
The moment of inertia for system about an axis that coincides with one side is \(2*m*L^2\) and that bisects two opposite sides is \(m*L^2\).

Step by step solution

01

Define the Mass and Distance for (a)

Given, Mass of each object = \(m\). There are four objects attached to a square of side \(L\), hence there are two masses at distance zero and two masses are at a distance \(L\) from the axis.
02

Calculating Moment of Inertia for (a)

Substituing the values into the formula of moment of inertia, we get \(I = \sum m*r^2 = 2*m*0^2 + 2*m*L^2 = 2*m*L^2\).
03

Define the Mass and Distance for (b)

On the other hand, for the axis that bisects two opposite sides, all four masses are the same distance from the axis, which is \(L/2\).
04

Calculating Moment of Inertia for (b)

Substituing these values into the formula, we get \(I = \sum m*r^2 = 4*m*(L/2)^2 = m*L^2\).

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