Question

find the moment of inertia of a uniform rod of length L about an axis prependicular to its end passing through a point at distance L/4 from an end

Answer 1

QUESTION

Find the moment of inertia of a uniform rod of length $L$ about an axis perpendicular to its end passing through a point at distance $L/4$ from an end

SOLUTION:

According to the parallel axis theorem, the moment of inertia of a rod about an axis perpendicular to its end passing through a point at distance $L/4$ from an end is:

$$I = I _ {0} + m \left(\frac {L}{4}\right) ^ {2}$$

Where

$I_0 = \frac{m\cdot L^2}{12}$ - the moment of inertia of a rod about an axis through its center of mass.

Hence

$$I = \frac {m \cdot L ^ {2}}{1 2} + m \left(\frac {L}{4}\right) ^ {2} = \frac {4 m \cdot L ^ {2} + 3 m \cdot L ^ {2}}{4 8} = \frac {7 m \cdot L ^ {2}}{4 8}$$

ANSWER

$$I = \frac {7 m \cdot L ^ {2}}{4 8}$$