Question

Find the moment of inertia of the two uniform joint rods having mass m each about point P as shown in figure. Using parallel axis theorem.

Answer 1

From the figure , A is the mid point of rod OB,

Using Pythagoras theorem $\Rightarrow AP=\sqrt{l^2+\frac{l^2}{4}}$= $\frac{\sqrt{5}}{2}l$,

Moment of inertia (MOI) of rod OP about point P= $\frac{m{l}^2}{3}$

Using parallel axis theorem, MOI of rod OB about point P=$\frac{m{l}^2}{12}+\frac{5}{4}m{l}^2=\frac{4}{3}m{l}^2$

Adding MOI= $\frac{m{l}^2}{3}$ + $\frac{4}{3}m{l}^2$= $\frac{5}{3}m{l}^2$