Hi coolkiddonald101, thanks for getting in touch. In order to find the moment of inertia of the helicopter rotor we need to use one of the formulas in Figure 8-20 on pg. 210 which gives a list of formulas for different shapes and positions of the axis of rotation. The question tells us to treat each blade as a rod with an axis of rotation at the end (the end in this case being the center of the rotor where it connects to the axel that goes to the motor). The moment of inertia formula for a rod with an axis of rotation at the end is $\dfrac{1}{3}ML^2$, so that's where the $\dfrac{1}{3}$ comes from: it's part of the appropriate formula. If you're asking why that formula has the $\dfrac{1}{3}$, then don't worry about it since it's a non-obvious result of using calculus, which is beyond the scope of a course in algebraic physics.

## Comments

please explain why you have (1/3)

Hi coolkiddonald101, thanks for getting in touch. In order to find the moment of inertia of the helicopter rotor we need to use one of the formulas in Figure 8-20 on pg. 210 which gives a list of formulas for different shapes and positions of the axis of rotation. The question tells us to treat each blade as a rod with an axis of rotation at the end (the end in this case being the center of the rotor where it connects to the axel that goes to the motor). The moment of inertia formula for a rod with an axis of rotation at the end is $\dfrac{1}{3}ML^2$, so that's where the $\dfrac{1}{3}$ comes from: it's part of the appropriate formula. If you're asking why that formula has the $\dfrac{1}{3}$, then don't worry about it since it's a non-obvious result of using calculus, which is beyond the scope of a course in algebraic physics.

Best wishes with your studies,

Mr. Dychko