Question

Question 2 A 70-kg wheel is 120-cm in diameter and has heavy spokes connecting the rim to the axle. To find moment inertia of the wheel experimentally, you mount the wheel on a low-friction bearing then wrap a light cord around the outside of the rim to which you attach a 20-kg bag of sand. When the bag is released from rest, it drops 3.77-m in 1.6-s during which time the wheel rotates through an angle of 2rt-radians. Find the wheels moment inertia. Hint: Use energy considerations.

Answer 1

Apply energy conservation

$mgh=\frac{1}{2}mv^{2}+\frac{1}{2}I\omega ^{2}$

$mgh=\frac{1}{2}m(\omega r)^{2}+\frac{1}{2}I\omega ^{2}$

where

$\omega =\frac{2\pi }{1.6}=3.925\: rad/s$

$20\times 9.81\times 3.77=\frac{1}{2}\times 20(3.925\times 0.6)^{2}+\frac{1}{2}I(3.925) ^{2}$

$I=88.826Kg/m^{2}\: \; \; \; \; {\color{Red} Ans}$