Answer to Question #115940 in Mechanics | Relativity for Hessa Alawadhi

Question

In the figure below, two particles with a mass m1= 0.83kg are fastened to each other and to a rotation axis at O by two thin rods each with length d=10 cm and mass=1.4 kg. The combination rotated around the rotation axis with angular speed w= 0.33 rad/s. Measures by O, what is the combination’s rotational inertia?

Answer 1

Since no figure or link for the figure was attached, assume that the situation looks like this:

Luckily, the moment of inertia is an additive quantity, which helps us to calculate the total rotational inertia. For the rod of mass 2m and total length 2d the moment of inertia will be

$$I_r=\frac{ML^2}{12}=\frac{2m\cdot(2d)^2}{12}=\frac{2md^2}{3}.$$

The moment of inertia of the two masses m₁:

$$I_m=2m_1d^2.$$

The total moment of inertia:

$$I=I_r+I_m=2d^2\bigg(\frac{m}{3}+m_1\bigg)=0.026\text{ kgm}^2.$$

Also, we can calculate the angular momentum of the system:

$$L=I\omega=8.6\cdot{ 10}^{-3}\text{ kg/s}\cdot\text{m}^2.$$