Question: A solid sphere of mass 2 kg and radius 0.5 m is rotating about an axis passing through its center with an angular speed of 5 rad/s. Calculate the moment of inertia of the sphere about this axis.
Answer: The moment of inertia (I) of a solid sphere rotating about an axis passing through its center is given by the equation:
Where:
Given: m = 2 kg r = 0.5 m ω = 5 rad/s
Substitute the given values into the equation: [I = \frac{2}{5} \times 2 \times (0.5)^2] [I = \frac{2}{5} \times 2 \times 0.25] [I = \frac{1}{5} \times 2 \times 0.25] [I = \frac{1}{5} \times 0.5] [I = 0.1 , \text{kg} \cdot \text{m}^2]
Therefore, the moment of inertia of the sphere about the given axis is 0.1 kg·m^2.