Question

A solid circular disk of 0.025 m thickness is used as a flywheel. The density of the disk material is 7800 kg/m³ and the mass moment of inertia of the disk about its center is 4.36 kg·m². The radius, in m, of the disk is ................. (round off to 2 decimal places).

• A. 0.32
• B. 0.33
• C. 0.34
• D. 0.36

Hint:

For moments of inertia, remember the formula \(I = \frac{1}{2} m r^2\) and use the correct mass calculation based on the volume and density of the disk.

Answer 1

The Correct Option is A

- The mass moment of inertia \(I\) for a solid disk is given by the formula: \[ I = \frac{1}{2} m r^2 \] Where \(m\) is the mass of the disk and \(r\) is its radius.
- The mass \(m\) of the disk can be calculated using the volume formula for a cylinder \(V = \pi r^2 h\), where \(h\) is the thickness of the disk. Thus, the mass is: \[ m = \text{density} \times V = 7800 \times \pi r^2 \times 0.025 \] - We substitute the values into the formula for \(I\) and solve for \(r\).