Question

A disk of radius Rₐ =5 cm and mass mₐ =20 g is placed on top of a larger disk of radius Rᵦ =40 cm and mass mᵦ =100 g. Assume they are rotating about a common axis through their center and perpendicular to the face of both disks. Calculate the moment of inertia for the combined system if the smaller disk is centered on top of the larger disk. Show your work.

Answer 1

The total moment of inertia for the combined system of two concentrically placed disks is 0.008025 kg·m², computed by adding the moments of inertia of the individual disks.

Step-by-step explanation:

The question asks us to calculate the moment of inertia for a system of two disks rotating about a common axis. The smaller disk, with radius Rᴀ = 5 cm and mass mᴀ = 20g, is placed on top of a larger disk with radius Rβ = 40 cm and mass mβ = 100 g.

To find the total moment of inertia for the system, we sum the moments of inertia for each disk about the common axis. The moment of inertia for a solid disk about its central axis is given by the formula I = ½ mR². Thus, for the smaller disk, the moment of inertia is Iᴀ = ½ (0.02 kg)(0.05 m)² and for the larger disk, it is Iβ = ½ (0.1 kg)(0.4 m)².

Performing the calculations, we have:

• Iᴀ = ½ (0.02 kg)(0.05 m)² = 0.000025 kg·m²
• Iβ = ½ (0.1 kg)(0.4 m)² = 0.008 kg·m²

Adding these together gives the total moment of inertia for the system:

Itotal = Iᴀ + Iβ = 0.000025 kg·m² + 0.008 kg·m² = 0.008025 kg·m²