Question

Moment of Inertia

Instruction: Analyze and solve the given probleme.

1. A uniform, thin, solid door has height 2.00 m, width 0.825 m, and mass 23.5 kg. . a) Find its moment of Inertia for rotation on Its hinges. b) Is any piece of data unnecessary on the given problem?

2.A system consists ( thin-hollowed sphere) of three email masses rotating at the same speed about the same fixed axis The masses and their radii of ratation are: 16 g at 256

mm, 23 g at 192 mm and 31 g at 176 mm. Determine (a) the moment of inertia of the system about the given axis.

Answer 1

1. The moment of inertia is

$$I=\frac13 mw^2=\frac13 ·23.5·0.825^2=5.33\text{ kg}·\text{m}^2.$$

The unnecessary piece of data is the height.

2. The moment of inertia of the system is

$$I=\frac23(m_1r_1^2+m_2r_2^2+m_3r_3^2),\\ I=1.9·10^{-3}\text{ kg}·\text{m}^2.$$