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Chapter 10: Problem 26

The shaft connecting a power plant's turbine and electric generator is a solid cylinder of mass \(6.8 \mathrm{Mg}\) and diameter \(85 \mathrm{cm} .\) Find its rotational inertia.

Short Answer

Expert verified
The rotational inertia of the shaft is \(I = \frac{1}{2} \times 6.8 \times 10^{6} kg \times (0.425 m)^2 kg \cdot m^2\).

Step by step solution

01

Convert mass and diameter to appropriate units

Convert the given mass from Mg to kg and diameter from cm to m: Mass \(M = 6.8 Mg = 6.8 \times 10^{6} kg\) and Diameter \(D = 85 cm = 0.85 m\).
02

Calculate the radius of the cylinder

The radius of the cylinder is half its diameter. So, \(R = \frac{D}{2} = \frac{0.85 m}{2} = 0.425 m\).
03

Calculate the rotational inertia

The rotational inertia of a solid cylinder \(I\) can be calculated by using the formula \(I = \frac{1}{2} m r^2\), where \(m\) is the mass and \(r\) is the radius. Substitute the values into the formula: \(I = \frac{1}{2} \times 6.8 \times 10^{6} kg \times (0.425 m)^2 \).

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