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Calculate the mass moment of inertia of a flywheel in the form of a disc with a diameter of 650 mm, a thickness of 70 mm, and a mass of 185 kg.

Answer :

To calculate the mass moment of inertia of a flywheel in the form of a disc, we can use the formula for the moment of inertia of a solid cylinder (or disc) about its central axis. The formula is given by:

[tex]I = \frac{1}{2} m r^2[/tex]

Where:

  • [tex]I[/tex] is the moment of inertia.
  • [tex]m[/tex] is the mass of the disc.
  • [tex]r[/tex] is the radius of the disc.

Given:

  • Diameter of the disc [tex]= 650 \text{ mm} = 0.65 \text{ m}[/tex]
  • Thickness of the disc, which does not directly affect the moment of inertia calculation, is [tex]70 \text{ mm} = 0.07 \text{ m}[/tex].
  • Mass of the disc [tex]= 185 \text{ kg}[/tex].

Steps:

  1. Calculate the radius of the disc:

    [tex]r = \frac{\text{Diameter}}{2} = \frac{0.65}{2} = 0.325 \text{ m}[/tex]

  2. Substitute the known values into the inertia formula:

    [tex]I = \frac{1}{2} \times 185 \times (0.325)^2[/tex]

  3. Perform the calculation:

    [tex]I = \frac{1}{2} \times 185 \times 0.105625 = \frac{1}{2} \times 185 \times 0.105625 = 9.77156 \text{ kg} \cdot \text{m}^2[/tex]

Therefore, the mass moment of inertia of the flywheel is approximately [tex]9.77 \text{ kg} \cdot \text{m}^2[/tex].

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