2.3.7. Calculating Radius of Gyration

Try these first

1. 1.

   What is the formula for radius of gyration based on moment of inertia?

   Hint

   Think about how mass is distributed.

2. 2.

   Define metacentric height in the context of ship stability.

   Hint

   Consider its relationship to where the ship would return after tilting.

3. 3.

   What does the radius of gyration measure?

   • Mass distribution
   • Weight
   • Volume
   • Density

   Hint

   Think about why this would be important for stability.

4. 4.

   True or False: A larger radius of gyration means a ship is more stable.

   • True
   • False

   Hint

   Think of the ship's ability to respond to waves.

5. 5.

   A ship has an inertia of 2000 kg·m² and a mass of 500 kg. Calculate its radius of gyration, then discuss how this would influence its rolling period in waves.

   Hint

   Think about how increasing mass affects the ship's behavior.

6. 6.

   If a ship's metacentric height is 0.8m and radius of gyration is 2m, how does this reflect its stability under maximum loading conditions?

   Hint

   Consider how weight distribution might affect height.