Q8
(a) Explain how the distribution of masses affects rolling and pitching.
(6)
(b) A ship turns in a circle of radius 100 metres at a speed of 15 knots. The GM is 2/3 metres and BG is 1 metre. If g=981 cm/sec2 and 1 knot is equal to 1.8532 Km/hour, find the heel due to turning.
(10)
Reference Answer
### Part (a): Effect of Mass Distribution on Rolling and Pitching The distribution of masses within a ship significantly influences its rotational motions, specifically rolling (transverse rotation) and pitching (longitudinal rotation). This effect is primarily governed by the ship's **Moment of Inertia** and its corresponding **Radius of Gyration** about the axis of rotation. **1. Fundamental Concepts:** * **Moment of Inertia (I):** This is a measure of a body's resistance to angular acceleration. It depends not only on the total mass but, crucially, on how that mass is distributed relative to the axis of rotation. A mass located further from the axis contributes more to the moment of inertia than the same mass located closer.
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