The leaning Tower of Pisa (see Fig.) is 55 m high and 7.0 m in diameter. The top of the tower is displaced 4.5 m from the vertical. Treating the tower as a uniform, circular cylinder, (a) what additional displacement, measured at the top, will bring the tower to the verge of toppling? (b) What angle with the vertical will the tower make at that moment? (The current rate of movement of the top is 1 mm/year.)

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Kevin Nash · Answer

(a)
Initially, the center of gravity of the tower lies at height $\frac{h}{2}$ , and in the middle of the base. When tower start to lean, the center of gravity moves to the right and will eventually align out of the base. This is the moment when the tower falls, and at this moment the center of gravity would have displaced horizontally by an amount $\frac{d}{2}$ .

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