A bicycle wheel has a diameter of 64.6 cm and a mass of 1.87 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 125 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.96 cm diameter sprocket if the wheel is to attain an acceleration of 4.49 rad/s22? (b) What force is required if the chain shifts to a 5.57 cm diameter sprocket?

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Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.