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A cylinder with moment of inertia I1 rotates about a vertical, frictionless axle with angular velocity ωi. A second cylinder, this one having moment of inertia I2 and initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular velocity ωf. a. Calculate ωf. b. Show that the kinetic energy of the system decreases in this interaction and calculate the ratio of the final to the initial rotational energy.

A cylinder with moment of inertia I1 rotates about a vertical, frictionless axle with angular velocity ωi. A second cylinder, this one having moment of inertia I2 and initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular velocity ωf. a. Calculate ωf. b. Show that the kinetic energy of the system decreases in this interaction and calculate the ratio of the final to the initial rotational energy.

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A cylinder with moment of inertia I 1 rotates about a vertical, frictionless axle with angular velocity ω i . A second cylinder, this one having moment of inertia I 2 and initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular velocity ω f . a. Calculate ω f . b. Show that the kinetic energy of the system decreases in this interaction and calculate the ratio of the final to the initial rotational energy.

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