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Unformatted text preview: Assignment 10 1. Two identical point masses, each of mass m , are attached by a massless horizontal rod of length as shown. They are rotating at angular velocity about a Fxed axle perpendicular to the rod, at distance d from its center. a. What is the moment of inertia of the system about the axle? Ans : m 1 2 2 + 2 d 2 ( ) . b. What is the magnitude of the angular momentum? Ans : m 1 2 2 + 2 d 2 ( ) . c. If the system consisted of both masses at the CM, rotating about this axle, what would be the angular momentum? Ans : 2 md 2 . d. What is the angular momentum of the actual system about its CM. Ans : 1 2 m 2 . e. Verify that the theorem that L tot = r CM M v CM + L (about CM) is obeyed. 2. The same two masses and rod are now made to rotate about the axle with the rod making angle with the axle, and the axle passing through the CM. a. At the instant shown, Fnd the horizontal and vertical components of the angular momentum. [Use L = r m v for each mass.] Ans : L x = L cos , L y = L sin , where L = 1 2 m 2 sin . b. What is the moment of inertia I of the system about the axle? Ans : 1 2 m 2 sin 2 . c. Show that L = I . d. If the axle has no friction it cannot exert a torque along its length. Discuss conservation of angular momentum for this system. PHY 53 Summer 2010 1 3. A child of mass m is dropped from rest (gently) onto the rim of a rotating carousel, a horizontal circular platform of moment of inertia I about its axle. As shown from above, the carousel was rotating at angular speed before the child landed on it at distance r from the axle....
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