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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 ω 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 ( ) ⋅ ω . 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 ω . d. What is the angular momentum of the actual system about its CM. Ans : 1 2 m 2 ω . 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 α 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 α , L y = L sin α , where L = 1 2 m 2 sin α ⋅ ω . b. What is the moment of inertia I of the system about the axle? Ans : 1 2 m 2 sin 2 α . c. Show that L = I ω . d. If the axle has no friction it cannot exert a torque along its length. Discuss conservation of angular momentum for this system. ω ω α 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 ω before the child landed on it at distance r from the axle....
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 Spring '07
 Mueller
 Physics, Angular Momentum, Mass, 1 M, α, Sting, Ly

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