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HW15 - Prof I Biaggio Solutions HW 15 Physics 90 Fall 2006...

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Prof. I. Biaggio Solutions HW 15 Physics 90, Fall 2006 1-4 Solutions Homework 15 44 This is just a review of the way how these physical quantities are defined, and how they relate to each other. Picture the Problem We can use their definitions to calculate the angular momentum and moment of inertia of the particle and the relationship between L , I , and ω to determine its angular speed. ( a ) Express and evaluate the magnitude of : L ! ( )( )( ) /s m kg 28.0 m 4 m/s 3.5 kg 2 2 ! = = = mvr L ( b ) Express the moment of inertia of the particle with respect to an axis through the center of the circle in which it is moving: ( )( ) 2 2 2 m kg 32 m 4 kg 2 ! = = = mr I ( c ) Relate the angular speed of the particle to its angular momentum and solve for and evaluate ω : " = L I = 28.0kg # m 2 /s 32kg # m 2 = 0.875rad/s 45 This is again a review of the definition of angular momentum. It wants to highlight the fact that also a particle that is moving in a straight line carriers angular momentum with respect to a point in space that is not on that line. The angular momentum of the particle is constant , but both its moment of inertia (with respect to that point) and its angular speed change. Picture the Problem We can use the definition of angular momentum to calculate the angular momentum of this particle and the relationship between its angular momentum and angular speed to describe the variation in its angular speed with time.
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