3. Consider a stick of length I, mass m, and uniform mass density. The stick is...

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3. Consider a stick of length I, mass m, and uniform mass density. The stick is pivoted at its top end and swings around the vertical axis. Assume that conditions have been set up so that the stick always makes an angle ở with the vertical. a) Figure out what the principal axes are. You do not necessarily need to diagonalize the I matrix. It will be obvious to find them. b) Calculate the diagonal components of the moment of inertia tensor. c) Find the magnitude and direction of the angular momentum L. d) Find the direction and magnitude of the change in angular momentum dL/dt. e) If we assume that gravity is the force which is keeping the stick to rotate at constant angle, what will the frequency w be? Please do all parts. 3. Consider a stick of length I, mass m, and uniform mass density. The stick is pivoted at its top end and swings around the vertical axis. Assume that conditions have been set up so that the stick always makes an angle ở with the vertical. a) Figure out what the principal axes are. You do not necessarily need to diagonalize the I matrix. It will be obvious to find them. b) Calculate the diagonal components of the moment of inertia tensor. c) Find the magnitude and direction of the angular momentum L. d) Find the direction and magnitude of the change in angular momentum dL/dt. e) If we assume that gravity is the force which is keeping the stick to rotate at constant angle, what will the frequency w be? Please do all parts.

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a The princi pal axes are thhe axis along the stick along with Two any ... View the full answer