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Physics 325 HW 12 Solutions

# Physics 325 HW 12 Solutions - Physics 325 Fall 2010...

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Physics 325, Fall 2010 Homework Assignment #12 Solutions 1. Taylor 9-18 (15 Points) A particle with mass m is confined to move, without friction, in a vertical plane, with axes x horizontal and y vertical up. The plane is forced to rotate with constant angular velocity Ω about the y axis. Find the equations of motion for x and y , solve them, and describe the possible motions. As seen in a frame rotating with the system, there are four forces on the mass: its weight - mg ˆ y , the centrifugal force m Ω 2 x ˆ x , the normal force N of the confining plane, and the Coriolis force F cor . The last two both act in the z direction (normal to the confining plane) and must cancel each other, because there is no motion in this direction. The equations of motion in the remaining two directions are ¨ y = - g with solution y = y 0 + v y 0 t - 1 2 gt 2 , and ¨ x = Ω 2 x with solution x = Ae Ω t + Be - Ω t . The vertical motion is the same as that of a body in free fall. Except in the special case that A = 0, the x

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Physics 325 HW 12 Solutions - Physics 325 Fall 2010...

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