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Theoretical_Exam_Question_1_English - Theoretical Question...

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Theoretical Question 1 A Swing with a Falling Weight A rigid cylindrical rod of radius R is held horizontal above the ground. With a string of negligible mass and length L ( R L π 2 ), a pendulum bob of mass m is suspended from point A at the top of the rod as shown in Figure 1a. The bob is raised until it is level with A and then released from rest when the string is taut. Neglect any stretching of the string. Assume the pendulum bob may be treated as a mass point and swings only in a plane perpendicular to the axis of the rod. Accordingly, the pendulum bob is also referred to as the particle . The acceleration of gravity is g . Let O be the origin of the coordinate system. When the particle is at point P , the string is tangential to the cylindrical surface at Q . The length of the line segment QP is called s . The unit tangent vector and the unit radial vector at Q are given by t ˆ and r ˆ , respectively. The angular displacement θ of the radius OQ , as measured counterclockwise from the vertical x -axis along OA , is taken to be positive.
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