IB Physics Motion in a Vertical Circle

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A sheet of vertical circle problems is given below.

  1. A mass m is tied to a string of length L and hangs vertically at rest. The mass is given an initial horizontal speed u. What is the initial acceleration of the mass?
  2. A mass on a string is released from rest swings as a simple pendulum. What is the speed of the mass when its vertical drop is ∆h?
  3. A mass m is placed on the end of a light rigid rod of length r and made to move in a vertical circle at a constant speed v. Is the magnitude of the acceleration of the mass a constant value of v2/r? (no, this is the radial component of the acceleration only)
  4. In the previous question draw a free-body diagram if the radius to the mass makes an angle 𝜽 with the vertical when 𝜽 < 90°. Show that the force exerted on the mass by the rod has a component mgsin𝜽 perpendicular to the rod and a component mv2/r - mgcos𝜽 parallel to the rod.
  5. In the previous question at what angle to the vertical is the force exerted by the rod maximum? (180°)