118 Circular Motion: Loop the Loop

(The dynamics for this demo is almost identical to that of a roller coaster’s loop-the-loop. Just replace the string’s tension with normal contact force of the coaster’s ramp, and everything is identical.)

Many students have the misconception that as long as the pendulum does not come to complete rest in the midst of motion, it can successfully loop-the-loop. That is wrong. The pendulum moves in a circular path only if the string is taut. However, when the pendulum is moving through the upper half of the circle, gravitational pull is actually tending to pull the pendulum inside the circle. If the pendulum is not moving fast enough, the component of gravitational pull in the centripetal direction will be larger than the required centripetal acceleration for circular motion at that speed and radius. This means the pendulum is being pulled by gravity towards the centre of the circle too quickly. The string becomes slack. Once that happens, the pendulum is no longer constrained to a circular path but goes into a parabolic path instead.

There is a minimum drop height in order for the pendulum to be moving fast enough to loop-to-loop successfully. The solution for the drop height is presented in this xmtutor video. So in theory, the limiting point for the experiment set up in this video is roughly when r = 25.0 cm.

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