Spinning Top
This photograph of a spinning top in motion demonstrates effective gravity and Einstein's equivalence principle. There are blue, pink, and silver beads attached by strings to the spinning top. The beads experience a centripetal acceleration a_c = rw^2 due to tension pointing towards the axis of rotation. As a result, the beads experience a fictitious force F_f = mrw^2 pointing away from the axis of rotation. According to the equivalence principle, in the bead’s non-inertial (accelerated) reference frame, F_f feels the same as an additional gravitational force pointing outwards; the beads cannot differentiate between being in a state of non-uniform motion and being in a gravitational field. The beads experience both the force of gravity F_g = mg downwards and the fictitious force F_f = mrw^2 outwards. Combining these two perpendicular force vectors, we get an effective gravity pointing in some angle from the vertical. Since the top is spinning so fast — many many revolutions per second — the angular velocity w in the F_f term is very large. Thus, the vertical component (F_g) of the net force is nearly negligible compared to the horizontal component (F_f), resulting in the strings being horizontal. The colorful beads spinning with the top added an aesthetic motion-blur element while illustrating effective gravity and the equivalence principle.
Manxi Shi
Description
Essay Title: Spinning Top
Category: Contrived
Photo Number: 5560
School: BASIS Independent Silicon Valley
Teacher Name: Leigh Myers