Physical Explanation
To observe the effect, the propeller attached to the end of the notched stick (the base) must not be pinned at its exact centre of mass. For a functioning whammy diddle, there should be a 'preferred' angle (i.e. when stationary, if the propeller is rotated around its axis and then released, it should return to its lowest-energy rest angle relative to the ribbed base.) Rubbing the ribbed base with another stick along the grooves then creates a vertical alternating driving force acting on the centre of mass of the propeller:
where and T is the time taken for the stick to move from one groove to the next; is some unknown scaling factor that characterizes the force with which the two sticks are pressed against one another. By rubbing a finger against these grooves on the side, one can also introduce a horizonal alternating driving force
where is a phase shift (describing the lag time between when the grooves contacts the moving rod, and finger respectively) and, again, X is some unknown scaling factor. Importantly, is the same frequency, and the two driving forces are said to be phase locked. The confluence of two phase matched driving forces in orthogonal directions gives rise to a rotational force on the centre of mass at the propeller end, and thus, rotation.
When the operator of the whammy-diddle surruptitiously changes the side at which his/her finger contacts the stick (e.g. by contacting with his thumb instead of his fore-finger, or by changing the side at which a finger contacts the grooves of the base) (s)he changes the sign of the phase, and thus reverses the rotation.
Read more about this topic: Gee-haw Whammy Diddle
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