spinning top farmuk (#), ferferé (#) Fr.: toupie A toy that with a quick or vigorous twist spins around its symmetry axis and balances on a point. Suppose a top is perfectly fashioned so that its → rotation axis passes through its → center of mass. If it is spun carefully such that it remains perfectly upright while rotating, it will spin at a steady → angular velocity almost indefinitely in the absence of → friction. Rotation creates an → angular momentum which is directed upward along the rotation axis, opposite to the → gravity vector. However, a slight mismatch between the rotation axis and the center of mass causes gravity to exert a → torque on the top due to its weight, acting through the center of mass. The torque gives rise to a time rate of change of angular momentum, so the top experiences → precession about its point of contact. The tip of the angular momentum vector can be perceived as precessing about the → vertical, thus describing the → precessional circle. The top's precession period is given by: T_{p} = (4π^{2}I)/(mgrT_{s}), where I is the → moment of inertia, m the mass of the top, g gravity, r the distance between the center of mass and the contact point, and T_{s} is the spinning period of the top. Precession is accompanied by another oscillatory phenomenon, called → nutation. Nutation is less influenced by the gravity torque and is determined by the inertia forces acting on the spinning body. → spin; → -ing; top M.E., from O.E. top, maybe related to Fr. toupie. Farmuk, ferferé "spinning top" (Dehxodâ), two words of unknown etymology. |