Centripetal force formula
F direction = mr ω 2 = mv 2/r
=mvω
=4π^2mr/T^2
=4π^2mrf^2
= 4 π 2n 2mr where: v is linear velocity, ω is angular velocity, m is mass of the object, r is radius of motion of the object, t is period of circular motion, f is frequency of circular motion, and n is rotational speed of circular motion.
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In Lenz's law, n is the number of turns of the coil, φ is the magnetic flux, d/dt is of course the derivative sign, and the negative sign indicates the direction: induced electromotive force tends to generate current, and the direction of current tends to prevent the change of magnetic flux that generates induced electromotive force.