A horizontal turntable rotates with angular speed . There is a clock at the center of the turntable and one at a distance r from

A horizontal turntable rotates with angular speed ω. There is a clock at the center of the turntable and one at a distance r from the center. In an inertial reference frame, the clock at distance r is moving with speed u = rω.

(a) Show that from time dilation according to special relativity, time intervals Δt₀ for the clock at rest and Δt_r for the moving clock are related by

(b) In a reference frame rotating with the table, both clocks are at rest. Show that the clock at distance r experiences a pseudoforce F_r = mrω² in this accelerated frame and that this is equivalent to a difference in gravitational potential between r and the origin of ф_r -ф₀ = ½r²ω². Use this potential difference in Equation 2 to show that in this frame the difference in time intervals is the same as in the inertial frame.

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