Introduction to Classical Mechanics · Problem 10.25

Relativity (Kinematics) — Morin

Physics — Mechanics · free-particle-motion

Problem

A particle slides on a frictionless turntable that rotates counterclockwise with constant frequency

\omega

. When viewed in an inertial frame, the particle simply travels in a straight line. But in the rotating frame of the turntable, show that the

F = ma

equations take the form,

\ddot{x} = \omega^2 x + 2\omega\dot{y},

\ddot{y} = \omega^2 y - 2\omega\dot{x},

and verify that the solutions to these differential equations are

\begin{aligned} x(t) &= (A + Bt)\cos\omega t + (C + Dt)\sin\omega t,\\ y(t) &= -(A + Bt)\sin\omega t + (C + Dt)\cos\omega t. \end{aligned}