Forces in the accelerated reference system of a pendulum: theoretical study and experimental results

Abstract In this work we initially lead a theoretical discussion about the forces acting on a physical pendulum oscillating without friction in an accelerated reference system. Such discussion allows us the statement that if an accelerometer is fixed on the center of oscillation of the pendulum, it will register an oscillating value in the radial axis and a null value in the tangential axis. To illustrate this proposition, we will present two simple situation for verification and then we inquire two instigating questions: a)What will happen to the air bubble of a mason level, if we position the same in the tangential direction while we cradle in a swing of a square? b) If we put a small sphere on oscillating swing, will the sphere be in rest during the oscillation? The answers for this counter intuitive questions are that both, the air bubble and small sphere, will stay in rest in relation to the swing if they are positioned on the center of oscillation of the pendulum. In order to elucidate the above questions, we designed an experimental apparatus composed of a physical pendulum, in which we attached an Arduino microcontroller board, an accelerometer sensor and a Bluetooth module.