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.摘要 本研究首先针对加速参考系中无摩擦摆动的物理摆所受作用力展开理论探讨。通过该讨论可得出如下结论：若将加速度计（accelerometer）固定于物理摆的摆动中心，其径向轴将采集到振荡的数值，而切向轴的读数则为零。为验证该命题，我们将呈现两个简易验证情境，并提出两个启发性问题：a) 若将泥瓦工水平仪的水准泡置于切向方向，并将该水平仪置于方形秋千上摆动，此时水准泡会发生何种变化？b) 若将一小球置于摆动的秋千上，该小球在摆动过程中是否会保持静止？针对这些反直觉问题的解答为：若将水准泡与小球均置于物理摆的摆动中心处，二者相对于秋千均会保持静止。为阐明上述问题，我们设计了一套由物理摆构成的实验装置，该装置搭载了Arduino微控制器、加速度计传感器以及蓝牙模块。