Estimating the internal friction and the rotational inertia of a homemade oscillatory system

Abstract In this work, we apply the dynamics of translation and rotation to a real system-a homemade mass-spring system composed of a cart-in which the rolling without slipping constraint of the cart's wheels may be violated at any moment. In this case, we demonstrate how modeling combined with video analysis can be powerful in determining the constraint forces acting on the system. In this case, the translational and rotational accelerations are determined, and the temporal behavior of all constraint forces can be identified. Initially, we show how rotations with slipping of the cart's wheels at the return points of the system's motion impact the system's kinematics. Finally, we apply the developed methodology to estimate the system's internal friction and rotational inertia. The estimates are compared with results from the literature and with a theoretical limit, in the case of rotational inertia, achieving good agreement.