A robotic surgical systems and methods of operating the same are provided. The system comprises a surgical tool, a manipulator having a plurality of joints and supporting the surgical tool, and a controller. A virtual simulation represents the surgical tool as a virtual rigid body having a virtual mass including an inertia about at least one of the j oints. The controller determines an expected joint torque for the joint. The expected joint torque is compared to an actual joint torque of the joint to determine a joint torque difference. The inertia of the virtual mass about the joint is determined. An angular acceleration about the joint is computed using the joint torque difference and the inertia. The angular acceleration is projected to the virtual mass to determine an external force. The controller simulates dynamics of the surgical tool in the virtual simulation in response to the external force.
