The tension T yields the torque t acting on the apparatus. Here r is the radius of the chosen pulley about which the thread is wound. The measured angular acceleration a yields the moment of inertia of the apparatus. The sum of the potential energies and rotational and translational energies of the system is a constant of motion. The measured position of the hanging mass at some time t yields its change in potential energy.
D U are negative.
The measured velocity of the hanging mass at that same time t yields its change in kinetic energy, since the mass starts from rest. The measured angular velocity of the rotating apparatus at that same time t yields the change in its rotational kinetic energy, since the apparatus is initially at rest. Students will compare their dynamically obtained value of the moment if inertia to the value they obtain when they determine the mass and dimensions of their apparatus. Attach the super pulley or mount a smart pulley so that you can guide a string over it. Under sampling options, choose to start your measurement when the position is above 0.01m and stop it when the position is above 0.4m.