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Using a rubber band chain, apply a known average torque through a known angular displacement to start the strap from rest.
Alternatively, use the momentum of a 'shot' rubber band or rubber band chain to start the strap from rest, taking any data necessary to determine the velocity and mass of the rubber band.
Take measurements sufficient to determine the velocity of the system immediately following the action of the rubber band.
Use your results to determine, within the limits of accuracy of the experiment, the moment of inertia of the strap.
Assuming that the moment of inertia is the same as for a thin rod of the same mass and length, determine the mass of the strap.
Repeat, this time with some dominoes balanced on the rod.