Radius for torque r = 5.65 cm | |||||
Mass for torque m = 15.2 g | |||||
Mass of pop can M = 386.8 g | |||||
Radius of pop can R = 3.3 cm | |||||
Angular Acceleration | Angular Acceleration | Angular Acceleration | |||
Average Moment of Inertia | |||||
Percentage of Solid Moment of Inertia |
I_{experimental} = 23.7 x 10^{-5} kg m^{2}
Moment of Inertia (low pressure): I_{L} = 4.14 x 10^{-5} kg m^{2}
Moment of Inertia (high pressure) I_{H} = 6.92 x 10^{-5} kg m^{2}
Now if the pop can is shaken up so that a lot of CO_{2} is released, tremendous pressure is built up inside and the liquid is pushed to the wall with greater force increasing the frictional force. Thus when the pop can is spun under high internal pressure, the liquid follows the container more closely and hence effective moment of inertia of the container increases (though still less than that of the solid can).
This effect can be verified by doing an experiment with the set up shown in he diagram above.
A known torque is applied to a platform which can rotate about a vertical axis. Data can be collected by a lab interface such as smart pulley. Linear acceleration and hence the angular acceleration is then obtained. The moment of inertia of the platform (without pop can on it) is thus given by I_{0} = t/a_{0}.
Now a pop can is placed on the platform coaxial with it. The liquid is at low pressure. Above procedure is repeated to determine the combined moment of inertia I_{1} of the platform + pop can at low pressure.
Now the pop can is shaken till no splashing sound of the liquid inside is heard an the procedure above is quickly repeated to determine the combined moment of inertia I_{2} of the platform + pop can at high pressure.
Thus I_{L} = I_{1}- I_{0} is the effective moment of inertia of the pop can at low pressure and I_{H} = I_{2}- I_{0} is the effective moment of inertia of the pop can at high pressure.
This lab is appropriate for AP Physics C students and probably with honors H.S. Physics students, too.
Various possible modifications/extensions of the lab are:
Above is the graph of one such trial. The results are inconclusive though.