10 November 2014: Moments of Inertia

Purpose: Determine the time which a cart slides a ramp attached to a rotating apparatus by using the moment of inertia of the apparatus.

This picture shows the apparatus' that we used for the lab. On top in the rotating disk with cylinders, in the middle is the ramp inclined at certain angle, and on the bottom, the cart.

Explanation: First, we calculated the relevant measurements to find the moment of inertia of the whole rotating apparatus, from that, we used video capture to calculate the angular deceleration of the apparatus. After this, we were able to find the frictional torque of the system. We then, were given a problem where a cart attached by a string to the apparatus was sliding down the ramp by 1 meter at certain angle and we needed to find the time of it. We had to do the calculations before actually setting up the experiment. After the calculations were done and revised by the professor, we set the experiment and ran it a couple times to see if our calculations matched the real life situation.

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This is the data table obtained by using video capture and logger pro.

This graph shows the velocity in the x and y direction as the rotational apparatus spins.

This is the graph of the tangential velocity of the system found by the equation Vt=sqrt(Vx^2+Vy^2)

 These are the calculations that we did to find the moment of inertia of the total system. It came out to be 1.92*10^-2 kg*m^2

This are the calculations that we did to find the frictional torque, the angular acceleration and the time in which the cart would drop 1 meter.

Summary: Unfortunately, our conclusion did not come as expected, because we calculated the time to be at around 9.5 seconds with the ramp angled at 46 degrees, however when we did the experiment, we were getting around 12.5 seconds. This 3 seconds difference is more than the percentage expected, which was around 4%. However, these were the values that we got, and the professor revised the calculations and apparently, they were correct; so the error could be either when plugging the numbers incorrectly in the calculator, which has little chance, given that various members of the group punched the numbers in their own calculator, or some external force changed the system.