18-May-2015: Moment of Inertia and Frictional Torque of the Big Wheel

Purpose:

Part 1: To find the frictional torque of the big steel wheel.

Part 2: To use this torque to find inertia of the wheel, that'll be used to then predict the time it takes for a cart to drop a meter that is attached to the wheel by a string wrapped around it.

Part 1: Finding the Frictional Torque

Set-Up:

The wheel being turned actually has three parts, the outside cylinders and the main wheel in the middle.

Experiment:


Over all, to find the frictional torque we need to find the angular deceleration of the wheel and the Inertia of the wheel.

1. To find the angular deceleration we set up a video capture on logger pro, using the camera shown above. This video would then be analyzed to find the angular deceleration of the wheel after we spin it.

2. To find the moment of inertia, we needed to measure the radius and mass needed, and then calculate it.

Data Analysis:

1. Using the video we marked every revolution recording it's time with video analysis, giving us revolutions per seconds or omega.

Blue Dots Represent Each Revolution

Next then plotted omega vs time to find the slope as our angular deceleration (where omega was translated into rad/s):

Angular Accerlation = -0.3768 rad/s/s

2. Since inertia depends on mass and how far it is from the center of rotation, we had to find the radius of each cylinder and the according mass shown below:

Since inertia for a disk is  I=.5mr^2, we were able to plug our values of radiuses and masses to find the inertia of the rotation apparatus:

Now that we had inertia and angular acceleration, we are able to find the frictional torque using Torque = Inertia * Angular Acceleration.

(where the y= represents the translation from slope found above into alpha)

Part 2: Finding time of Cart Going Down a Slope for 1 Meter

Set-Up:

We set up a ramp in which the cart attached to a string would roll down. The string would also be wrapped around the big wheel, rotating the whole mass of the big wheel and the two cylinders on each side:

Experiment:

We then recorded the measurable data needed in calculating a predicted time, recording the angle the ramp was at and the weight of the cart.

We then ran the cart down the ramp for one meter three times each and recorded the time it took.

Data Analysis:

We then calculated the predicted, "true" value of the time the cart should take in rolling down the meter ramp by taking the torque of the cart and subtracting the frictional torque and setting that equal to the inertia of the big wheel and it's angular acceleration. Since the acceleration was the unknown that would help us find time, we had to derive an equation to find it using the force equation of the cart and assuming that the acceleration of the cart and the tangential acceleration of the big wheel were the same. Calculations show below:

If you look above, the experimental values are also shown below the calculated time of 7.34seconds.

Conclusion:

In considering factors such as assumptions being made like acceleration of the cart being exactly the same as the tangential acceleration of the wheel as well as a possibly incorrectly recorded frictional torque (uncertain due to possible measuring errors and inaccurate video analysis), we compared our results:

With a percent error less than 5% we successfully completed our experiment, realizing how to find frictional torque and a mass' inertia and using these properties to find the tangential acceleration of that mass if a torque was applied it.