11-May-2015 Moment of Inertia and Frictional Torque

Purpose

The purpose of this experiment is to calculate the moment of inertia of the large spinning disk as well as find the frictional torque of the disk. This is done so that we can predict how long it will take the cart to travel down the ramp.

Experiment

This experiment is set up with an apparatus with a large disk and to the disk we have tied a string to it that is then wrapped around the axis of the disk. This is so that as the cart goes down the ramp the disk will spin as well. We then set up a ramp and place the cart on the ramp, but the ramp is angled so that when the the sting is parallel to the track. 

Before we can conduct the experiment we first have to find the inertia of the disk, then the frictional torque of the disk, and finally the theoretical time that it will take the cart to reach the bottom of the track. To start off we found the inertia of the big disk by first finding the mass of the large disk by finding the volume of both the small and large disk. Then from there we used a ratio to find the mass of the small disk which is then used to subtract from the whole apparatus to ind the mass of the large disk. Once we knew the mass of the large disk we were able to find the inertia of the disk by using the formula for the inertia or a disk I= (1/2) mr^2

Next we had to find the rotational deceleration of the disk which we did by using rotational kinematics. We first counted how many times the disk spun and how long it took before it came to a stop then using rotational kinematics we found out the rotational deceleration, this was done a total of four time. After we got four rotational deceleration we took the average of them because we wanted to be more accurate instead of just using the first deceleration as is. There is a typo however in the picture where it is divided by three instead of four, but the answer is for the average acceleration is correct in that the sums are being divided by four not three.

From here we took our calculated values and solved for the tangential acceleration which is then used to find the theoretical time that the cart would reach the bottom of the track. The method we used to approach this was newtons second law and kinematics.

Now that we have our theoretical time we then actually conduct  the experiment by releasing the cart on the incline to see how long it takes for it to reach the bottom of the track. We did 2 trials of the run so that we can check how accurate the our calculations were. Once we have gotten the actual time of how long it too for the cart to reach the bottom of the track we finally calculate the percent difference between our theoretical time and the experimental time.

The sources of our errors would be that the track was not completely frictionless, the uncertainty from the measurement of the angle, the reaction speed of starting and stopping the timer, and the string was not completely parallel to the track.