Lab 18

Moment of Inertia and Frictional Torque

Kyle Garibaldi

Sam Chen

John Valle

11-16-16

Goal:

 Determine inertia of a pulley and its frictional torque. Determine acceleration of a cart hanging from the pulley.

Summary:

We start with a pulley, and we initially know that this pulley has some degree of frictional torque because if spun it will eventually stop. Our objective is to measure this friction and use it to determine the effect it will have if we attach a cart to the pulley by a string and allow the cart to roll down an incline. The pulley is composed of two small cylinders and one large cylinder. We know the mass of the entire pulley, but not of the individual pieces.

Procedure:

In order to determine the frictional torque we need to know both the moment of inertia of the pulley and the deceleration it experiences due to friction. First we find the total volume and percentage volume that each piece of the pulley occupies.

We can then use the percentage volume each piece occupies to determine the mass of each piece, which we will need to know to calculate inertia.

Now that we have the mass of each cylinder we can determine the moment of inertia of the entire pulley, which is the sum of the inertia of the individual pieces.

The second thing needed to calculate frictional torque is angular acceleration, so in order to find the alpha we spun the wheel and took slo-mo video that we analyzed in logger pro in order to determine alpha.

 Logger pro plots in the xy coordinate plane so we created a calculated column to display angular velocity, the slope being angular acceleration.

We can calculate our frictional torque value.

The second part of this lab requires us to predict how long it will take a cart to roll 1 meter down a 40 degree incline while hanging from our pulley. This requires some algebra to set up.

Mass of cart = 0.55 kg

Our predicted time to travel the meter is 7.1 seconds.

Trial times
Trial 1: 7.16 sec
Trial 2: 7.22 sec
Trial 3: 7.43 sec

Conclusion:

Our predicted time closely matches the experimental times, an encouraging sign after so many calculations. The fact that we can so closely match reality is a testament to the value of physics. We can conclude that our given equations and constructed models are effective. Physics is cool.

Lab 17

Finding the moment of inertia of a uniform triangle about its center of mass.

Kyle Garibaldi
Partners: Sam Chen, John Valle
Date: 11-16-16

Goal:

We are determining the moment of inertia of a right triangle about its center of mass, for two orientations: upright and laying on it's side.

Summary:

The setup of this lab involves using the torque pulley device. (picture here)
We hang a weight from a string connected to the disk holding the triangle. The weight is pulled downwards by gravity, accelerating the disk and triangle system proportional to the moment of inertia of the triangle. We measure angular acceleration of the disk without the triangle and with the triangle to determine the difference. This difference is the moment of inertia of the triangle. We will compare and analyze this experimental moment of inertia to the theoretical moment of inertia and see if our theory holds true.

We need to have calculations prepared that will enable us to compare experimental I to theoretical I, shown below.

Procedure:

The experimental apparatus is set up as pictured below. We took appropriate measurements necessary in order to complete our calculations. We connected a computer/logger pro setup to the apparatus in order to measure angular speed of the disk. We graphed the data, and took the slope of the resultant line to get angular acceleration.

Apparatus setup with laying triangle

Graph of angular velocity vs. time,
slope is angular acceleration

radius of torque pulley: 0.027 m
hanging mass : 0.025 kg
triangle mass : 0.4536 kg
triangle height : 0.1463 m
triangle base : 0.098 m

Analysis:

With all our data combined, we form captain planet!

Experimental vs. Theoretical Inertia

Conclusion:

In regards to the upright triangle, our experimental and theoretical values are virtually identical. This indicates that we ran a effective experiment that matched our theoretical model. Regarding the laying triangle, our experimental and theoretical outcomes had a 9% difference which indicates we made some errors somewhere along the way, either in the form of data measurements or assumptions. The fact that one model had little to no error while the other had significant error is puzzling, and makes me think that perhaps the laying triangle measurements might be at fault.