Lab Partners: Max McCandless and Vincent Mele
Date of Completion: 04-22-14
Date of Completion: 04-22-14
Purpose
The purpose of this lab is to predict the moment of Inertia for the system.
Theory
Some elements taken into account when deriving an equation are as follows:
Sum of torque = Inertia * velocity
Torque = radius * force (when tangential to circle)
Sum of force = mass * acceleration
Rotational acceleration = tangential acceleration / radius
Weight = mass * gravity
First, the sum of the torques must be found, then rearranged for an unknown tension. Next, the forces acting on the system are summed, and also solved for the unknown tension. The equations for each unknown tension are then set equal to one another and solved for inertia, in terms that are already known. This equation can then be used to solve for inertia.
Sum of torque = Inertia * velocity
Torque = radius * force (when tangential to circle)
Sum of force = mass * acceleration
Rotational acceleration = tangential acceleration / radius
Weight = mass * gravity
First, the sum of the torques must be found, then rearranged for an unknown tension. Next, the forces acting on the system are summed, and also solved for the unknown tension. The equations for each unknown tension are then set equal to one another and solved for inertia, in terms that are already known. This equation can then be used to solve for inertia.
Experimental Technique
1. Set up the rotary motion sensor
2. Attach mass to the end of fishing line 3. Loop fishing line around rotary motion sensor 4. Screw in the rod with masses attached 5. Put fishing line on pulley 6. Set up data studio 7. Hit start and drop mass 8. Use data studio to show the slope of the graph, which is the angular acceleration 9. Measure and record the radius of the pulley and the hanging mass 10. Calculate Inertia based on equation 11. Compare with calculated geometric Inertia |
Data
Analysis
From the information gained via data studio, the Inertia can be calculated using the equation that was previously derived. (Shown on bottom right) This result can then be compared to the result of finding the geometric moment of Inertia of the system. (Shown on bottom left)
Conclusion
In this lab, moment of Inertia was investigated. Using the angular acceleration, radius of pulley, and hanging mass of a system, Inertia can be calculated using a derived equation. This can then be compared to the geometric Inertia of the system. When done, it is found that the calculated result does not differ much from the geometric result. This result helps confirm that equations concerning inertia that are used theoretically are indeed correct. Some possible sources of error would be the the wind resistance encountered as the apparatus spins, difficulty in precisely measuring some values, error in measuring equipment, and shaking as the hanging mass fell.
Resources
The Physics Classroom.com. Retrieved on April 22nd, 2014, from http://www.physicsclassroom.com