Name: Zach Christoff
Lab Partners: Alyssa Jordan and Jake Hoffner
Date: 3/2/16
Lab Partners: Alyssa Jordan and Jake Hoffner
Date: 3/2/16
Purpose
The purpose is to compare the moment of inertia of a thin rod rotated about the center using two different equations: one accepted and one derived.
Theory
To find inertia (I), we must derive an equation in terms of radial acceleration, radius, and mass. The FBD represents the massing falling down from the pulley, hence the acceleration downwards. Since tension (T) is the same at the pulley and at the mass (m), the force used to create torque is T. Since we don't know what tension is, we need to find a relationship for tension in terms of variables we know. We must sum the forces acting on mass in to solve for tension. One last substitution must be made for acceleration in order to get the equation in terms we have numbers for. The described derivation is shown below.
Below, the second equation for the moment of inertia was derived. This equation uses the geometry of the object in order to come up with an equation. The rod and two point masses must all be considered separately when constructing the equation. The rod (thin rod) has a moment of inertia defined in the book. All other point masses have moment of inertia mr^2, where r is distance from its center of mass to the center of the rod. Instead of r, an l was used to keep the consistency of the equation.
Experimental Technique
The picture to the left shows the apparatus that was used to conduct radial acceleration. A hanging mass (blue object with gold mass) was attached to the string which was wound up around the axis of rotation of the rod and through the pulley. DataStudio measured the radial acceleration once the hanging mass was released. This radial acceleration, and all of the other measurements that were, will allow me to determine the moment of inertia of the thin rod and compare it to the moment of inertia using a different equation.
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Data
The following numbers were used in the calculations for the moment of inertia. The top set of numbers was used for the geometrical equation, while the bottom set was used for the derived equation
Analysis
Conclusion
This lab was performed in order to compare the moment of inertia of a thin rod rotated about the center using two different equations, both using different variables. The geometrical equation used mass & length of the rod, and masses and distance from the center of the rod of the point masses. The equation that we derived used radius of the pulley, hanging mass, and angular acceleration of the pulley. Both yielded fairly similar results, but there was a significant % difference of about 10.19%. This could be improved by taking multiple runs with different masses to find a "better" angular acceleration because only one test run was done. There were a few measurements that involved parallax error, and with very small numbers, a minor error can throw off the entire lab. Also, the way the string was wound, depending if it was piled up, could contribute to error because the pulley radius is very small.
References
Bowman, Doug. "Moment of Inertia Lab." Lahs Physics. Web. 22 Jan. 2016.
Wolfs, F. L. H., and Douglas C. Giancoli. Student Study Guide & Selected Solutions Manual : Physics for Scientists & Engineers with Modern Physics,
Wolfs, F. L. H., and Douglas C. Giancoli. Student Study Guide & Selected Solutions Manual : Physics for Scientists & Engineers with Modern Physics,