![]() Using the angular velocities and moment of inertias, determined much like they were in part one, the angular moments before and after the ring were dropped were calculated and compared. The second part of the experiment was performed much like part one of the experiment using the disk alone, only this time shortly after the string had unraveled, the ring was dropped onto the spinning disk. ![]() The moment of inertia was also calculated a second way, using the radii and masses of the disk and ring. These values, along with the force of kinetic friction, found by determining the minimum force needed to get the disk spinning, were used to find the moment of inertia. The angular acceleration was found from the slope of this graph up to that point. The weight was allowed to free fall and the resulting graph of velocity versus time was used to find the final angular velocity by taking the mean of the segment after which the string had completely unraveled from the shaft. The force coercing the disk to spin was a 300 g weight attached to the shaft of the disk using a string a pulley system. Conclusionĭuring the first part of the lab, the moments of inertia for a spinning disk with and without a weighted ring on top were calculated using two different methods. The ring would need to fit in the grooves like a puzzle piece in order to be positioned dead center to yield the least amount of error. We were able to drop the ring into the grooves of the disk, but there was still some wiggle room in those grooves. The limitations of the experimental setup were that it is difficult to drop the ring on the spinning disk perfectly. The percent difference is 11.7%, which I suppose isn’t a huge discrepancy, but it could be better. ![]() ![]() The results somewhat support the theory of conservation of momentum. How well do your results support the theory of conservation of momentum? What are the limitations of the experimental setup? As the angular velocity decreased, so did the moment of inertia.ģ. No, there appears to be a direct relationship between moment of inertia and angular velocity. Does there appear to be an inverse relationship between moment of inertia and angular velocity? The angular momentum before the ring is dropped onto the disk is greater than the angular momentum after the ring is dropped onto the disk. How do your values for the angular momentum before and after the ring is dropped onto the disk compare? What is the percent difference? The other equation takes more variables into account, mainly for calculation torque, which I feel leads to increased error. I think the better way to calculate the moment of inertia is to use I = ½ MR 2, as it is a more elegant equations that takes into account less variables. The values are extremely close, as the percent difference for the disk alone is 9.5% and the disk plus the ring is 0% (they are of equal value). How well do your two values agree with each other? What is the percent difference? Which do you think is likely a better way to calculate a value for moment of inertia? One is found from the theoretical equation for moment of inertia that is introduced in the Theory section and other is an experimental value obtained using Newton’s 2 nd law for rotational motion, τ = Iα, in conjunction with the definition of torque, τ =rF. In your data table in Part 1, you have two values for the moment of inertia. Angular velocity before ring is dropped (ω i)Īngular velocity after ring is dropped (ω i)Īngular momentum before ring is dropped (L = I iω i)Īngular momentum before ring is dropped (L = I fω f)ġ.
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