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Purpose

Purpose. Investigate which factors affect moments of inertia (such as length, mass, and shape). C alculate moments of inertia for various shapes to check our results. Equipment.

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Purpose

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  1. Purpose • Investigate which factors affect moments of inertia (such as length, mass, and shape). • Calculate moments of inertia for various shapes to check our results.

  2. Equipment Inclined board on which you can place round objects at the top of the board and let them accelerate towards the bottom:

  3. Activity I:Data Collection • Note that for constant acceleration (like in out setup today) the velocity increases linearly with time. Therefore, • where • To measure vaverage, all you need is a stopwatch (time t) and a ruler (distance d). • By the way, the acceleration is

  4. Activity II:Calculating Moments of Inertia • Simply use conservation of energy, which we quickly see from the figure below is • Since we can’t measure w, we use the fact that • to see that

  5. With this equation we can solve for I, which is the moment of inertia of the rolling object and calculate I from the measured data. • For many round objects I can be calculated as I = Kmr2, where r is the radius, m is the mass, and K is a number dependent on the mass distribution and shape. • To compare your results to theory, write I as I = Kmr2in the equation above and then solve the equation for K. Then you will have an expression for K as a • function of g, h, and vf. • Use this formula to calculate K for three different objectsfrom your measured data. • Compare your experimental K-values to those in the literature. (e.g., for a disk K=1/2 as we saw in the “Rotational Motion” lab” last week).

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