Moment of Inertia

2 Question 1. Both barbells have the same total mass, so what is it about Barbell 2 that makes it difficult to move quickly? 3. Each of the two masses ࠵? on a barbell can be treated as a point-like mass having moment of inertia ࠵? = ࠵?࠵? ! , so the total moment of inertia of one barbell is ࠵? total = 2࠵?࠵? ! (we are ignoring the moment of inertia of the rod here). Use a meter stick to measure and record ࠵?, the distance of the mass from the axis of rotation. Do this for each barbell, then estimate the ratio of the moment of inertia of Barbell 1 to that of Barbell 2. (Do you need the mass to do this?). Report your value as a multiplicative factor: ࠵? Barbell 2 = ______ ∗ ࠵? Barbell 1 Question 2. Recall that for translational motion it takes more force to accelerate a larger mass, which is explained by Newton’s 2 nd Law: ࠵? Net = ࠵?࠵? . This law also holds in rotation form: ࠵? Net = ࠵?࠵? . In the rotational version of the law, force is replaced by torque ࠵? , and acceleration is replaced by angular acceleration ࠵? ; what takes the place of mass? Question 3. Another group has hypothesized that adding 100 g extra mass to the center of the barbell where the hand is placed would have no effect on the ability of the person to rotate the barbell back and forth. Do you agree or disagree? Why? Question 4. If you were to double the mass, but halve the radius of one of the barbells, how would the moment of inertia compare to the original value? Question 5. If you were a tightrope walker, which barbell would you rather be carrying? Part II. Newton’s 2 nd law for rotation From ࠵? Net = ࠵?࠵? we see that torque causes angular acceleration (a.k.a. rotational acceleration). For example, a torque on a wheel can cause the wheel to rotate faster (or slower depending on the direction of the torque). As we saw before, the amount of angular acceleration very much depends on the moment of inertia in the same way that linear acceleration depends on the mass. Here we’ll measure the angular acceleration of a disk caused by a known torque, then we’ll compare our measured value to the value we’ve predicted. The net torque in our experiment will be provided by the force of gravity acting on 5 g mass hanger hanging from a pulley of radius ࠵? p . This will cause the rotation of the entire system including the disk and ball bearings. ࠵? = ࠵? hanger ࠵?࠵? p = ࠵?࠵? = (࠵? disk + ࠵? bb ) ࠵? (1) Note that the total moment of inertia is the sum of the individual moments of inertia of the disk and ball bearings, in the same way that total mass is the sum of individual masses.