A playground can provide a valuable physics education laboratory. For example, Taylor et al.¹ describe bringing teachers in a workshop to a playground to examine the physics of a seesaw and slide, and briefly suggest experiments involving a merry-go-round. In this paper, we describe an experiment performed by students from a Society of Physics Students organization and their faculty advisor on a merry-go-round at a local park. The goal of the activity was for everyone to gain a greater understanding of the concepts of angular velocity, centripetal acceleration, moment of inertia, and conservation of angular momentum through their own personal experience—and to have fun, too.

The official objective of this field trip was to find the moment of inertia of the merry-go-round (MGR). The procedure we developed was for two of us to start off in the center of the MGR and then quickly move to the edge of the MGR, or vice versa (see Fig. 1). The physics describing this situation is just the conservation of angular momentum, or

Figure 1.

We developed two ways of determining the angular velocity of the MGR: (a) measure the centripetal acceleration (a_c = r²) at a known radius using a low-g accelerometer connected to a Vernier LabPro and TI-83+ calculator (see Fig. 2); and (b) analyze video of the experiment with iMovie² and determine the period (T = 2/) of its rotation. The accelerometer was duct-taped at the edge of the MGR (r = 1.49 m), while the LabPro was positioned in the center of the MGR. During the moving inward experiments, an additional person sat in the middle of the MGR to start the LabPro—this person's mass added a negligible contribution (of order 1 kg · m²) to the moment of inertia of the MGR.

Figure 2.

We did four runs before we began to feel queasy from the experience—one where we moved outward, and three where we moved inward. We analyzed two of these four runs since the first two of the moving inward experiments were complicated by our difficulties in moving inward when the MGR was rotating. Table I summarizes the results from these two experimental runs. The uncertainty in calculated from a_c originates from the variation in a_c, while the uncertainty in calculated from the video originates from the uncertainty in measuring the angular displacement of the MGR between video frames. The uncertainty in I_MGR is due to the uncertainty in and the uncertainty in determining the radius of the center of mass of each person in the video.³

The 's determined using our two methods were close (an average difference of 4%), and some of that may be due to not determining at the same instant on the LabPro and in the video. All but one of the I_MGR values agree within the experimental uncertainty, but calculating a larger I_MGR for moving inward than moving outward could originate from ignoring friction acting on the MGR. Friction would add a torque that would affect our calculations for moment of inertia as:

where t is the time interval between measurements of _i and _f. If we assume that all of the difference between the values of I_MGR calculated from the video were due to friction, we would require a frictional torque of 5 Nm. With a friction torque of that magnitude, the MGR would take approximately two minutes to come to a full stop from an angular velocity of 2 rad/s (a typical value in our experiments), which seems reasonable. Unfortunately, we did not videotape a long enough time to measure the angular deceleration due to friction, and we could not go back and test this prediction since the merry-go-round was removed from the park that summer.