Rotation, Moments of Inertia and the Incline

Overview

In a previous experiment we encountered the "strange result" that for a sphere or cylinder rolling down an incline the measured acceleration was significantly less than the value a = gsinq . We now realize that this theory of motion on an incline is invalid when rotation is involved. In this experiment we will investigate the acceleration of real (ie. non-point) objects as they roll down an incline.

PreLab:Working Through the Expressions

We will spend some time working out the expected accelerations for:

• a uniform density sphere
• a uniform density cylinder
• an annulus
• a non-uniform object

The Experiment

In this experiment we will use inclined planes equipped with photogate timers and Logger Pro units. The experiment is simple, we will measure the time needed for the various objects (sphere, cylinder, annulus, golf ball) to roll 1 m down an incline. From this data we will calculate the acceleration of the object and compare this to our theory of motion for these objects.

In particular...

• make 10 (min) measurements of the time of descent
• find the average and standard deviation of these times and use this data to calculate the acceleration and the error in the acceleration
• determine the angle of inclination for the incline

What to Hand In...

I want two things...

1. A table that summarizes the measurements that you made for the acceleration of the uniform sphere, cylinder and annulus. You must include a formal error analysis here. How well do your findings support our "improved" theory of motion?

2. A value for the moment of inertia of the golf ball and a discussion of what you think the density profile of the golf ball might be. In this discussion you should provide evidence for why you suspect that the density is not uniform.

Due Date: Next Week