Help using data to determine if rigid object is rolling or slipping along a curved surface.

Donald Krolak
3 Posts

Hi

I am a high school math teacher my students completed a project published on the University of Colorado's Teach Engineering Website. The project is titled "Mathematically Designing a Frictional Roller Coaster" and can be found at (https://www.teachengineering.org/activities/view/ind-1996-frictional-roller-coaster-design-project-calculus).

We used Tracker to gather experimental data to compare against our theoretical data. The theoretical velocities generated by project formulas were much much less than the experimental velocities measure by tracker. The theoretical formulas are premised on the fact that the marble must always be rolling and never sliding. I am trying to investigate the source of the large discrepancy between predicted and experiential velocity and I suspect the marble may be sliding at times instead of rolling. I looked at the data and noticed that on the uphill portion of the track the angular velocity of the marble turns positive. Would this indicate that the linear velocity of the marble as it enters the uphill incline is so large that it is causing the marble to slide up the incline with a slight counterclockwise rotational velocity.

The exported data final is attached of one such project. We limited the slope as per the project guideline but I am suspecting that our initial slopes limit of -2.5 is generated too much linear velocity.

Re: Help using data to determine if rigid object is rolling or slipping along a curved surface. -

Douglas Brown
353 Posts

I would start by double-checking your calibration as this is often an issue, especially if, as you mention in your other post, you might have calibrated prior to correcting for perspective. Also, you should check that the perspective correction did not introduce a horizontal stretch or compression relative to the vertical.

Even if you're confident of the calibration, it is certainly possible the marble could slide as well as roll. Is there enough resolution in your video to see and/or measure the rotational motion independent of the translation?

Searching the ComPADRE collection for "rolling"brought up a number of Tracker projects and EJS models. You might find this one of interest: https://www.compadre.org/osp/items/detail.cfm?ID=8606

Doug

I am a high school math teacher my students completed > a project published on the University of Colorado's > Teach Engineering Website. The project is titled > "Mathematically Designing a Frictional Roller Coaster" > and can be found at (https://www.teachengineering.org/activities/view/ind-1996-frictional-roller-coaster-design-project-calculus). > > > We used Tracker to gather experimental data to compare > against our theoretical data. The theoretical velocities > generated by project formulas were much much less > than the experimental velocities measure by tracker. > The theoretical formulas are premised on the fact > that the marble must always be rolling and never > sliding. I am trying to investigate the source of > the large discrepancy between predicted and experiential > velocity and I suspect the marble may be sliding at > times instead of rolling. I looked at the data and > noticed that on the uphill portion of the track the > angular velocity of the marble turns positive. Would > this indicate that the linear velocity of the marble > as it enters the uphill incline is so large that it > is causing the marble to slide up the incline with > a slight counterclockwise rotational velocity. > > The > exported data final is attached of one such project. > We limited the slope as per the project guideline > but I am suspecting that our initial slopes limit > of -2.5 is generated too much linear velocity.