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Demonstration Highlight: Ring and Disc on Inclined Plane

In recent years, the classic term “moment of inertia” has started to be largely retired in favor of the more descriptive “rotational inertia;” likely a good choice, as “moment” has long since ceased to have any non-time-related usage in everyday English. But call it what you will, it can be a challenging concept for beginning students to wrap their heads around.

Demonstration D2-01: Ring and Disc on Inclined Plane is a useful illustration for clarifying this concept. Two objects of similar mass and radius, a metal ring and a solid wooden disc, are placed on an inclined plane with no initial velocity. As they are accelerated by gravity, the disc quickly outpaces the ring. You can invite students to make a prediction ahead of time about their behaviour, presenting it as a race between the two objects, and invite them to discuss the results afterwards.

A wooden disc and a metal ring sit on a table next to a wooden ramp

One thing that students sometimes find confusing is that the behaviour of rolling bodies is often presented just after they have finally internalized the idea that all objects under the same gravity fall at the same rate - and now here appears to be a violation of that principle! Of course, that's not what's happening at all, gravity has the exact same force on both objects. But here we are moving not in free fall, but on a surface. And more importantly, with rolling objects we need to concern ourselves not only with force, but with torque, which is affected not just by mass but by the distribution of mass, and so the object where most of the mass is farther from the center of rotation is delayed.

 

A simulation to let students try this themselves in various combinations pairs well with using this demonstration in class. Two to consider that offer a variety of options:

Moment of Inertia, at Javalab https://javalab.org/en/moment_of_inertia_en/

Moment of Inertia: Rolling and Sliding Down an Incline, at oPhysics https://ophysics.com/r3.html

 

For expanded options in class, also take a look at D2-02: Miscellaneous Objects on Inclined Plane and D1-61: Rolling vs Sliding .

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