How do you distinguish a shaken can of carbonated beverage from an unshaken one? Watch the video to find out.

 

Why is this?

Looking at the Physics of Cylinders

A hollow cylinder rolls down a ramp or an inclined plane slower than a full cylinder of equal weight and equal size.

The moment of inertia, J, describes the different distribution of the mass, m, around the axis of rotation of an object: J = 1/2 mr² with r = radius of an object). The higher the moment of inertia, the slower the cylinder rolls down the ramp.

r and m of both cylinders are the same. However, the distribution of m is different: In a hollow cylinder, most of the mass is far away from the axis of rotation. The hollow cylinder has a larger moment of inertia. Therefore, it starts to rotate more slowly than the full cylinder. With the full cylinder, part of the mass is located directly near the axis of rotation. The full cylinder has a lower moment of inertia and starts to rotate faster.

 

What Does This Mean for the Beer Cans?

Both cans of beer have the same mass, m, and radius, r. Both cans contain an aqueous liquid and CO₂.

In the can that has not been shaken, a large CO₂ bubble sits on top of the liquid in the can. If the can rolls down the inclined plane, this air bubble tries to remains at the top of the liquid. Therefore, the liquid remains almost still at the bottom of the can and does not fully follow the rolling movement of the can.

When the can of beer is shaken, many small CO₂ bubbles form at small impurities at the walls of the can. As a result, the friction between the can and the liquid changes. More beer is set in rotation when the can is rolled down the inclined plane than with the not shaken can. The shaken can has a greater moment of inertia and rolls more slowly.

The moment of inertia of a beer can thus depend on whether the beer rotates in the can or not. As the video shows, the shaken can loses the race to the can that has not been shaken.

 

Sources

• David Kagan, The shaken-soda syndrome, The Physics Teacher 2001, 39(5), 290–292. https://doi.org/10.1119/1.1375467
• Reinhard Remfort, Methodisch korrektes Biertrinken, Ullstein Verlag, Berlin, Germany, 2017. ISBN-13 9783548375878 (in German)