Moment of Inertia: The Great Soup Can Race
If two identical cans are released from rest to roll down an incline at the same time, will the top can catch up with the bottom can? Does it matter what the contents of the cans are? This project deals with how things roll.
What You Need
- 2 cans of thick soup (such as mushroom soup)
- 1 can of thin soup (such as chicken broth)
- Verify that the external shape of each of the three cans is the same.
- Set up an incline about 1 meter in length. The height should be about 30 cm.
- Hold the two cans of mushroom soup on the incline with a distance of about 10 cm between them, as shown in Figure 60-1. Call the top can A and the bottom can B.
- Predict what will happen when the cans are released: a) the distance between them will increase b) the distance between them will decrease c) the distance between them will remain the same.
- Place one of the mushroom soup cans (A) and the can of broth (C) on the incline with A 10 cm higher than C.
- Predict what will happen when the cans are released: same options as number 4.
- Try this again with can C as the upper can this time.
The two cans with the same contents will accelerate at the same rate. Because both cans start from rest, the distance between them remains constant. However, the mushroom soup has a greater density than the broth and it will roll more slowly.
Why It Works
When an object rolls, some of its energy is associated with moving from one point to another (called translation). The more mass the object has and the faster it goes, the more energy it has. In addition, some of the energy of a rolling object is related to the fact that it is rolling. The amount of this rotational energy is related to the way the mass is distributed around the center of rotation. A greater density center (mushroom soup) requires more energy to roll at the same rate as a lower density center (broth).
Physics alert: A property called moment of inertia measures how mass is distributed around a center of rotation. A can of dense soup has a greater moment of inertia than a can of thin soup and, as a result, ties up more energy as it rolls.
Other Things to Try
An interesting follow-up would be to drop both types of soup cans from a distance and reestablish the principle that they both accelerate at the same rate in free-fall. Translation (falling) is different than rolling. The effect of rolling makes the difference here and gives the less-dense soup the advantage.
A force applied to a cylindrical object can cause it either to translate or rotate or some combination of both.
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