Center of Gravity Paradox - Rob Vondrak

Author

Rob Vondrak

Principle(s) Illustrated

When balancing an object on your hand, the object will want to tip and fall to one side.

- However it tips, it is actually rotating around a point in your hand. The gravitational pull is creating a torque on the object. When objects rotate, the rate of rotation about a point is called the angular acceleration. If the angular acceleration is too large, you wont be able to adjust your hand to keep the object balancing.

Using Newton's second law, we know that the larger the mass, the smaller the acceleration on the object.

In angular terms, the larger the moment of inertia, the small the angular acceleration.
The further the center mass is from the axis of rotation, the greater the moment of inertia is.

With a larger moment of inertia, the angular acceleration will be smaller and you will be able to adjust your hand to continue balancing the object.

Standards

NGSS Science & engineering standards
- Analyzing and Interpreting Data
- Constructing Explanations
NGSS Cross-cutting concept standards
- Cause and Effect
NGSS Disciplinary core idea standards
- PS2.A:Forces and Motion

Questioning Script

Prior knowledge & experience:

Students should know about Newton's laws of motion and center of gravity. Students should have some knowledge of moment of inertia and and angular acceleration or alternatively, torque.

Root question:

Which orientation will allow you to balance a weighted rod for a longer time? Or tennis racket or hammer.

Target response:

By orienting the weight on the top, you've increased the moment of inertia and the rod will have a smaller angular acceleration around your hand. This smaller acceleration will allow you to adjust your hand and balance the rod longer than if the mass were located near the base(your hand).

Common Misconceptions:

If the mass is at the bottom, that creates a lower center of gravity. Things with low centers of gravity are more stable. If objects are top heavy they tend to flip. SUVs are known for rolling over during high speed turns.

Photographs and Movies

Applications to everyday life

Tightrope walkers and balancing

References

A science catalog description

An explanation of why things topple over

Information about moment of inertia

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