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Name: Dania
Status: Student
Grade: 9-12
Location: AZ
Country: USA
Date: N/A 

Currently in physics we are working with projectile motion. I am attempting to calculate the center of mass of a dog in motion. Specifically, while she is leaping over a hurdle. I have a video of the dog, and I need to locate the center of mass in each frame. My question is, how do I calculate the center of mass of a 3D, irregular object, such as a dog? Several methods exist for humans (segment mass and such) yet not for animals/canines. Any ideas?

I'm not into book promotion, but the book "Back-of-the-Envelope Physics" by Clifford Swartz is good reading to see how to approach such a problem as you describe. The philosophy is that many quantities, like the center of mass, are not very sensitive to a value calculated for a much simpler model.

First, How big is the dog? If the dog is small enough you (and maybe a classmate or two) can try to balance the animal on a padded broomstick, or extended arm. You know the the center of mass is symmetric along the nose-to-tail axis, so you need to know where the dog "balances" its front end and back end. Be sure to treat the dog gently so it is not hurt or the process is not painful. When you (and clasmates) find the ring of symmetery about the dog's trunk, assume your dog is a cylinder -- problem solved. This also gives you an estimate of the dog's volume.

If the dog is small, e.g. a Shih Tzu, you can find this ring just by gently gripping the dog about its midriff and lifting and you can feel the place where the dog neither tilts forward or backward. Now if the dog is a Doberman, I would not recommend this method, for obvious reasons.

A totally different approach is to as a vet or dog trainer. They may have procedures that they use in their practice -- or even "know the answer" because of the nature of their practice. Just by experience they may be able tell you that the center of gravity is some fraction of the length of the dog.

Good Luck. Woof Woof

Vince Calder
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