Why having a low center of mass guarantee stability?

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SUMMARY

The discussion centers on the relationship between a low center of mass (CM) and stability in physical objects, specifically rectangular prisms. It establishes that while both low and high CM configurations experience forces and torques, the torque required to flip an object with a low CM is significantly greater. Additionally, the area of the base plays a crucial role in determining stability, as a larger base area contributes to a higher resistance against tipping. Ultimately, a low CM enhances stability but does not guarantee it, as the tilt angle required for toppling varies.

PREREQUISITES
  • Understanding of torque and forces in physics
  • Familiarity with concepts of center of mass
  • Knowledge of stability principles in mechanics
  • Basic geometry related to shapes and areas
NEXT STEPS
  • Research the mathematical principles of torque in physics
  • Explore the concept of center of mass in different geometric shapes
  • Study the effects of base area on stability in engineering contexts
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Students of physics, engineers, and anyone interested in mechanics and stability analysis in physical systems.

physics user1
I know that, i studied it, but i can't actually make a picture in my mind, i can't really figure out why, i mean the forces and the torques are the same no? What's the big deal? What am i missing?
 
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The torques are not the same. Imagine a rectangular prism sitting on a horizontal surface. Then incline it by some angle.
Look at the torque of the weight for two situations: low center of mass and high center of mass (for the same area of the base).
This is just part of the answer. The area of the base is also important for stability.

But no matter how low is CM there is no "guarantee". The body is just more stable, it takes a larger torque to flip it over.
 
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The tilt required for fall over is different.
 

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