Angular Velocity: What's the Difference between Horizontal and Vertical Circles?

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SUMMARY

The discussion clarifies the distinction between angular velocity in horizontal and vertical circles. When considered as a scalar quantity, angular velocity remains unchanged regardless of the orientation of the circle. However, when treated as a vector, angular velocity points along different axes depending on the circle's orientation; it points along the z-axis for horizontal circles and along the x-axis for vertical circles. Additionally, the conservation of energy principles apply differently in vertical circles compared to horizontal ones, where angular velocity remains constant.

PREREQUISITES
  • Understanding of angular velocity as both a scalar and vector quantity
  • Familiarity with the concepts of horizontal and vertical motion
  • Basic knowledge of conservation of energy in physics
  • Ability to visualize motion in different coordinate systems
NEXT STEPS
  • Research the mathematical definitions of angular velocity in different coordinate systems
  • Explore the principles of conservation of energy in vertical circular motion
  • Study the effects of gravitational forces on angular velocity in vertical circles
  • Learn about the applications of angular velocity in real-world scenarios, such as in amusement park rides
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Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of circular motion.

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Can someone please explain the difference in Angular Velocity for a Horizontal and a Vertical circle? :confused:
 
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If you view it as a scalar quantity, there is none. Just by relabeling the x, y and z axis you can always get the circle to lie in the (x, y) plane and make it "horizontal". If you view the angular velocity as a vector, the difference will be that it points along one axis ("z") in one case and along another (e.g. "x") in the other.

So what exactly do you mean by "horizontal" and "vertical" circle, how do you define angular velocity and how would it be different?
 
I'm thinking of it in terms of conservation of energy. I believe Motion in a vertical circle, conservation of energy applies. In a horizontal v=(omega)r and omega is constant.

Can anyone explain this theory further?
 

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