Laser experiment, determine angular velocity

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SUMMARY

The discussion focuses on determining the angular velocity (ω) of a spinning circular cannister filled with a reflective liquid. The relationship between the height of the liquid surface (h(r)) and the radius (r) is defined by the equation h(r) = h(0) + (ω²/2g)r², where g is approximately 9.82 m/s². The problem involves calculating ω based on the intersection point of two laser beams, which is found to be 22 cm above the surface. The solution also references the use of a parabolic mirror with a radius of curvature of 0.44 m.

PREREQUISITES
  • Understanding of angular velocity and its calculation
  • Familiarity with parabolic equations and their properties
  • Basic knowledge of physics principles, particularly those related to gravity (g ≈ 9.82 m/s²)
  • Experience with vector equations and gradients
NEXT STEPS
  • Study the derivation of parabolic equations from curvature
  • Learn about angular motion and its applications in physics
  • Explore the principles of laser beam alignment and reflection
  • Investigate the use of parabolic mirrors in optical systems
USEFUL FOR

Students in physics or engineering, particularly those working on problems involving rotational dynamics and optics, will benefit from this discussion.

Gauss M.D.
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Homework Statement



A circular cannister of some reflective liquid is spinning at some ω. The distance between the cannister and the surface is given by

h(r) = h(0) + (ω2/2g)r2

Where g ≈ 9.82 and r is the distance to the axis of revolution. When we shine two parallell laser beams on the surface, we find that they meet at a point 22 cm above the surface.

Find ω.

Homework Equations



f = R/2

The Attempt at a Solution



We have a parabolic mirror with radius of curvature = 0.44 m. But I'm not really sure how to find the equation for a parabola given the curvature. I was well on my way to taking the gradient of the parabola and setting up some kind of system of vector equations, but I suspect that would be overkill...
 
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Figured it out.
 

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