Does Spin have rotational kinetic energy?

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SUMMARY

Rotational kinetic energy is defined by the formula KE = ½ I Ω², where KE is the energy in joules, I is the moment of inertia in kg*m², and Ω is the angular velocity in radians/sec. The discussion raises two key questions regarding the application of this formula to quantum spin, defined as J, which equals a half-integer times h/2π, where h is Planck's constant. The first question proposes whether the rotational kinetic energy associated with spin can be expressed as KE = ½ J Ω. The second question inquires if the maximum rotational kinetic energy related to spin can be represented as KE = ½ J c/R, where c is the speed of light and R is the radius.

PREREQUISITES
  • Understanding of rotational kinetic energy and its formula.
  • Familiarity with quantum mechanics concepts, specifically spin and Planck's constant.
  • Knowledge of angular velocity and its relation to linear velocity.
  • Basic grasp of units in physics, particularly joules, kg*m², and radians/sec.
NEXT STEPS
  • Research the implications of quantum spin on rotational kinetic energy calculations.
  • Explore the relationship between angular velocity and linear velocity in quantum systems.
  • Investigate the significance of Planck's constant in quantum mechanics.
  • Examine the concept of moment of inertia in various physical contexts.
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Physicists, students of quantum mechanics, and anyone interested in the relationship between rotational dynamics and quantum spin.

Jeff Byram
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I have two questions regarding rotational kinetic energy. I know that rotational kinetic energy is defined as:

KE = ½ I Ω^2

Where KE is the rotational kinetic energy [in units of: joules; kg*m^2/s^2], I is the Moment of inertial [in units of: kg* m^2], and Ω is angular velocity [in units of: radians/sec^2 or 1/s^2] so that the units check.

If (Electron or Nuclear) Spin is defined as J, with values equal to a half integer * h/2π, where h is Plank’s constant [in units of: Joule *seconds or kg*m^2/s],

#1, Is the rotational kinetic energy associated with Spin: KE = ½ J Ω ? (so the units check).

Since V = Ω R, where V is velocity, and R is the radius (or the Electron or Nucleus), so Ω = V/R, and since the fastest possible speed is the speed of light, c,

#2, Is the greatest possible rotational kinetic energy associated with Spin: KE = ½ J c/R ? (so the units check).

Please advise,

Jeff Byram
 
Physics news on Phys.org
Hello Jeff, I see this question is almost 2 years old. Did anyone ever answer you?
 

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