Kinetic Energy of Body at Constant Angular Speed

Theorem

Let $B$ be a body rotating at an angular speed $\omega$ about some axis of rotation $R$.

Let $I$ denote the moment of inertia of $B$ about $R$.


Then the kinetic energy $T$ of $B$ brought about by this rotation is given by:

$T = \dfrac {I \omega^2} 2$


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): kinetic energy
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): moment of inertia
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): kinetic energy
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): moment of inertia
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