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Torque and angular momentum

Newton's second law has a rotational counterpart: torque gives angular acceleration, just as force gives acceleration. Angular momentum is conserved when no external torque acts on the system, just as momentum is conserved without an external force.

\tau = I\alpha

Newton's second law for rotation

L = I\omega

angular momentum

E_{rot} = \tfrac12 I\omega^2

rotational kinetic energy

Symbols

$\tau$	torque	Nm
$\alpha$	angular acceleration	rad/s²
$L$	angular momentum	kg·m²/s

Example

A flywheel with $I = 0.50$ kg·m² is acted on by $\tau = 2.0$ Nm. The angular acceleration is $\alpha = \tau/I = 2.0/0.50 = 4.0$ rad/s².

A skater pulling their arms in reduces

I

and increases

\omega

– the angular momentum

L = I\omega

stays conserved.

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Part of Physics: Energy and rotation.