Angular Momentum Conservation

Angular Momentum Conservation

Visualizing the conservation of angular momentum for a particle in motion

Understanding Angular Momentum

Angular momentum is a fundamental quantity in physics that describes the rotational motion of an object. For a particle moving with constant velocity, the angular momentum about any fixed point remains constant throughout the motion, demonstrating the principle of conservation of angular momentum.

Key Equations

Angular momentum definition: \( \mathbf{L} = \mathbf{r} \times \mathbf{p} \)

Magnitude calculation: \( L = r p \sin\theta = m v r \sin\theta = m v d \)

Where:

  • \( \mathbf{r} \) = position vector from reference point to particle
  • \( \mathbf{p} = m\mathbf{v} \) = linear momentum of the particle
  • \( \theta \) = angle between \( \mathbf{r} \) and \( \mathbf{v} \)
  • \( d = r \sin\theta \) = perpendicular distance from reference point to velocity vector

Why Angular Momentum is Conserved

For a particle moving with constant velocity:

  1. The perpendicular distance (d) remains constant throughout the motion
  2. The direction of \( \mathbf{L} \) (perpendicular to the plane of motion) doesn't change
  3. No external torque acts on the system (\( \tau = \frac{d\mathbf{L}}{dt} = 0 \))

This conservation principle is fundamental to understanding rotational dynamics and appears in many physical systems from planetary orbits to quantum mechanics.

Interactive Simulation

Observe how angular momentum remains constant as a particle moves with constant velocity. The simulation shows the relationship between position, velocity, and the perpendicular distance that determines angular momentum.

Velocity (v)
5 m/s
Perpendicular Distance (d)
50 m
Angular Momentum (L)
250 kg·m²/s
Torque (τ)
0 N·m

Note: The simulation shows a 2D projection. The angular momentum vector would point out of the screen (right-hand rule).

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