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:
- The perpendicular distance (d) remains constant throughout the motion
- The direction of \( \mathbf{L} \) (perpendicular to the plane of motion) doesn't change
- 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.
Note: The simulation shows a 2D projection. The angular momentum vector would point out of the screen (right-hand rule).