calculate_angular_momentum
Calculate angular momentum vectors and magnitudes for rotating systems using moment of inertia and angular velocity components. This physics tool helps analyze rotational motion and conservation principles.
Instructions
Calculate angular momentum: L = I × ω.
Angular momentum is the rotational equivalent of linear momentum.
It's conserved in the absence of external torques (like ice skater spinning).
Args:
moment_of_inertia: Moment of inertia in kg⋅m²
angular_velocity_x: X component of angular velocity in rad/s
angular_velocity_y: Y component of angular velocity in rad/s
angular_velocity_z: Z component of angular velocity in rad/s
Returns:
Dict containing:
- angular_momentum: L vector [x, y, z] in kg⋅m²/s
- magnitude: L magnitude in kg⋅m²/s
Tips for LLMs:
- Angular momentum is conserved when no external torques act
- Ice skater pulls arms in → I decreases → ω increases (L constant)
- Gyroscopes resist changes in angular momentum direction
Example - Spinning figure skater:
# Arms extended: I = 3.0 kg⋅m², ω = 5 rad/s
result = await calculate_angular_momentum(
moment_of_inertia=3.0,
angular_velocity_x=0.0,
angular_velocity_y=5.0,
angular_velocity_z=0.0
)
# L = 15 kg⋅m²/s (conserved when arms pulled in)Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| moment_of_inertia | Yes | ||
| angular_velocity_x | Yes | ||
| angular_velocity_y | Yes | ||
| angular_velocity_z | Yes |