check_angular_momentum_conservation
Verify whether total angular momentum is conserved by comparing initial and final values within a tolerance, indicating if external torques acted on the system.
Instructions
Verify conservation of angular momentum.
Checks whether total angular momentum is conserved. Angular momentum
is conserved when no external torques act on the system.
Args:
initial_angular_momentum: Initial L [x, y, z] in kg⋅m²/s (or JSON string)
final_angular_momentum: Final L [x, y, z] in kg⋅m²/s (or JSON string)
tolerance: Tolerance (fraction, default 0.01 = 1%)
Returns:
Dict containing:
- initial_L_magnitude: Initial |L| in kg⋅m²/s
- final_L_magnitude: Final |L| in kg⋅m²/s
- L_difference: Difference [x, y, z]
- L_difference_magnitude: |ΔL|
- L_difference_percent: % difference
- is_conserved: Whether L is conserved within tolerance
Tips for LLMs:
- Conserved when no external torques (isolated rotation)
- Ice skater spinning: pull arms in → I decreases → ω increases (L constant)
- Gyroscope: resists changes to L direction
- Planets orbiting: L conserved → elliptical orbits
Example - Figure skater:
# Arms extended → Arms pulled in
result = await check_angular_momentum_conservation(
initial_angular_momentum=[0, 15, 0], # kg⋅m²/s
final_angular_momentum=[0, 15.05, 0],
tolerance=0.01
)Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| initial_angular_momentum | Yes | ||
| final_angular_momentum | Yes | ||
| tolerance | No |
Implementation Reference
- MCP @tool decorated async handler for check_angular_momentum_conservation. Parses input vectors (list or JSON string), delegates to core calculation function from ..conservation, and returns the response dict.
@tool # type: ignore[arg-type] async def check_angular_momentum_conservation( initial_angular_momentum: Union[list[float], str], final_angular_momentum: Union[list[float], str], tolerance: float = 0.01, ) -> dict: """Verify conservation of angular momentum. Checks whether total angular momentum is conserved. Angular momentum is conserved when no external torques act on the system. Args: initial_angular_momentum: Initial L [x, y, z] in kg⋅m²/s (or JSON string) final_angular_momentum: Final L [x, y, z] in kg⋅m²/s (or JSON string) tolerance: Tolerance (fraction, default 0.01 = 1%) Returns: Dict containing: - initial_L_magnitude: Initial |L| in kg⋅m²/s - final_L_magnitude: Final |L| in kg⋅m²/s - L_difference: Difference [x, y, z] - L_difference_magnitude: |ΔL| - L_difference_percent: % difference - is_conserved: Whether L is conserved within tolerance Tips for LLMs: - Conserved when no external torques (isolated rotation) - Ice skater spinning: pull arms in → I decreases → ω increases (L constant) - Gyroscope: resists changes to L direction - Planets orbiting: L conserved → elliptical orbits Example - Figure skater: # Arms extended → Arms pulled in result = await check_angular_momentum_conservation( initial_angular_momentum=[0, 15, 0], # kg⋅m²/s final_angular_momentum=[0, 15.05, 0], tolerance=0.01 ) """ # Parse inputs parsed_L_i = ( json.loads(initial_angular_momentum) if isinstance(initial_angular_momentum, str) else initial_angular_momentum ) parsed_L_f = ( json.loads(final_angular_momentum) if isinstance(final_angular_momentum, str) else final_angular_momentum ) from ..conservation import ( AngularMomentumConservationCheckRequest, check_angular_momentum_conservation as check_L, ) request = AngularMomentumConservationCheckRequest( initial_angular_momentum=parsed_L_i, final_angular_momentum=parsed_L_f, tolerance=tolerance, ) response = check_L(request) return response.model_dump() - Core calculation function that verifies angular momentum conservation by computing vector magnitudes, difference, and comparing against tolerance. Returns AngularMomentumConservationCheckResponse.
def check_angular_momentum_conservation( request: AngularMomentumConservationCheckRequest, ) -> AngularMomentumConservationCheckResponse: """Verify conservation of angular momentum. Args: request: Angular momentum conservation check request Returns: Angular momentum conservation analysis """ L_initial = request.initial_angular_momentum L_final = request.final_angular_momentum L_initial_mag = _vector_magnitude(L_initial) L_final_mag = _vector_magnitude(L_final) L_diff = _vector_subtract(L_initial, L_final) L_diff_mag = _vector_magnitude(L_diff) L_diff_percent = (L_diff_mag / L_initial_mag * 100.0) if L_initial_mag > 0 else 0.0 is_conserved = L_diff_mag <= request.tolerance * L_initial_mag return AngularMomentumConservationCheckResponse( initial_L_magnitude=L_initial_mag, final_L_magnitude=L_final_mag, L_difference=L_diff, L_difference_magnitude=L_diff_mag, L_difference_percent=L_diff_percent, is_conserved=is_conserved, ) - AngularMomentumConservationCheckRequest Pydantic model defining input schema: initial/final angular momentum vectors [x,y,z] and tolerance.
class AngularMomentumConservationCheckRequest(BaseModel): """Request for angular momentum conservation verification.""" initial_angular_momentum: list[float] = Field( ..., description="Initial angular momentum [x, y, z] in kg⋅m²/s" ) final_angular_momentum: list[float] = Field( ..., description="Final angular momentum [x, y, z] in kg⋅m²/s" ) tolerance: float = Field( default=0.01, description="Tolerance for conservation check (fraction)", ge=0.0 ) - AngularMomentumConservationCheckResponse Pydantic model defining output schema: magnitudes, difference vector, percentage, and conservation boolean.
class AngularMomentumConservationCheckResponse(BaseModel): """Response for angular momentum conservation verification.""" initial_L_magnitude: float = Field( ..., description="Initial angular momentum magnitude in kg⋅m²/s" ) final_L_magnitude: float = Field(..., description="Final angular momentum magnitude in kg⋅m²/s") L_difference: list[float] = Field( ..., description="Angular momentum difference [x, y, z] in kg⋅m²/s" ) L_difference_magnitude: float = Field( ..., description="Angular momentum difference magnitude in kg⋅m²/s" ) L_difference_percent: float = Field( ..., description="Angular momentum difference as percentage" ) is_conserved: bool = Field( ..., description="Whether angular momentum is conserved within tolerance" ) - src/chuk_mcp_physics/server.py:38-61 (registration)Registration via importing .tools.conservation module in server.py. The @tool decorator on the async function auto-registers it with the MCP server framework.
# Import all tools modules to register their @tool decorated functions from .tools import ( basic, rotational, oscillations, circular_motion, collisions, conservation, fluid as fluid_tools, kinematics_tools, statics, convert_units as unit_conversion_tools, ) # Silence unused import warnings - these imports register @tool decorated functions _ = ( basic, unit_conversion_tools, rotational, oscillations, circular_motion, collisions, conservation, fluid_tools,