calculate_centripetal_force

Instructions

Force required to keep an object moving in a circle.
Always points toward the center of the circular path.

Args:
    mass: Mass in kg
    velocity: Speed (velocity magnitude) in m/s
    radius: Radius of circular path in meters

Returns:
    Dict containing:
        - centripetal_force: F_c in Newtons
        - centripetal_acceleration: a_c in m/s²

Tips for LLMs:
    - Not a new force - it's the net inward force (tension, friction, gravity)
    - Faster speed → much more force needed (v² relationship)
    - Tighter turn → more force needed
    - Use for: car turns, satellite orbits, centrifuges

Example - Car turning:
    result = await calculate_centripetal_force(
        mass=1500,  # kg
        velocity=20,  # m/s (72 km/h)
        radius=50  # meter turn radius
    )
    # F_c = 12000 N (provided by friction between tires and road)

Implementation Reference

• src/chuk_mcp_physics/circular_motion.py:110-126 (handler)

  Core calculation function: computes centripetal force (F_c = m * v² / r) and centripetal acceleration (a_c = v² / r). Takes a CentripetalForceRequest and returns a CentripetalForceResponse.

  def calculate_centripetal_force(request: CentripetalForceRequest) -> CentripetalForceResponse:
      """Calculate centripetal force: F_c = m * v² / r.
  
      Args:
          request: Centripetal force request
  
      Returns:
          Centripetal force and acceleration
      """
      m = request.mass
      v = request.velocity
      r = request.radius
  
      a_c = (v * v) / r
      F_c = m * a_c
  
      return CentripetalForceResponse(centripetal_force=F_c, centripetal_acceleration=a_c)

• src/chuk_mcp_physics/circular_motion.py:16-21 (schema)

  Pydantic request model for centripetal force calculation with mass (>0), velocity (>=0), and radius (>0) fields.

  class CentripetalForceRequest(BaseModel):
      """Request for centripetal force calculation."""
  
      mass: float = Field(..., description="Mass in kg", gt=0.0)
      velocity: float = Field(..., description="Velocity magnitude in m/s", ge=0.0)
      radius: float = Field(..., description="Radius of circular path in meters", gt=0.0)

• src/chuk_mcp_physics/circular_motion.py:24-28 (schema)

  Pydantic response model containing centripetal_force (N) and centripetal_acceleration (m/s²).

  class CentripetalForceResponse(BaseModel):
      """Response for centripetal force calculation."""
  
      centripetal_force: float = Field(..., description="Centripetal force in Newtons")
      centripetal_acceleration: float = Field(..., description="Centripetal acceleration in m/s²")

• src/chuk_mcp_physics/tools/circular_motion.py:6-49 (registration)

  MCP @tool-decorated async wrapper that registers calculate_centripetal_force as an MCP tool. Accepts mass, velocity, radius as float parameters, delegates to the core calculation function, and returns the result as a dict.

  @tool  # type: ignore[arg-type]
  async def calculate_centripetal_force(
      mass: float,
      velocity: float,
      radius: float,
  ) -> dict:
      """Calculate centripetal force: F_c = m v² / r.
  
      Force required to keep an object moving in a circle.
      Always points toward the center of the circular path.
  
      Args:
          mass: Mass in kg
          velocity: Speed (velocity magnitude) in m/s
          radius: Radius of circular path in meters
  
      Returns:
          Dict containing:
              - centripetal_force: F_c in Newtons
              - centripetal_acceleration: a_c in m/s²
  
      Tips for LLMs:
          - Not a new force - it's the net inward force (tension, friction, gravity)
          - Faster speed → much more force needed (v² relationship)
          - Tighter turn → more force needed
          - Use for: car turns, satellite orbits, centrifuges
  
      Example - Car turning:
          result = await calculate_centripetal_force(
              mass=1500,  # kg
              velocity=20,  # m/s (72 km/h)
              radius=50  # meter turn radius
          )
          # F_c = 12000 N (provided by friction between tires and road)
      """
      from ..circular_motion import CentripetalForceRequest, calculate_centripetal_force as calc_fc
  
      request = CentripetalForceRequest(
          mass=mass,
          velocity=velocity,
          radius=radius,
      )
      response = calc_fc(request)
      return response.model_dump()