Extract Physical Ai Formulas

Formula: The extracted formula in LaTeX or plain-text
Description: Explanation of the formula and its purpose
Variables / Units: Meaning and units of each variable
Application / Example: How the formula is used in robotics

Quality Criteria

• Formulas must be accurate and correctly formatted
• Explanations should be clear and concise
• Include observable outcomes or examples when possible
• Maintain relevance to Physical AI and humanoid robotics

Example

Input: "The torque τ required for a robotic joint can be calculated using τ = I * α, where I is the moment of inertia and α is the angular acceleration."

Output:

• Formula: τ = I * α
• Description: Torque τ equals the moment of inertia I multiplied by angular acceleration α
• Variables / Units: τ [Nm], I [kg·m²], α [rad/s²]
• Application / Example: Used to calculate torque requirements for joint actuators in humanoid robots