#4696 First Principles: Motorized Disc Dynamics
#4696 First Principles: Motorized Disc Dynamics #4696 Apply first principle to a simple motorized disc where force is applied on the circumference System Definition & Primitive Variables A motorized disc driven or loaded at its circumference can be broken down into five fundamental physical primitives: mass distribution, kinematics, force interaction at the contact interface, torque balance, and energy conservation. Disc Radius: R Total Mass: M Angular State: Angular velocity omega , angular acceleration alpha = dot{omega} Applied Tangential Force at Rim: F_t Normal Clamping/Contact Force: N Friction Coefficient: Static mu_s , Kinetic mu_k Kinematics & Mass Distribution Velocity and Acceleration Mapping: Every point on the circumference translates angular motion to tangential linear motion: v_t = \omega R a_t = alpha R = dot{\omega} R Mass Moment of Inertia ( I ): Derived from the continuous integral of mass distribution about the central rotational axis z : I = int_...