I've been reading my physics book and there they derived the formula ∑τ = Iα where τ is torque, I is moment of inertia of a rigid body and α is the angular acceleration. They did by taking an arbitrary particle on the rigid body with an applied external force tangent to the rotation. τ1 = Ftan * r1 = m1 * a1 * r1 = m1 * r12 * α where m is the particles mass and r is the particles distance from the center of rotation and a is the particles linear acceleration. They sum this into ∑τ = α∑miri2 = Iα What I don't understand is why the torque beside the first particle matters. In the image I attached an external force is applied to the blue particle so its torque is Ftan * r1 but if you take any other particle there is no external force applied there so Ftan * r1 should be zero? I mean the internal force of particles in a rigid body cancel out each other right? And the force that the blue particle exert on other particles is an internal force right? I understand that for an infinitesemal mass m1 the angular acceleration must be super high to become Ftan so I am quite puzzled.