The angular acceleration of a rigid body does not depend on the choice of reference point because angular acceleration is a measure of how quickly the body's rotational velocity is changing, regardless of where the rotation is centered.
When we calculate angular acceleration, we consider the rate of change of angular velocity. Angular velocity is the rate of change of angular displacement per unit time. It is a vector quantity that represents the rotational speed and direction of the rigid body.
The angular acceleration of a rigid body is determined by the net torque acting on it. Torque is the rotational equivalent of force, and it causes objects to rotate about an axis. The torque acting on a rigid body is given by the product of the force and the perpendicular distance from the axis of rotation to the line of action of the force.
The torque equation is expressed as follows: Torque = force × lever arm
The choice of reference point affects the torque calculation because it affects the lever arm (the perpendicular distance). However, when we calculate the angular acceleration, we consider the net torque acting on the body, which is the sum of all the torques due to the forces acting on the body. The choice of reference point cancels out in this summation process.
In other words, while the torque acting on a rigid body depends on the choice of reference point, the net torque (which determines the angular acceleration) is the sum of all the torques acting on the body and is independent of the choice of reference point. Therefore, the angular acceleration of a rigid body does not depend on the choice of a reference point.