A swinging pendulum does experience centripetal acceleration, which is greatest at the bottom of the swing when the velocity is highest and momentarily zero at the top. The discussion highlights the relationship between centripetal acceleration and radius, emphasizing that centripetal acceleration equals velocity squared divided by radius. Users express confusion about calculating the radius when using varying velocity readings and centripetal acceleration values. It is noted that if the radius is constant, it should not change, and accurate measurements should be taken directly. The conversation revolves around ensuring consistent values for radius and acceleration to validate the calculations.