Generalization of the laws of dynamics to noninertial frames is based on the kinematic transformation formula for accelerations relative to different frames. A new approach is proposed to treat this problem. The relationship between accelerations relating to different frames of referenceRandR′ is stated in the forma=a′+aP+2ω×v′ which is derived in this paper from fundamental geometrical properties, without referring to any actual coordinate system. HereaPis the ‘‘conveyer acceleration,’’ that is the acceleration (relative toR) of the pointPofR′ where the material point is found at the given instant. The conventional detailed transformation formula follows then from the well‐known kinematic formula of rigid bodies,afterhaving chosen a translational point inR′ serving as the origin of thecoordinatesystemK′:aP=a0+ω×(ω×r′)+β×r′.