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We study influence of noncommutativity of coordinates and noncommutativity ofmomenta on the motion of a particle (macroscopic body) in uniform andnon-uniform gravitational fields in noncommutative phase space of canonicaltype with preserved rotational symmetry. It is shown that because ofnoncommutativity the motion of a particle in gravitational filed is determinedby its mass. The trajectory of motion of a particle in uniform gravitationalfield corresponds to the trajectory of harmonic oscillator with frequencydetermined by the value of parameter of momentum noncommutativity and mass ofthe particle. The equations of motion of a macroscopic body in gravitationalfiled depend on its mass and composition. From this follows violation of theweak equivalence principle caused by noncommutativity. We conclude that theweak equivalence principle is recovered in rotationally invariantnoncommutative phase space if we consider the tensors of noncommutativity to bedependent on mass. So, finally we construct noncommutative algebra which isrotationally invariant, equivalent to noncommutative algebra of canonical type,and does not lead to violation of the weak equivalence principle.

Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle