  We consider a semi-classical approximation to the dynamics of a point
particle in a noncommutative space. In this approximation, the noncommutativity
of space coordinates is described by a Poisson bracket. For linear Poisson
brackets, the corresponding phase space is given by the cotangent bundle of a
Lie group, with the Lie group playing the role of a curved momentum space. We
show that the curvature of the momentum space may lead to rather unexpected
physical phenomena such as an upper bound on the velocity of a free
nonrelativistic particle, bounded motion for repulsive central force, and
no-fall-into-the-centre for attractive Coulomb potential. We also consider a
superintegrable Hamiltonian for the Kepler problem in $3$-space with $su(2)$
noncommutativity. The leading correction to the equations of motion due to
noncommutativity is shown to be described by an effective monopole potential.
