Puntmassa

Puntmassa, a Dutch term for point mass, is an idealization used in classical mechanics in which the mass of an object is assumed to be concentrated at a single point. This abstraction neglects the object's size, shape, rotation, and internal structure, and is applied to study translational motion without accounting for rotational effects.

Mathematical description follows Newton's second law. If m is the total mass and r(t) the position of the point mass in an inertial frame, the motion satisfies m d^2r/dt^2 = F_ext(r,t), where F_ext is the sum of external forces. In a gravitational field, F_ext can be written as m g or as the negative gradient of a potential, F_ext = -∇Φ. The trajectory is determined by the initial position and velocity and the forces acting on the mass. For motion under gravity near Earth, this yields familiar projectile or orbital paths, depending on the force law.

Applicability and center of mass relation. The point-mass model is valid when the object's size is negligible compared with the problem's length scales and when rotation or deformation does not affect the quantity of interest. For a system of particles, the motion of the center of mass R obeys M R'' = F_ext, where M is the total mass and R is the center-of-mass position; the center of mass then behaves like a single point mass under external forces.

Limitations. The model cannot describe rotation, moments of inertia, torques, or internal stresses, and it fails for extended bodies where size or deformation matters, such as in collisions or flexible objects.

See also: center of mass, rigid body, point particle, Newton's laws.