Fundamental Concepts in Mechanics and Gravitation

Work-Energy Theorem

The work (Wt) done by the net force on an object is equal to the variation in its kinetic energy (ΔEc). This can be expressed as: Wt = ΔEc = Ec2 - Ec1, where Ec1 is the initial kinetic energy and Ec2 is the final kinetic energy.

Gravitational Potential Energy

Gravitational potential energy is the energy associated with a system of two masses attracted by a gravitational force. It is also defined as the work required to move a mass 'm' from infinity to a specific distance 'r' from the Earth.

Variation of Potential Energy

The variation of potential energy is the work required to move a mass 'm' from a first point to a second point within a force field.

Moment of a Force (Torque)

The moment of a force (F) represents the ability of that force to cause rotation around an axis. It is also known as torque. The moment of a central force is zero because the force vector is parallel to the position vector.

Angular Momentum (L)

Angular momentum (L) of a particle is defined as the cross product of its position vector and its momentum vector (P). L measures the amount of curvilinear motion of an object. Angular momentum is a fundamental quantity in rotational dynamics.

Gravitational Field of a Mass 'm'

The gravitational field of a mass 'm' refers to the set of points in space influenced by the effects of this mass. At any point within a gravitational field, two quantities can be defined to characterize its effects: the intensity of the gravitational field and the gravitational potential.

Gravitational Acceleration (g)

Gravitational acceleration at a point (g) is defined as the field strength at that point, representing the force that would act on a unit mass located there. Importantly, 'g' can be measured at a point without the necessity of placing a mass at that location. It is a vector field because each of its points has an associated vector, 'g'.

Gravitational Potential (V)

Gravitational potential at a point (V) is defined as the potential energy a unit mass would have if located at that point. It is a scalar quantity. It can also be defined as the work that must be done to move a unit mass from infinity to that specific point.

Lines of Force

Lines of force represent the paths that would be followed by a mass if it were abandoned at a point in a gravitational field. The line of force passing through a specific point indicates the direction and sense of 'g' at that point. These lines originate at infinity and terminate in the mass, and they are perpendicular to the equipotential surfaces.

Equipotential Surfaces

Equipotential surfaces are surfaces consisting of points that all have the same gravitational potential. These surfaces are always perpendicular to the lines of force.