Newton's Laws

Central to Newtonian mechanics are Newton’s three laws of motion, which provide the foundation for understanding how forces affect the movement of particles and rigid bodies. The first law, the law of inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force. The second law quantitatively relates the net force acting on an object to its acceleration (), while the third law asserts that for every action, there is an equal and opposite reaction. This framework has been instrumental in explaining a wide range of phenomena—from the trajectories of projectiles to the motions of celestial bodies—and continues to serve as a cornerstone in both physics and engineering applications.

Mass, Force, Velocity, and Acceleration

Velocity and Speed

Velocity of an object is the rate of change of its position with respect to time, i.e. . It is a vector quantity. Speed is the magnitude of velocity.

Acceleration

Acceleration of an object is the rate of change of its velocity with respect to time, i.e. . Notice that it is also a vector quantity.

Newton’s Laws

Newton's First Law

An object will not change its motion unless a force acts on it.

Newton's Second Law

The time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it:

Newton's Third Law

When two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction.

Hooke's Law & Stiffness

Hooke’s law is an empirical law which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance: where constant is called stiffness of that spring.