Newton’s law

Newton’s first law (the law of inertia)

The body keeps its speed constant (uniform rectilinear motion v=const, a=0) or is at rest while the body is not affected by external forces.

F=0

F — force, N.

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Newton’s second law

The force acting on a body is equal to the product of mass and acceleration.

F=ma

m — mass, kg;
a — acceleration, m/s².

Newton’s second law applies only to terrestrial bodies moving at a low speed. An example of Newton’s second law is the motion of a body along an inclined plane discovered by Galileo Galilei.

N+F_friction+mg=ma

N — the reaction force of the support.
F_friction — friction force, determined by the formula F_friction=µN
μ is the coefficient of rolling friction.
X-аxis:

F_friction−mgsinθ=ma

Y-аxis:

N−mgcosθ=0

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Newton’s third law

The forces acting on each other are opposite in direction and equal in modulus

F₁₂=−F₂₁

m₁₂a₁₂=−m₂₁a₂₁