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Mechanics · Forces & Newton's laws

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The idea

Newton's laws and F = ma

Newton's three laws and the one equation that runs all of dynamics — the RESULTANT force equals mass times acceleration — applied along a line and to forces given as 2-D vectors, why weight is mg and the normal reaction is whatever balances the rest, and how a lift problem is just F = ma done vertically.

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Mechanics · Forces & Newton's laws

Newton's laws and F = ma

Newton's three laws and the one equation that runs all of dynamics — the RESULTANT force equals mass times acceleration — applied along a line and to forces given as 2-D vectors, why weight is mg and the normal reaction is whatever balances the rest, and how a lift problem is just F = ma done vertically.

Why it works

Three laws

  • Newton's first law. A body stays at rest or moves with constant velocity unless a resultant force acts. So constant velocity needs no net force — the forces are balanced. A car cruising at a steady 30 m s−130\ \text{m s}^{-1} has its driving force exactly cancelled by resistance.
  • Newton's second law. A resultant force makes a body accelerate, in the same direction, with Fnet=ma.\mathbf{F}_{\text{net}} = m\mathbf{a}. This is the workhorse. The force in it is the resultant of all forces, never just one of them.

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