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Non-uniform circular motion

Free notes · JEE Main Physics

Formulas

arad=v2r,atan=dvdta_{rad} = \frac{v^2}{r},\quad a_{tan} = \frac{dv}{dt}

The two components

Worked example

A particle moves on a circle of radius 2 m; its speed grows at 3 m/s² while its speed is 4 m/s. Find the magnitude of the total acceleration.

  1. Centripetal: a_c = v²/r = 16/2 = 8 m/s².
  2. Tangential: a_t = 3 m/s² (given).
  3. Total: a = √(8² + 3²) = √73 ≈ 8.54 m/s².

Answer: √73 ≈ 8.54 m/s².