Physics

Physics

Problem

A particle describes uniform circular motion of radius AA with angular speed ω=2 rad s−1\omega=2\,\text{rad s}^{-1}. Its projection on a fixed diameter starts from the centre of the circle at t=0t=0. The time taken by the projection to reach its extreme positive position is a) 1.57 s1.57\,\text{s} b) 3.14 s3.14\,\text{s} c) 0.79 s0.79\,\text{s} d) 0.39 s0.39\,\text{s}
Intuitive explanation

The key is recognizing that a particle in uniform circular motion has a projection onto any diameter that behaves like simple harmonic motion. Since the particle starts at the center of the circle (the equilibrium position of the projection), you need to find when that projection reaches its maximum displacement AA from center. This is a quarter-period of the oscillation—think about where the particle itself must be on the circle for its projection to be at maximum.

Intuitive explanation

The key is recognizing that a particle in uniform circular motion has a projection onto any diameter that behaves like simple harmonic motion. Since the particle starts at the center of the circle (the equilibrium position of the projection), you need to find when that projection reaches its maximum displacement AA from center. This is a quarter-period of the oscillation—think about where the particle itself must be on the circle for its projection to be at maximum.

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