Problem

Problem

A particle is moving in a circular path with a constant speed. If θ\theta is the angular displacement, then starting from θ=0\theta = 0, the maximum and minimum change in the linear momentum will occur when value of θ\theta is respectively a. 45∘45^\circ and 90∘90^\circ b. 90∘90^\circ and 180∘180^\circ c. 180∘180^\circ and 360∘360^\circ d. 90∘90^\circ and 270∘270^\circ
Intuitive explanation

The key insight is that linear momentum is a vector, so its change depends on both the direction change and the geometry of the circular path. Since speed is constant, the magnitude of momentum stays the same—only its direction rotates. The change in momentum is largest when the velocity vectors point in opposite directions (maximum angle between them), and smallest when they point nearly the same way. Think about how the angle between initial and final velocity vectors grows as the particle moves around the circle.

Intuitive explanation

The key insight is that linear momentum is a vector, so its change depends on both the direction change and the geometry of the circular path. Since speed is constant, the magnitude of momentum stays the same—only its direction rotates. The change in momentum is largest when the velocity vectors point in opposite directions (maximum angle between them), and smallest when they point nearly the same way. Think about how the angle between initial and final velocity vectors grows as the particle moves around the circle.

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