vertical circular motion

Question

A particle of mass 0.5 kg is moving in a vertical circle of radius 2 m. What is the minimum velocity at the highest point for the particle to complete the circle? (g = 10 m/s²)

RankGuru · Accepted Answer

1. **Critical Condition**: At the highest point of a vertical circle, the minimum velocity is achieved when the string tension becomes zero ($T = 0$).
2. **Force Balance**: Centripetal force is provided by weight alone at this limit.
   - $mg = m v^2 / r$.
3. **Isolate velocity**: $v = \sqrt{rg}$.
4. **Variables**:
   - $r = 2$ m.
   - $g = 10$ m/s$^2$.
5. **Calculation**: $v = \sqrt{2 	imes 10} = \sqrt{20}$ m/s.
6. **Note**: If $v < \sqrt{rg}$, the particle will fall away from the circular path.

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vertical circular motion

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