circular motion

Question

A particle moves in a circle of radius 2 m with a constant speed of 4 m/s. What is its centripetal acceleration?

RankGuru · Accepted Answer

1. **Concept**: In uniform circular motion, despite constant speed, acceleration exists because the direction of velocity changes.
2. **Centripetal acceleration ($a_c$)**: $a_c = v^2/r$.
3. **Substitute Values**:
   - $v = 4$ m/s.
   - $r = 2$ m.
4. **Calculation**:
   - $a_c = 4^2 / 2 = 16 / 2 = 8$ m/s$^2$.
5. **Direction**: This acceleration is always directed towards the center of the circle.

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