Acceleration In Circular Motion

Question

A particle performs uniform circular motion with angular velocity ω. What is the magnitude of its acceleration at any instant if the radius of the circle is r?

RankGuru · Accepted Answer

1. **Concept**: Centripetal acceleration is $a_c = v^2/r$ directed toward the center.
2. **Angular relation**: The linear velocity $v$ and angular velocity $\omega$ are linked by $v = r \omega$.
3. **Substitution**:
   - $a_c = \frac{(r\omega)^2}{r} = \frac{r^2 \omega^2}{r}$.
4. **Result**: $a_c = \omega^2 r$.
5. **Note**: In uniform circular motion, tangential acceleration is zero, so this centripetal acceleration is the total acceleration.

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Acceleration In Circular Motion

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