Centripetal Acceleration

📊 beginner

$$a_c = \frac{v^2}{r}$$

The acceleration directed toward the center of a circular path.

Variables & Units

$a_c$

Centripetal Acceleration

Unit: $m/s^2$

$v$

Tangential Velocity

Unit: $m/s$

$r$

Radius of curvature

Unit: Meter ($m$)

Key Information

📐 Derived From

Vector differentiation of position in polar coordinates.

💡 Example

Acceleration of a car taking a turn of radius $50 m$ at $10 m/s$.

🔧 Applications

Highway design and centrifuge operation.

⚠️ Constraints

Uniform circular motion.

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