Centripetal acceleration is the acceleration to keep an object rotating around a circle

To derive centripetal acceleration, assume the following:

• Acceleration is the change in velocity over the change in time
• Angular velocity is described as $\omega =\frac{v}{r}\Rightarrow v=\omega r$
• The arc length of a circle is $s=r\theta$
• Use the image below as a visual aid for the derivation
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• $\mathrm{△}ABC,\mathrm{△}PQR$ are similar triangles
• Angle in $\mathrm{△}PQR$ is the same angle in $\mathrm{△}ABC$