- Define _centripetal acceleration_ - Solve problems involving centripetal acceleration --- Centripetal acceleration is the acceleration of an object moving in [[Circular Motion|uniform circular motion]]. ### Derive centripetal acceleration - Consider the object at two different points on the circular path, separated by a very small time interval $\Delta t$. - The velocity vectors at these two points are tangential to the circle and have the same magnitude, but different directions. $\Delta \theta = \frac{\Delta v}{v} \tag{1}$ Rearrange to: $\Delta v = v \cdot \Delta \theta \tag{2}$ Divide both sides by $\Delta t$ $a = \frac {v \cdot \Delta \theta}{\Delta t}$ where $\omega = \frac{\Delta \theta}{\Delta t}$ which leads to $a = v \cdot \omega$ Substitute in the $\omega = \frac{v}{r}$ To give the formula for centripetal acceleration. $a_c = \frac{v^2}{r}$ ### Related Topics --- [[Home|Home]] | [[Circular Motion]] | [[Centripetal Acceleration]] | [[Notes Vault/Physics Notes Vault/Circular Motion/Centripetal Force|Centripetal Force]]