Proof:
1. $F=\frac{m v^2}{r}$ (using centripetal force)
2. $F=m a$ (using Newton's 2nd law)
We can rewrite this as:
3. $a=\frac{F}{m}$
Substituting the value of $F$ from equation (1) into equation (3):
4. $a=\frac{m v^2}{r} \div m$
Simplifying:
5. $a=\frac{v^2}{r}$
This is the required expression for acceleration in circular motion.
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