Define centripetal acceleration derive an expression for it./What is centripetal acceleration derive an expression for it.
Answer (1)
17th Jan, 2022
Centripetal acceleration is the acceleration of a body that is travelling across a circular path. When a body undergoes a circular motion, its direction constantly changes and thus its velocity changes (velocity is a vector quantity) which produces an acceleration.Derivation:
$F=\frac{m v^2}{r}$ (using centripetal force)
$F=m a$ (using Newton's second law)
We can rewrite this as:
$a=\frac{F}{m}$
Substituting the value of $F$
\$a=\frac{m v^2}{r} \div m$
$a=\frac{v^2}{r}$
Thus, the centripetal acceleration is given by $a=\frac{v^2}{r}$.
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