Question

Which expression can be used to calculate centripetal acceleration?

StartFraction 2 pi r over T EndFraction
StartFraction 4 pi squared r over r squared EndFraction
StartFraction 4 pi squared r over T EndFraction
StartFraction left parenthesis 2 pi r right parenthesis squared over r squared EndFraction

Answer 1

Centripetal acceleration is a_c = v^2 / r. Using the period T (v = 2πr / T) this becomes

a_c = (2πr / T)^2 / r = 4π^2 r / T^2.

None of the four options you listed matches that exactly:
- (2πr)/T is the speed v, not an acceleration.
- 4π^2 r / T (option 3) is missing a T (should be T^2).
- 4π^2 r / r^2 simplifies to 4π^2 / r (option 2), which is wrong.
- ((2πr)^2)/r^2 simplifies to 4π^2 (option 4), which is also wrong.

So the correct expression is 4π^2 r / T^2 (equivalently v^2/r or ω^2 r).