Which formula can be used to find the centripetal acceleration of an orbiting object?

• A. $a=\frac{v^2}{r}$
• B. $a=\frac{F}{m}$
• C. $a=v\ast r$
• D. $a=\frac{r}{v}$

Answer: (A)

Verified step by step guidance

1. Understand that centripetal acceleration is the acceleration directed towards the center of a circular path that keeps an object moving in that circle.
2. Recall the relationship between velocity, radius, and centripetal acceleration for an object moving in a circle at constant speed.
3. Use the formula for centripetal acceleration, which relates the speed \(v\) of the object and the radius \(r\) of the circular path: \(a = \frac{v^2}{r}\).
4. Note that this formula shows acceleration increases with the square of the speed and decreases with a larger radius.
5. Recognize that other formulas given, such as \(a = \frac{F}{m}\) (Newton's second law), are general but not specific to centripetal acceleration.