Questions: Which formula can be used to find the centripetal acceleration of an orbiting object? ac = sqrt(v)/T ac = v^2/T ac = v^2/r ac = sqrt(v)/r

Solution Steps

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. The formula for centripetal acceleration is derived from the relationship between velocity, radius, and acceleration in circular motion.

We are given four options for the formula of centripetal acceleration:

1. \( a_{c} = \frac{\sqrt{v}}{T} \)
2. \( a_{c} = \frac{v^{2}}{T} \)
3. \( a_{c} = \frac{v^{2}}{r} \)
4. \( a_{c} = \frac{\sqrt{v}}{r} \)

The correct formula for centripetal acceleration is:

\[ a_{c} = \frac{v^{2}}{r} \]

where \( v \) is the tangential velocity of the object and \( r \) is the radius of the circular path.

Final Answer