# Question e35d4

Jun 5, 2014

It is a resultant force perpendicular to an object's velocity at all times that is always directed toward the centre of a circle. It causes the object to move in a circular path.

The centripetal force, ${F}_{c}$, is not a type of force in the same way that gravitational, tension, normal reaction and friction are types of forces. It is the resultant of these forces acting on an object.

Some examples of centripetal forces:

1. A satellite orbiting the Earth. ${F}_{c}$ is provided by the gravitational attraction between the Earth and the satellite.
2. An aeroplane banking to turn. ${F}_{c}$ is provided by the horizontal component of the lift (e.g. Lsinθ).
3. A roller coaster loop the loop. ${F}_{c}$ is provided by the resultant of the weight and normal reaction forces. At the bottom of the loop F_c = N–w#, at the sides ${F}_{c} = N$ ($w$ is tangential to the loop), at the top ${F}_{c} = N + w$.

The equation for centripetal acceleration: ${a}_{c} = {v}^{2} / r$

The equation for Newton's Second Law for a mass that remains constant is: $F = m a$. In this case the acceleration is the centripetal acceleration so:
${F}_{c} = \frac{m {v}^{2}}{r}$