C7 CENTRIPETAL FORCE AND CENTRIPETAL ACCELERATION

The centripetal force will cause an acceleration in the direction of the force according to Newton’s second law and this is called centripetal acceleration (acentripetal) which is defined by Fcentripetal = m. acentripetal (C7.1) This centripetal acceleration causes the object to move in a circle. If an object rotates about a circle of radius of rotation (r) and constant angular velocity (w) then the centripetal acceleration is given by the equation acentripetal = r. w2 (C7.2) As v = w . r (see Section A4) then equation C7.2 can be developed to give an alternative expression for the centripetal acceleration as acentripetal = r. (v 2 / r2) = v2 / r (C7.3) Equations C7.2 and C7.3 can be substituted into equation C7.1 as appropriate to provide two expressions for the centripetal force.