# Centripetal Acceleration Formula

The centripetal ('center-seeking') acceleration is the motion inwards towards the center of a circle. The acceleration is equal to the square of the velocity, divided by the radius of the circular path.

a_{c} = v^{2}/r

a_{c} = acceleration, centripetal, m/s^{2}

v = velocity, m/s

r = radius, m

Centripetal Acceleration Formula Questions:

1) You are whirling a ball attached to a string such that you describe a circle of radius 75 cm, at a velocity of 1.50 m/s. What is the acceleration of the ball?

Answer: The radius, r = 75 cm = 0.75 m; the velocity, v = 1.50 m/s

a_{c} = v^{2}/r

a_{c} = (1.50 m/s)^{2} / 0.75 m

a_{c }= 3 m/s^{2}

2) What is the acceleration of a motor-bike rider, if his velocity is 25 m/s on a circular track with a radius of 125 m?

Answer: The radius, r = 125 m and the velocity, v = 25 m/s.

a_{c} = v^{2}/r

a_{c} = (25 m/s)^{2} / 125 m

a_{c} = 5 m/s^{2}