# Centripetal Force Formula

The Centripetal ('center-seeking') force is the force which keeps an object moving along the axis of rotation of a curved path. This force always acts towards the center.

Centripetal force = (mass of the object)(velocity of the object)^{2}/ radius

F_{c} = mv^{2}/ r

F_{c} = centripetal force

m = mass

v = velocity

r = radius of circular path

Centripetal Force Formula Questions:

1) If a 150g ball is tied to a pole with a rope of length 1.5 m, and it spins around the pole at 30 m/s, what is the Centripedal Force?

Answer: The mass of the ball, m = 150 g = 0.150 kg. The radius, r = 1.5 m, and the velocity, v = 30 m/s.

F_{c} = mv^{2}/ r

F_{c} = (0.150 kg)(30 m/s)^{2} / 1.5 m

F_{c} = 135 kgm^{2}/s^{2}/ 1.5 m

F_{c} = 90 kg m/s^{2} = 90 Newtons

2) Susan is holding on to the outer edge of a merry-go-round that is 1.8 m in diameter. Susan's weight is 40 kg, and the velocity of the merry-go-round is 2.5 m/s. What is the centripedal force?

Answer: The radius, r = 1/2 d = 1/2 x 1.8 m = 0.9 m. The mass, m = 40 kg, and the velocity, v = 2.5 m/s.

F_{c} = mv^{2}/ r

F_{c} = (40 kg)(2.5 m/s)^{2}/ 0.9 m

F_{c} = 250 kg m^{2}/s^{2}/ 0.9 m

F_{c} = 277.77 Newtons

Related Links:centripetal vs. centrifugal Force, Mass, Acceleration Quiz Mass Examples Gravity Examples Force Formula Potential Energy: Two-Body Gravitation Formula |