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 = mv²/ 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 = mv²/ r

F_c = (0.150 kg)(30 m/s)² / 1.5 m

F_c = 135 kgm²/s²/ 1.5 m

F_c = 90 kg m/s² = 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 = mv²/ r

F_c = (40 kg)(2.5 m/s)²/ 0.9 m

F_c = 250 kg m²/s²/ 0.9 m

F_c = 277.77 Newtons