Centripetal force is developed by the centripetal acceleration towards the center of the circular path.
Consider an object of mass m is tied to a string of radius r and rotated with velocity of v. The string would follow a circular path
which is against the Newton’s law of motion that tells the natural tendency of any object is to follow a straight path. The radial
force developed is forcing the object to take the circular path. Centripetal acceleration of the object is
According to Newton’s second law
Force = mass x acceleration
As the centripetal force is directed along the same direction as the centripetal acceleration therefore,
Force = mass x v2
Or, Force = m x v2
represents radial or centripetal acceleration.
A wooden ball of mass 5 kg is rotating with velocity of 4 m/s around a circle of radius 0.4 m. What is the centripetal
Centripetal force is given as
/r ----------- (1)
Mass of the ball = 5 kg, radius of the circle = 0.4 m and velocity of the rotation = 4 m/s.
Placing the values in equation 1 we get
= (5 x 42
= 80/ 0.4
= 200 N
How much force would be required to keep a stone of mass 0.01 kg whirling around a circle of radius 0.1 m with
velocity of 4 m/s?
Centripetal force provides the minimum force that is required to keep a stone whirling around a circle. Centripetal
force is given as
/r ---------- (1)
Mass of the stone = 0.01 kg, radius of the circle = 0.1 m and velocity of the stone = 4 m/s.
Placing the values in equation 1we get
= (0.01 x 42
= 0.16/ 0.1
= 1.6 N