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
ac = v2 /r
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 /r
Or, Force = m x v2 /r
Fr = mv2 /r
Fr represents radial or centripetal acceleration.
Example 1: 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
force?
Explanation: Centripetal force is given as
Fr = mv2 /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
Fr = (5 x 42)/ 0.4
Fr = 80/ 0.4
Fr = 200 N
Example 2: 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?
Solution: Centripetal force provides the minimum force that is required to keep a stone whirling around a circle. Centripetal
force is given as
Fr = mv2 /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
Fr = (0.01 x 42)/ 0.1
Fr = 0.16/ 0.1
Fr = 1.6 N
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
ac = v2 /r
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 /r
Or, Force = m x v2 /r
Fr = mv2 /r
Fr represents radial or centripetal acceleration.
Example 1: 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
force?
Explanation: Centripetal force is given as
Fr = mv2 /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
Fr = (5 x 42)/ 0.4
Fr = 80/ 0.4
Fr = 200 N
Example 2: 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?
Solution: Centripetal force provides the minimum force that is required to keep a stone whirling around a circle. Centripetal
force is given as
Fr = mv2 /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
Fr = (0.01 x 42)/ 0.1
Fr = 0.16/ 0.1
Fr = 1.6 N
