4.14 Centripetal Force
We have studied that an object can move in a circular path with uniform speed only if a force perpendicular to its velocity is acting constantly on it. This force is always directed towards the centre of the circle. It is called centripetal force.
lightbulbThe force that causes an object to move in a circle at constant speed is called the centripetal force.
For an object of mass m moving with uniform speed v in a circle of radius r, the magnitude of the centripetal force F_c acting on it can be calculated by:
F_c = m v² / r ............ (4.11)
Example 4.6
A 150 g stone attached to a string is whirled in a horizontal circle at a constant speed of 8 m s⁻¹. The length of the string is 1.2 m. Calculate the centripetal force acting on the stone. Neglect effects of gravity.
Solution:
Mass of stone = m = 150 g = 0.15 kg Speed of stone = v = 8 m s⁻¹ Radius of circle = r = 1.2 m Centripetal force = F_c = ?
Using Eq. (4.11):
F_c = m v² / r
F_c = (0.15 kg × (8 m s⁻¹)²) / 1.2 m
F_c = (0.15 × 64) / 1.2
F_c = 8 N