Circular Motion

Students calculate the speed of the objects moving with uniform circular motion

When a body moves in a uniform circular motion, its direction changes continuously. Thus according to the Newton’s first law, the body must be accelerating. As the speed is uniform so, the acceleration must be perpendicular to the path towards the center. This acceleration is known as centripetal acceleration or radial acceleration and this acceleration is produced by the force known as centripetal force.

Thus centripetal force can be defined as the radial force acting towards the center on the body exhibiting circular motion. With the change in the direction of the position of the body in the circular path, the direction of the centripetal force also changes but it always acts radially.

The centripetal force is given as:

 

where the body of mass m is moving with uniform speed v in a circular path of radius r.

Let us understand the centripetal force by the thread-stone system. When the stone is whirled in a circular path, the tension in the string provides the required centripetal force which always acts radially and pulls the stone towards the centre.

The direction of the stone at any instant is the tangent drawn perpendicular to the radial length as shown in the Fig. 1.

Fig.1

 

Can you guess what will be the direction of the stone if the thread suddenly gets snapped? As the centripetal force acting on it is suddenly removed, from Newton’s first law of motion, the body will remain in its state of motion in the same direction at the instant of snapping. That means that the stone will fly off in a tangential direction as shown in the Fig. 2.

Fig.2

 

The motion of the moon around the earth and the motion of earth around the sun are nearly circular so the centripetal force also acts here. Here the gravitational attractive force provides the centripetal force.

Centrifugal reaction:

Newton’s third law of motion states that every action has equal and opposite reaction, thus for the centripetal force there must be a reaction force. This reaction force opposite to the direction of centripetal force i.e. directed away from the center is known a…