Why does a cyclist lean to one side, while going along a curve? In what direction does he lean?

Hint: This question is related to the topic laws of motion, and concept of centripetal force , where Newton's laws of motion states that . In the first law, an object will not change its motion unless and unless external forces have not acted on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, every object has an equal and opposite reaction.

Complete answer:
When force is applied it results in change in direction, change in momentum and change in kinetic energy. Mechanics is the study of movement of objects. Newton's laws of motion are the foundation of classical mechanics. In the special case of Earth's circular motion around the sun or any satellite circular motion around any celestial body , the CENTRIPETAL FORCE causing the motion is the result of gravitational attraction between them . Centripetal forces are always directed toward the Center of the circular path. When the track is banked, then the inclination of the surface of the road with the horizontal is known as the angle of banking. As the speed of the vehicle increases , the centripetal force needed for the circular motion of the vehicle also increases. Without proper friction, a vehicle will not be able to move on the curved road with a large speed. To avoid this we may increase the force of friction making the road rough. Also, the force of friction is not always reliable because it changes when roads are oily or wet due to rains etc, to eliminate this difficulty the curved roads are generally banked. Due to banking the necessary centripetal force is provided by the component of the normal reaction. A cyclist leans while going along a curve because a component of normal reaction of the ground provides him the centripetal force while he requires for turning. He has to lean inwards from his vertical position, that is, towards the centre of the circular path.

Note: When a vehicle moves along a curved path with very high speed, then there is a chance of overturning of the vehicle. Inner wheel leaves the ground first .A cycling race track is called Velodrome which has a saucer-shaped track. The rider has to take position on a track as per his/her speed.