When a cyclist leans inwards while negotiating a curve, what is the main physical reason for this leaning?

Introduction / Context:
When watching a cyclist or motorcyclist take a turn, you can observe that the rider leans towards the inside of the curve. This is not just for style; it has a clear physical purpose related to balancing forces and ensuring that the required centripetal force is supplied without slipping. This question asks you to identify the main reason for this inward leaning in terms of the forces acting on the cyclist and cycle.

Given Data / Assumptions:
- The cyclist is moving along a curved path at some speed.
- The surface provides a normal reaction and frictional force as required.
- We assume a steady turn without skidding and neglect air resistance for simplicity.

Concept / Approach:
For circular motion, a centripetal force directed towards the centre of the curve is required to continually change the direction of velocity. If the cyclist remained perfectly upright, the forces might not line up correctly, and there would be a risk of tipping over. By leaning inwards at an appropriate angle, the line of action of the combined weight and normal reaction passes through the centre of the circular path, and the horizontal component of the normal reaction (along with friction if needed) can supply the necessary centripetal force. This keeps the cyclist balanced and allows safe turning.

Step-by-Step Solution:
Step 1: Recognise that moving in a circular path requires a centripetal force towards the centre of the curve. Step 2: Identify the forces acting on the cyclist–cycle system: gravitational force downward, normal reaction from the road, and friction between tire and road. Step 3: When the cyclist leans inwards, the normal reaction is no longer purely vertical; it has a horizontal component. Step 4: This horizontal component of the normal reaction can provide (or help provide) the centripetal force needed to keep the cyclist moving along the curved path. Step 5: At the correct lean angle, the resultant of weight and normal reaction passes through the centre of curvature, balancing the tendency to fall outward or inward. Step 6: Therefore, the primary reason for leaning is to obtain the required centripetal force from the horizontal component of the normal reaction.

Verification / Alternative check:
You can analyse the situation using vector diagrams. In a properly banked turn, the normal reaction is tilted so that its horizontal component provides centripetal force. The cyclist, by leaning, effectively creates a similar geometry: the combined effect of weight and reaction force passes through a line that points towards the centre of the circular path. This is similar in principle to a banked road that lets vehicles turn with less reliance on friction. This conceptual similarity reinforces the explanation based on horizontal components of the normal reaction.

Why Other Options Are Wrong:
So that the cyclist may increase speed: While leaning may allow safe riding at higher speeds, the primary reason is to balance forces and obtain centripetal force, not simply to increase speed.
So that the cyclist’s weight may be reduced: Leaning does not reduce actual weight; weight depends only on mass and gravitational acceleration.
So that no frictional force is produced: In reality, some friction is still present; leaning does not eliminate friction between the wheels and the road or axle.

Common Pitfalls:
A common misunderstanding is to think that leaning is only about avoiding toppling, without connecting it to centripetal force. Another mistake is to believe that friction alone provides centripetal force. While friction plays an important role, the correct explanation emphasises how the direction of the normal reaction changes and how its horizontal component contributes. Visualising free-body diagrams for tilted riders helps clarify the physics involved.

Final Answer:
A cyclist leans inward mainly so that the necessary centripetal force comes from the horizontal component of the normal reaction due to the track.