Animated Solution for Physics - Laws of Motion: During paddling of a bicycle, the force of friction exerted by the ground on the two wheels is such that it acts (1990)

Imagine you are riding a bicycle. It might look like just two simple wheels connected by a metal frame, but from a physics perspective, these two wheels operate under completely different mechanical conditions. The classic JEE problem asks us to determine the direction of friction on both wheels while pedaling. To solve this, we must completely dissect the mechanics of rolling and the true nature of static friction.

The Engine of Forward Motion

The first critical step is to understand the distinct roles of the two wheels. The rear wheel is the 'driven' wheel—it is mechanically coupled to your pedals via the chain. When you push down on the pedals, the chain pulls on the rear cassette. This action applies a powerful clockwise torque, ${\tau }_{pedal}$, to the rear wheel, attempting to spin it.

Now, visualize the exact point where the rubber meets the road. Because the wheel is being forced to rotate clockwise by the engine (your legs), that bottom-most contact point has a strong tendency to scrape and slip backward against the ground. Imagine if you were pedaling hard on a muddy surface—the dirt would fly backward!

This is where friction steps in as the hero. A fundamental law of physics is that friction always opposes relative slipping between two surfaces in contact. Since the tire is trying to slip backward, the ground exerts a static frictional force, $f_{rear}$, in the exact opposite direction, which is forward!

Here is the beautiful catch: this forward friction is the actual external force that propels the entire bicycle forward. This is where many students make a critical mistake. People often memorize that "friction always opposes motion," but in the case of a driven wheel, friction is the very force creating the forward motion!

The Reluctant Follower

Now, let's shift our gaze to the front wheel. There is no chain here, and absolutely no pedaling torque. It is an 'undriven' wheel. So how does it move? As the rear wheel drives the bike forward, the rigid frame of the bicycle simply pushes the front wheel's axle in the forward direction with a force $F_{push}$.

If the ground were made of perfectly smooth, frictionless ice, this forward push at the axle would just cause the entire wheel to slide forward without rotating at all. The contact point has a clear tendency to slip forward.

To prevent this forward sliding, the ground must "grab" the bottom of the tire. It applies a frictional force, $f_{front}$, in the backward direction. This backward force not only arrests the sliding but also provides the essential clockwise torque required to make the front wheel roll smoothly. Without this backward friction, the front wheel wouldn't roll; it would just skid!

When we put it all together, we see a magnificent interplay of forces. When pedaling, the friction on the rear wheel acts in the forward direction to propel the bike, while the friction on the front wheel acts in the backward direction to force it to roll. Therefore, the correct answer is that friction acts backward on the front wheel and forward on the rear wheel, matching option (a).