Calculating Total Distance Traveled By Bicycle On Circular Track

Introduction

In the realm of physics, understanding motion is fundamental. This article delves into the specific scenario of a bicycle moving along a circular track. We aim to calculate the total distance traveled by the bicycle in one complete revolution, given the radius of the circular track and the time taken for one revolution. This problem is a classic example of applying concepts from circular motion, a crucial topic in introductory physics. By understanding the relationship between distance, radius, and time in circular motion, we can gain valuable insights into the mechanics of rotating objects and their movements.

Problem Statement

A bicycle moves on a circular track with a radius of 100 meters. It takes 50 seconds to complete one full revolution around the track. What is the total distance traveled by the bicycle in one revolution?

Solution

To determine the total distance traveled by the bicycle, we need to calculate the circumference of the circular track. The circumference represents the length of the path the bicycle travels in one complete revolution. The formula for the circumference (C) of a circle is given by:

C = 2πr

Where:

• C is the circumference (total distance traveled)
• π (pi) is a mathematical constant approximately equal to 3.14159
• r is the radius of the circle

In this case, the radius (r) of the circular track is 100 meters. Plugging this value into the formula, we get:

C = 2 * 3.14159 * 100 meters C ≈ 628.32 meters

Therefore, the total distance traveled by the bicycle in one revolution is approximately 628.32 meters.

Detailed Explanation of the Solution

The problem at hand requires us to calculate the total distance a bicycle covers when it completes one full circle on a track. This scenario falls under the principles of circular motion, a fundamental concept in physics that describes the movement of an object along a circular path. The key to solving this problem lies in understanding the relationship between the circle's radius and its circumference.

Firstly, let's define the terms. The radius of a circle is the distance from the center of the circle to any point on its edge. In our case, the track has a radius of 100 meters. The circumference, on the other hand, is the total distance around the circle. It's essentially the path the bicycle travels when it completes one full lap around the track. The circumference is the key to answering our question about the total distance traveled.

The mathematical relationship between a circle's radius and its circumference is given by the formula: C = 2πr. This formula is a cornerstone in geometry and physics, allowing us to calculate the circumference (C) if we know the radius (r). The symbol π (pi) is a mathematical constant, approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter.

Now, let's apply this to our problem. We know the radius (r) is 100 meters. We also know the value of π. Plugging these values into the formula, we get:

C = 2 * π * r C = 2 * 3.14159 * 100 meters

Performing the multiplication, we find that C is approximately 628.32 meters. This means that the total distance the bicycle travels in one complete revolution around the track is approximately 628.32 meters.

In conclusion, this problem highlights how a simple formula, derived from the principles of geometry and physics, can be used to calculate real-world distances. By understanding the relationship between a circle's radius and its circumference, we can easily determine the distance traveled by an object moving along a circular path.

Visualizing the Problem

To further solidify the understanding, it's helpful to visualize the problem. Imagine a circle drawn on the ground. The center of the circle represents the center of the circular track. The radius, 100 meters in this case, is the distance from the center to the edge of the track. Now, picture the bicycle starting at a point on the edge of the circle and traveling along the circular path until it returns to its starting point. The path the bicycle travels is the circumference of the circle, and that's what we calculated to be approximately 628.32 meters.

Conclusion

The total distance traveled by the bicycle in one complete revolution around the 100-meter radius circular track is approximately 628.32 meters. This calculation demonstrates the application of the circumference formula in determining the distance traveled in circular motion. Understanding such concepts is crucial for analyzing various physical phenomena involving rotational movement.

This problem illustrates a fundamental principle in physics: the relationship between the geometry of a circle and the motion of an object along its circumference. By applying the formula for circumference, we can easily determine the distance traveled in one revolution. This understanding is essential for analyzing various real-world scenarios involving circular motion, from the movement of planets around the sun to the rotation of gears in a machine.

Keywords

Circular motion, circumference, radius, total distance, revolution, physics, calculation, formula