Understanding the Period of a Car Traversing a Circular Track: A Detailed Analysis

Introduction:

The question poses a scenario where a car travels in a circular track and completes 6 revolutions per minute. The period of one revolution is the time interval for the car to complete a single circuit around the track. This concept is fundamental in understanding the motion of objects in a circular path and is crucial in various fields such as physics, engineering, and sports.

Calculating the Period of One Revolution

When a car is traveling in a circular track with a constant speed and completes 6 revolutions in one minute, we can determine the period of one revolution using a straightforward mathematical approach. The period (T) is defined as the time taken to complete one full revolution.

Given that:

The period of one revolution is calculated as:

T 60/6 10 seconds

Note that the radius of the circular track (50 meters in this case) is not relevant to the calculation of the period. The period depends only on the frequency of revolutions and the time taken.

Implications of the Period in Circular Motion

The period of the car's revolution (10 seconds) is a critical parameter that defines the car's oscillatory motion. In the context of circular motion, the period (T) and the frequency (f) are related as:

T 1/f

Given that the car completes 6 revolutions per minute, the frequency (f) is:

f 6 rev/min 0.1 rev/s

Hence, the period (T) is:

T 1/f 1/0.1 10 seconds

Linear Speed Analysis

Let's further analyze the linear speed of the car as it moves in a circular path. The circumference of the circular track is given by:

C 2πr 2π(50) 100π meters

Since the car completes 6 revolutions in 60 seconds, the linear distance traveled by the car per second is:

Distance per second 600π/60 10π meters/second

The linear speed (v) of the car is:

v 10π meters/second

Conclusion

The period of a car traversing a circular track is a fundamental concept in analyzing the dynamics of circular motion. The time taken for one revolution, in this case, 10 seconds, not only helps in understanding the speed of the car but also in various applications. This period is equally important in fields like mechanics, control systems, and sport engineering.

The relation between period and frequency in oscillatory or cyclic phenomena is paramount, emphasizing the importance of precise measurements and calculations in real-world scenarios.