why is the total distance traveled by a mass traveling in a circle of radius R during n revolutions =2piRn. The average speed is the distance traveled divided by the elapsed time, so:
v=2piRn/delta T, where delta T is the elapsed time.
Why?
the distance around the circle once is 2PI*radius. If one goes n times around, then total distance is 2PI*radius*n
and of course, avgspeed is total distance/time.
To understand why the total distance traveled by a mass traveling in a circle of radius R during n revolutions is equal to 2πRn, let's break it down step by step:
1. One revolution of a circular path covers a circumference equal to the circumference of the circle: C = 2πR. Here, R represents the radius of the circle.
2. Since the mass completes n revolutions, we need to multiply the circumference of each revolution by the number of revolutions: Total distance = n * (2πR).
3. Multiplying n by 2πR gives us the total distance traveled by the mass in terms of the radius and the number of revolutions.
Now, let's discuss the relationship between average speed and distance traveled:
1. Average speed is defined as the total distance traveled divided by the elapsed time: v = total distance / delta T.
2. We derived that the total distance traveled is equal to 2πRn, so we can substitute that into the average speed equation: v = (2πRn) / delta T.
Therefore, the expression v = 2πRn / delta T represents the relationship between average speed, distance traveled, and elapsed time when a mass travels in a circle of radius R during n revolutions.