A electric model train travels at 0.339 m/s around a circular track of radius 1.75 m. How many revolutions does it perform per second, i.e, what is the motion's frequency?

ω=v/R

ω =2πf
v/R=2πf
f=v/2πR= …

To find the number of revolutions the electric model train performs per second, we need to determine its frequency. Frequency is defined as the number of complete cycles or revolutions per unit time. In this case, we want to find the frequency in revolutions per second.

First, let's analyze the motion of the electric model train. It travels around a circular track with a constant speed of 0.339 m/s. This means that it covers the circumference of the circular track in one second.

The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

In this case, the radius is given as 1.75 m, so the circumference is:
C = 2π(1.75) = 3.5π

Now, we know that the train covers the circumference of the circle in one second. Therefore, the number of revolutions it performs in one second is equal to the ratio of the distance traveled (circumference) to the circumference of the circle.

Number of revolutions per second = Distance traveled / Circumference

Number of revolutions per second = 0.339 m/s / 3.5π

To simplify this expression, we can convert 3.5π into its approximate decimal value:

3.5π ≈ 10.9956

Number of revolutions per second ≈ 0.339 m/s / 10.9956

Calculating this expression gives us the final answer:

Number of revolutions per second ≈ 0.0308 revolutions per second

Therefore, the train performs approximately 0.0308 revolutions per second.