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A car is traveling at 25 mph. If its tires have a diameter of 25​ inches, how fast are the tires​ rotating? express the answer in revolutions per minute​ (rpm). If​ necessary, round answer to two decimal places.

Respuesta :

Lanuel

The angular speed of the rotation of the car tires is 336.09 rpm.

Given the following data:

  • Velocity = 25 mph to in/min = 26400 in/min.
  • Diameter = 25 inches

Conversion:

Radius = [tex]\frac{Diameter}{2} =\frac{25}{2}[/tex] = 12.5 inches.

To calculate the angular speed of the rotation of the car tires:

How to calculate angular speed.

Mathematically, angular speed is given by this formula:

[tex]\omega = \frac{V}{r}[/tex]

Where:

  • r is the radius.
  • V is the velocity.

Substituting the given parameters into the formula, we have;

[tex]\omega = \frac{26400}{12.5}\\\\\omega =2112\;in/min[/tex]

In revolutions per minute​ (rpm):

[tex]\omega = \frac{2112}{2 \pi}\\\\\omega = \frac{2112}{2 \times 3.142}[/tex]

Angular speed = 336.09 rpm.

Read more on angular speed here: https://brainly.com/question/4183355

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