if a 22 inch tire rotates 40 times per 2 minutes, determine the linear and angular speed of the tire.
assuming that Earth is a sphere of a radius 6378 kilometers, what is the difference in the latitudes of Lynchbug, Virginia, and Myrtle Beach, South Carolina, where Lynchbug is 400 kilometers due north of Myrtle Beach?
To determine the linear and angular speed of the tire, we need to use the formulas:
Linear speed = Circumference of the tire × Angular speed
Angular speed = 2π × Frequency
First, let's calculate the circumference of the tire. The circumference of a circle is given by the formula:
Circumference = 2πr,
where r is the radius of the tire. Since we have the diameter of the tire (22 inches), we can calculate the radius as:
Radius = Diameter / 2 = 22 / 2 = 11 inches.
Now, substituting the value of the radius into the formula, we get:
Circumference = 2π × 11 inches.
Next, let's calculate the angular speed using the given information that the tire rotates 40 times per 2 minutes. The frequency is the number of complete rotations per unit time. In this case, we have:
Frequency = Number of rotations / Time = 40 rotations / 2 minutes.
Now, let's calculate the angular speed using the formula:
Angular speed = 2π × Frequency.
Substituting the value of the frequency, we get:
Angular speed = 2π × (40 rotations / 2 minutes).
Finally, let's calculate the linear speed using the formula:
Linear speed = Circumference × Angular speed.
Substituting the values for the circumference and angular speed, we get:
Linear speed = (2π × 11 inches) × (2π × (40 rotations / 2 minutes)).
Calculating this expression will give us the linear speed in inches per minute.
Note: If you want the answer in a different unit, you can convert it accordingly using appropriate conversion factors.