Final answer:
The tangential speed of a point at the edge of the compact disc rotating at 500 rev/min with a diameter of 120 mm is approximately 188.4 m/min.
Step-by-step explanation:
The tangential speed of a point at the edge of the compact disc can be calculated by multiplying the angular speed (in radians per minute) by the radius of the disc. First, we need to convert the angular speed from revolutions per minute to radians per minute. Since 1 revolution is equal to 2π radians, the angular speed can be calculated by multiplying the given rev/min value by 2π:
Angular speed = (500 rev/min) x (2π radians/1 rev) = 1000π radians/min
Next, we can calculate the tangential speed using the formula:
Tangential speed = Angular speed x Radius
Given that the diameter of the disc is 120 mm, the radius is half of that, or 60 mm (or 0.06 m).
Tangential speed = (1000π radians/min) x (0.06 m) = 60π m/min
Using a calculator, we can approximate the value of π to 3.14. Therefore, the tangential speed is approximately:
Tangential speed = (60 x 3.14)m/min ≈ 188.4 m/min
Therefore, the tangential speed of a point at the edge of the compact disc is approximately 188.4 m/min.