Question

A hard drive disc has a diameter of 120 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 170 RPM (revolutions per minute). Find the linear speed in meters per second. Round to 2 decimal places. m/s

Answer 1

Answer: 1.13 m/s

Explanation:

To find the linear speed of the disc, we need to use the formula:

linear speed = radius x angular speed

We are given that the diameter of the disc is 120 millimeters, which means the radius is half of that or 60 millimeters.

We are also given that the angular speed at the outer edge of the disc is 170 RPM.

To convert RPM to radians per second, we need to multiply by 2π/60, which gives us:

angular speed = 170 x 2π/60 = 17π/3 radians per second

So the linear speed is:

linear speed = 60 x 17π/3 = 340π/3 millimeters per second

To convert millimeters per second to meters per second, we divide by 1000:

linear speed = (340π/3) / 1000 = 1.13 meters per second (rounded to 2 decimal places)

Therefore, the linear speed of the disc is approximately 1.13 meters per second.