A digital audio compact disc carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.60 mm of the track. A CD player turns the disc to carry the track counter-clockwise above a lens at a constant speed of 1.16 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.40cm.

Question

A digital audio compact disc carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.60 mm of the track. A CD player turns the disc to carry the track counter-clockwise above a lens at a constant speed of 1.16 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.40cm.

Answer 1

To find the required angular speed at the beginning of the recording, we can use the formula:

Angular speed (ω) = Linear speed (ν) / Radius (r)

Given that the linear speed is 1.16 m/s and the radius is 2.40 cm, we need to convert the radius to meters:

Radius (r) = 2.40 cm = 0.024 m

Now we can substitute the values into the formula:

Angular speed (ω) = 1.16 m/s / 0.024 m

Calculating the division, we get:

Angular speed (ω) = 48.33 rad/s

Therefore, the required angular speed at the beginning of the recording is approximately 48.33 rad/s.