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.
the inside track has a circumference of 2pi*2.4 = 4.8pi = 7.54cm
so, we have 116cm/s / 7.54cm/rev = 15.38 rev/s
angular speed a = 15.38*2pi = 96.6rad/s
To find the required angular speed, we can use the formula:
Angular speed = Linear speed / Radius
First, let's convert the radius from centimeters to meters:
Radius = 2.40 cm = 0.024 m
Next, substitute the values into the formula:
Angular speed = 1.16 m/s / 0.024 m
Angular speed = 48.33 rad/s
Therefore, the required angular speed at the beginning of the recording is approximately 48.33 rad/s.