The information on a compact disc is scanned by a laser initially at a radius of 2.4 cm and then out to a maximum of 6.0 cm.Because the dimensions of the pit information remains constant with radius the disk motor adjusts so that the tangential velocity remains a constant.What is the ratio of the inner to outer rotational frequencies?
A)0.16
B)6.3
C)1.0
D)2.5
E)0.40

Question

Quizplus · Accepted Answer

The tangential velocity (v) is given by v = rω, where r is the radius and ω is the angular velocity (or rotational frequency). Since the tangential velocity is constant across the radius, we have r₁ω₁ = r₂ω₂. To find the ratio of the inner to outer rotational frequencies (ω₁/ω₂), we rearrange the equation to ω₁/ω₂ = r₂/r₁. Substituting the given radii, we get ω₁/ω₂ = 6.0 cm / 2.4 cm = 2.5.

The Information on a Compact Disc Is Scanned by a Laser