Question

The outside diameter of the playing area of an optical Blu-ray disc is 11.75 cm, and the inside diameter is 4.50 cm. When viewing movies, the disc rotates so that a laser maintains a constant linear speed relative to the disc of 6.70 m/s as it tracks over the playing area. 1) What is the minimum angular speed (in rad/s) of the disc? (Express your answer to three signifi

Answer 1

The minimum angular speed 57.0 rad/s

Step-by-step explanation:

In this exercise we must use the relationships between the angular and linear magnitudes, for the speeds we have

v = w r

As they give us that linear velocity is constant, we will calculate the angular velocity for the two radii, external and internal

r1 = 11.75 cm (1 m / 100cm) = 0.1175 m

w1 = v / r1

w1 = 6.70 / 0.1175

w1 = 57.0 rd / s

R2 = 4.50 cm = 0.0450 m

w2 = 6.70 / 0.0450

w2 = 148 rad / s

The minimum angular speed 57.0 rad / s