Acd player rotates at a variable speed so that a laser can scan pits and lands on the disk’s bottom surface at a constant tangential speed of 1.2 m/s. the disk has a moment of inertia of 1.2 x 10-4 kg m2and the music is first detected when the laser is located 15 mm from the disk’s center. assuming the disk started from rest, find the work done by the motor during this start-up.

W = 0.384 J

Explanation:

Work and energy in the rotational movement are related

    W = ΔK = - K₀

    W = ½ I ² - 1 /2 I w₀²

where W isthe work, I is the moment of inertia and w angular velocity

With the system part of the rest the initial angular speed is zero (w₀ = 0)

The angular and linear quantities are related

    v = w r

    w = v / r

Let's replace

    W = ½ I (v / r)²

Let's calculate

    W = ½  1.2 10⁻⁴ 1.2² / (1.5 10⁻²)²

    W = 0.384 J

    W = 38.4 J