Question

A Blu-ray disc approximately 12 centimeters in diameter. The drive motor of the Blu-ray player is able to rotate up to 10,000 revolutions per minute, depending on what track is being read. Find the maximum angular speed (in radians per second) of a Blu-ray disc as it rotates. Find the maximum linear speed (in meters per second) of a point on the outermost track as the disc rotates.

Answer 1

Answer:

a) 1000π/3 (rad/sec) b) 62,8 (m/sec)

Explanation:

Answer 2

The maximum angular speed of the Blu-ray disc is 1,047.33 rad/s and the maximum linear speed of the Blu-ray disc is 62.84 m/s.

The given parameters;

• Diameter of the Blu-ray disc, d = 12 cm
• Number of revolution of the motor, N = 10,000 rev/min

The radius of the Blu-ray disc is calculated as;

$r = \frac{d}{2} = \frac{12 \ cm}{2} \\\\r = 6 \ cm = 0.06 \ m$

The maximum angular speed of the Blu-ray disc is calculated as follows;

$\omega = 2\pi N\\\\\omega =\frac{2\pi \ rad}{rev} \times \frac{10,000 \ rev}{\min} \times \frac{1 \min}{60 \ s} \\\\\omega = 1,047.33 \ rad/s$

The maximum linear speed of the Blu-ray disc is calculated as;

v = ωr

v = (1,047.33 x 0.06)

v = 62.84 m/s

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