The outside diameter of the playing area of an optical Blu-ray disc is 11.75 cm,

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 6.90 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 significant figures.)

2. What is the minimum angular speed (in rpm) of the disc? (Express your answer to three significant figures.)

3. What is the maximum angular speed (in rad/s) of the disc? (Express your answer to three significant figures.)

4. What is the maximum angular speed (in rpm) of the disc? (Express your answer to three significant figures.)

5. What is the average angular acceleration of a Blu-ray disc as it plays an 4.5-h set of movies? (Express your answer to two significant figures.)

Explanation / Answer

Here ,

do = 11.75 cm

ro = 11.75/2 = 5.875 cm

ri = 4.5/2 = 2.25 cm

linear speed , v = 6.90 m/s

1)

for the minimum angular speed is w

as v = ro * w

6.90 = 0.05875 * w

w = 117.44 rad/s

the minimum angular speed of the disc is 117.44 rad/s

2)

minimum angular speed of the disc = 117.44 rad/s

minimum angular speed of the disc = 117 * 60/2pi rpm

minimum angular speed of the disc = 1121.75 rpm

3)

let the maximum angular speed is wm

v = ri * wm

6.90 = 0.0225 * wm

wm = 306.7 rad/s

the maximum angular speed of the disc is 306.7 rad/s

4)

maximum angular speed of the disc = 306.7 rad/s

maximum angular speed of the disc = 306.7 * 60/(2pi) rpm

maximum angular speed of the disc = 2929 rpm

the maximum angular speed of the disc is 2929 rpm

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