SOLUTION: A Blu-Ray disc is 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

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Question 1048738: A Blu-Ray disc is 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.
a) Find the maximum angular speed (in radians per second) of a Blu-Ray disc at it rotates.
b) Find the maximum linear speed (in meters per second) of a point on the outermost track as the disc rotates.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A Blu-Ray disc is 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.
a) Find the maximum angular speed (in radians per second) of a Blu-Ray disc at it rotates.
rate = 10,000 rev/60 sec = 10,000*(2pi)/60 sec = 333.33pi/sec
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b) Find the maximum linear speed (in meters per second) of a point on the outermost track as the disc rotates.
Perimeter = 12pi cm
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speed = 10,000*12pi cm/min = 100*12pi/60 meters/sec = 20 pi meters/sec
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum linear distance will be
read on the outside track
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The angular speed is the same for
the all the tracks
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The angular speed of the drive is
[ radian measure of a circle ] / [ time for 1 revolution ]
+%28+2%2Api+%29+%2F+%28+1%2F10000+%29+
+20000%2Api+ radians/min
[ radians/min ] x [ min/sec ] = [ radians/sec ]
+%28+20000%2Api+%29%2A%28+1%2F60+%29+=+333.333+ radians/sec
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The maximum linear speed for the outside track is:
[ circumference in cm ] / [ time for 1 revolution ]
+%28+12%2Api+%29+%2F+%28+1%2F10000+%29+=+120000%2Api+ cm/min
[ cm/min ] x [ min/sec ] x [ m/cm ] = [ m/sec ]
+%28120000%2Api%29%2A%28+1%2F60+%29%2A%28+1%2F100+%29+=+120000%2Api+%2F+6000+
+120000%2Api%2F6000+=+20%2Api+ m/sec
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Check my math & get a 2nd opinion too