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harkovskaia [24]
3 years ago
15

A CD with a diameter of 120 millimeters rotates a rate of 45 revolutions per minute. Find the linear speed of the CD in millimet

ers per minute. And find the angular speed of the CD in radians per minute
Mathematics
1 answer:
ale4655 [162]3 years ago
6 0

9514 1404 393

Answer:

  • 16,965 mm/min
  • 90π ≈ 282.7 radians/min

Step-by-step explanation:

The circumference of the CD is ...

  C = πd

  C = π(120 mm) ≈ 376.99 mm

This is the distance a point on the edge of the CD will travel when making one revolution. It will travel 45 times this far when making 45 revolutions:

  (376.99 mm/rev)(45 rev/min) ≈ 16,965 mm/min

__

There are 2π radians in each revolution, so the angular speed is ...

  (2π rad/rev)(45 rev/min) = 90π rad/min ≈ 282.7 rad/min

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