Final answer:
The linear speed of a CD with a radius of 6 cm rotating at 237 revolutions per minute is approximately 1.49 meters per second. The process includes converting rpm to rps, finding the CD's circumference, and then multiplying by the number of revolutions per second to obtain the speed in m/s.
Step-by-step explanation:
The question requires us to find the linear speed in meters per second of a CD with a radius of 6 centimeters rotating at a speed of 237 revolutions per minute. To find the linear speed of the CD, we first need to convert the rotational speed from revolutions per minute (rpm) to meters per second.
Here is the calculation process:
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- First, convert the rotational speed to revolutions per second (rps) by dividing 237 rpm by 60 seconds: 237/60 ≈ 3.95 rps.
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- Next, we need to find the circumference of the CD, which is the path that a point on the edge of the CD will travel in one revolution. The formula for the circumference (C) is C = 2πr, where r is the radius of the CD. Hence, C = 2⋅π⋅6 cm = 12π cm.
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- Convert the circumference to meters by dividing by 100: C = 12π / 100 meters.
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- Lastly, calculate the linear speed (v) by multiplying the circumference by the number of revolutions per second: v = C⋅3.95. This gives us the linear speed in meters per second, which would be v = (12π / 100) ⋅3.95 ≈ 1.49 m/s.
The linear speed of the CD is therefore approximately 1.49 meters per second.