How Do You Calculate the Velocity of a Point on a Rotating Disc?

AI Thread Summary
To calculate the velocity of a point on a rotating disc at 800 rpm, first convert the rotation speed to revolutions per second (40/3 rps). The period T is then determined as 3/40 seconds. The velocity v can be calculated using the formula v = (2πr) / T, resulting in v = (80πr) / 3 m/sec. It's crucial to maintain the "seconds" unit throughout the calculation to ensure the final result is in distance/time. This method confirms the correct approach to finding the velocity of a point on the rotating disc.
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Homework Statement



Find the velocity v of a general point on a plate rotating at 800 rpm which is r meters from the center.

This is literally a copy and paste job.

Homework Equations



period = T = 1 / f ; f = frequency

The Attempt at a Solution



This is what I did please tell me if it is correct

800 rpm = 40 / 3 rps = f

T = 1 / f = 3 / 40

v = distance / time = (2 pi r) / (3 / 40) = (80 pi r) / 3
 
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That is correct.
You could also have seen that 40/3 rps can be directly translated into a speed by replacing the r in rps with the distance covered in 1 revolution (2 pi r).
That would give you the same result ##\frac{80 \pi r}{ 3}##m/sec.
 
Yes, that works. You need to carry the "seconds" unit through to the end though. The period T has seconds as its unit.

Otherwise you'll end up with a "velocity" with units of distance rather than distance/time.
 
RUber said:
That is correct.
You could also have seen that 40/3 rps can be directly translated into a speed by replacing the r in rps with the distance covered in 1 revolution (2 pi r).
That would give you the same result ##\frac{80 \pi r}{ 3}##m/sec.
Awesome! Thank you.
 
gneill said:
Yes, that works. You need to carry the "seconds" unit through to the end though. The period T has seconds as its unit.

Otherwise you'll end up with a "velocity" with units of distance rather than distance/time.
Ohh... I see. Thank you
 
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