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

[JJK1503]

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

 

[RUber]

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.

 

[gneill]

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.

 

[JJK1503]

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.

 

[JJK1503]

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