Convert meters per second to radians per second

[robertin75]

Hello:

As the title says I am trying to convert 5.277 m/s to radians/second for a tire with 3200 millimeters of circumference.

A person sent me what is supposed to be the correct formula and data but I think it's wrong.

Angular Speed rad/s = ((Linear Speed m/s) / (Tire Diameter m x Pi)) x 2Pi x 100

This is what the solution is supposed to be:

w = ((5.277 m/s) / (3.2 meters X Pi)) X 2 Pi X 100 = 329 rad / sec

but according to me the 3.2 meters of the tire diameter should be 1018 millimeters (or 1.018 meters) instead. So:

w = ((5.277 m/s) / (1.018 meters X Pi)) X 2 Pi X 100 = 1036 rad / sec

What do you guys think?

Thanks and help is greatly appreciated.

[JohnS]

Originally Posted by robertin75

Hello:

As the title says I am trying to convert 5.277 m/s to radians/second for a tire with 3200 millimeters of circumference.

A person sent me what is supposed to be the correct formula and data but I think it's wrong.

Angular Speed rad/s = ((Linear Speed m/s) / (Tire Diameter m x Pi)) x 2Pi x 100

This is what the solution is supposed to be:

w = ((5.277 m/s) / (3.2 meters X Pi)) X 2 Pi X 100 = 329 rad / sec

but according to me the 3.2 meters of the tire diameter should be 1018 millimeters (or 1.018 meters) instead. So:

w = ((5.277 m/s) / (1.018 meters X Pi)) X 2 Pi X 100 = 1036 rad / sec

What do you guys think?

Thanks and help is greatly appreciated.

I think the various "formulas" are resulting in confusion between radius, diameter, and circumference, and I have np idea where the fctor of 100 arose. One complete turn of the tire (ie, the circumference) represents 2*pi radians, so
5.277 m/s x 2*pi radians/3.2 m = 10.36 radians/s

[robertin75]

Thanks a lot for the simplified formula.

So using an equation the formula would be:

w = (v * (2 * Pi) ) / circumference

where w = angular speed
v = linear speed
Pi = 3.1416

w = (5.277 m/s * (2 * 3.1416)) / 3.2 mts

Kindly confirm.

Thanks

[JohnS]

Originally Posted by robertin75

Thanks a lot for the simplified formula.

So using an equation the formula would be:

w = (v * (2 * Pi) ) / circumference

where w = angular speed
v = linear speed
Pi = 3.1416

w = (5.277 m/s * (2 * 3.1416)) / 3.2 mts

Kindly confirm.

Thanks

That is correct

[robertin75]

Hello:

Can that formula still be simplified more without involving Pi as follows:

w = (2 * v) / d

where:

w = angular speed
v = linear speed in meters / second
d = diameter in meters

w = (2 * 5.277 m/s) / 1.018 meters

w = 10.36 rad / sec

This way we don't have to deal with floating point values when using this algorithm on an embedded C language program where floating point variables are not allowed.

Thanks

[JohnS]

Originally Posted by robertin75

Hello:

Can that formula still be simplified more without involving Pi as follows:

w = (2 * v) / d

where:

w = angular speed
v = linear speed in meters / second
d = diameter in meters

w = (2 * 5.277 m/s) / 1.018 meters

w = 10.36 rad / sec

This way we don't have to deal with floating point values when using this algorithm on an embedded C language program where floating point variables are not allowed.

Thanks

Yes, since the circumference is pi*diameter, it will cancel out

[robertin75]

Ok, thanks a lot !

easy formula

V=rj

v=velocity
r=radius
j=angular velocity