speed

[cris15]

If a wheel of 700mm diameter is turning at 192 RPM what would it's speed be in MPH?

[johnny7]

If my calculations are correct, it is travelling at 15.78mph.

My calculations are as follows just in case you're interested:

c = 2 π r
c = 2 x π x 0.00035km (350mm)
c = 0.0022km
c = 0.00137 miles

In 1 minute, the wheel can travel 0.26304 miles (192 x 0.00137miles),

In 1 hour, the wheel can travel 15.78 miles (0.26304 miles x 60mins),

the speed of the wheel is 15.78 MPH,

and thus, lick my balls!

[cris15]

Thanks for your answer, I made it 15.73 MPH
(rounded pi and KMH/MPH conversion)
Don't want to lick your balls.

[mibn2cweus]

15.7416954725mph

multiply diameter by pi to obtain circumference
multiply by RPM to obtain distance in mm/minute
multiply by 60 to obtain mm/hour
divide by 1609344 to convert mm to miles

[kempie]

I no longer calculate. Instead I Google-ate...

http://www.google.co.uk/search?q=(700*pi*192)+ mm/minute+in+mph

[cris15]

Thanks for your time mibn2cweus and kempie.

[rov1200]

I always thought it should be angular velocity and the term should be in rads/sec x 60 x 60?

[rov1200]

http://en.wikipedia.org/wiki/Angular_velocity

[chakka35]

Odd that everyone except rov1200 assumes that the wheel is travelling along the ground when the question does not say that.

[mibn2cweus]

Chakka . . . You assume that I assumed "that the wheel is travelling along the ground" when I in fact was considering the speed at the perimeter of the wheel being as its diameter was specified, however, all in all a relatively safe assumption in light of the designated parameter . . . MPH ~ ~ ~ ~ ~ ~ ~ <o/ "\o>

[eltelioni]

If it is spinning freely on its axis then a point on the rim will travel at 15.74mph as the others said. No argument there, but then someone suggested it may be rolling along the ground. In that case the axle moves at 15.74mph relative to the ground. The bottom of the wheel is in contact with the ground and is stationary, but the top of the wheel is zipping along at 31.48mph.

I vaguely remember a documentary about the land speed record where some guy was explaining the problems that arise when the car is doing Mach0.5 - at that speed the top of the wheel is breaking the sound barrier and bad things can happen if you don't design for it.

[kempie]

Angular velocity is a vector quantity and introduces the axis of rotation, an unnecessary term in regards of the question.

As phrased, the question is concerned with the scalar property of linear speed i.e. the speed at which a point on the edge of the object travels in its circular path around the center of the object. This is (as has been shown in the examples above) calculated from the scalar angular speed (or angular frequency).

The Wiki page on angular velocity linked above opens with the caveat "Do not confuse with angular frequency".

[ummmm]

I've just woke up...