How do I calculate DC motor speed for a given load?

[dzlan]

A Wheel of a self balancing skateboard of radius 7 cm is rotating at 2600RPM with torque for motor is 1.76Nm,current is 10.4Amp and 24v and total load is 90kg (10kg for skateboard and 80kg for user). What is the speed of self balancing skateboard the in km/hr with load?

 

[HallsofIvy]

I'm not sure I understand this question. It appears to say that the "wheel" of the skate board has radius 7 cm and is rotating at 25600 RPM with that load. If it is the speed that is asked, most of what is given is irrelevant. Calculate the circumference of the wheel from $2\pi r$ and then multiply that by 25600 RPM to determine the distance moved (assuming no slipping) in one minute to get units of "cm/min". Then convert that to "km/hr".

(That's one heck of a fast skate board. You are not getting me on it!)