Calculating Torque & Power of a Rotating Disk

[kostantina]

Homework Statement

So I am calculating torque and power for a disk of radius 0.5 m that is subjected to a force of 50 N at its periphery and is rotating at angular velocity of 100 rad/s. Find torque and power.[/B]

Homework Equations

Torque= radius x Force = 0.5m *50N = 25Nm

Power= dW/dt= F*w(omega)= 25Nm * 100 rad/sec ... WHy the solutions book has an answer 2500 Nm/s. Why did they ignore the radians. I was thinking to convert the radians into meters or something like that. What am I not understanding here?

 

[gneill]

Radians are a sort of "unitless" unit. They arise out of ratios of like units, such as the ratio of the circumference of a circle to its radius (with suitable unitless constants involved). So when they get mixed up with "real" units they have a tendency to disappear. So, rad*m = m, rad*kg = kg, and so on.

 

[kostantina]

Thank you for the response. It makes sense now. Will do further research on this to make sure I understand.