Selecting the proper motor to spin a brush

[pdfmech]

Hello I need to select the proper motor to spin a 12 inch brush that cleans a window. There is about 5 pound of horizontal force on the window and the brush will spin at 200 rpm . My issue in finding what torque needs to be supplied by the motor. When a DC motor is turned on it almost immediately achieves the velocity corresponding to a certain voltage. How can I determine this acceleration. I selected a motor that I feel would be more than enough http://www.pololu.com/catalog/product/1104" but I need to show calculations for my project. Maybe I will use a controller to slowly increase the speed and then assume no angular acceleration. Any help would be greatly appreciated.

 

[Unrest]

torque = rotational inertia * angular acceleration.

With some maths, perhaps calculus, and the speed-torque curve of the motor (200 RPM free-run, 170 oz-in stall.), you can predict the time taken to reach 190RPM, or something else close enough.