Your picture is of the ends for slow speed dental handpieces. You need an air or electric motor to drive them. It needs to use E style attachments. Air motors start about $230 and electric ones start around $2,000 with a speed control. The fastest air motors turn 20,000 rpm but don't have much torque. High torque air motors turn 5,000 rpm. Electric motors with brushless motors turn 40,000 rpm and are controllable to 2,000 rpm in 1,000 rpm increments. They are way too expensive to consider for modifying motors.
Air turbine dental handpieces turn 200,000 to 400,000 rpm with little torque. They are much less expensive and work for 3.5 size motors. You need carbide or industrial diamond burs.
Lohring Miller