some permanent magnet DC motor calculations based on the NXT motors. If these motors are used without the encoders and operated at full speed they function as permanent magnet DC motors with approximately the following parameters: (assuming you didn't include external gearing).

No Load Speed: 163 rpm

No Load Current: 60 mA

Stall Torque: 40 N?cm

Stall Current: 1.26 A

a) Determine an equation for angular velocity,  (in rad/sec) versus Torque (in Nm).

b) Determine an equation for current (in amps) versus Torque (in Nm).

c) Based on these equations, determine the maximum power point. This is the value of and T that result in maximum power. State the power and the (,T) values. Do not assume this happens at 0.5T. The best way to do this is to make an Excel spreadsheet.

d) Based on these equations, determine the maximum efficiency point. This is the value of ? and T that result in maximum efficiency. State the efficiency and the (,T) values. Assume the battery is operating at 9 Volts. Do not assume this happens at 0.25T.

e) If the battery is replaced with a 6 Volt battery it was experimentally determine that the no load speed is reduced to 120 rpm. For this situation, determine a new equation for angular velocity,  (in rad/sec) versus Torque (in N?m).

f) Determine the theoretical maximum linear speed of your robot if the following assumptions are made:

I. A 9 Volt battery powers the motor so you use the derived equations from parts a) & b)

II. Your robot weighs 8 lbs. and the weight is evenly distributed over a 2 wheel vehicle with each wheel connected to a separate motor.

III. Assume your speed is measured at a situation where the vehicle is moving on level ground and rolling friction ?r is the only friction that is included in the calculation. Assume the robot is moving on pavement with a r value of 0.015. Assume your robot is pushing an object that weighs 2 lbs.

IV. You are using wheels that are two inches in diameter.

g) Calculate the efficiency of the motors at the conditions of part f.