An absolute encoder is mounted to the motor driving the X-axis lead screw of a CNC milling machine. If the encoder has a spec of 1250 PPR, a lead of 1.5 mm, and the lead screw moves a distance of 250 mm, how many revolutions of the lead screw will the encoder count and what is the resolution of the X-axis?

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?