How Do Gear Ratios Affect Stepper Motor Performance in Lock Systems?

[AC130]

Homework Statement

The number of teeth in the dial gear of the combination lock system is 40
The number of teeth in the stepper motor gear of the combination lock system is 10
The number of teeth in the dial-stepper connecting wheel of the combination lock system is 80

1) What are the gear ratios between the motor/wheel and motor/dial?
2) If the dial is turned one complete revolution, how many turns do you get on the stepper motor shaft?
3) What is the number of steps in the stepper motor for one complete revolution of the dial?

Homework Equations

The Attempt at a Solution

Attempt on question 1

Ratio between motor/wheel = 10/80 = 0.125
Ratio between motor/dial = 10/40 = 0.25
Hence ratio between motor/wheel and motor/dial = 0.125/0.25 = 0.5

Attempt on question 2
40/10 = 4 turns

Attempt on question 3
Step angle = 360/steps per revolution = 360/4 = 90°/step

This step angle seems very high as usually a step angle is something like 1.8°/step so does that mean that this step angle is wrong?
Can someone please check if these calculations are right?

 

[haruspex]

I assume this is a simple gear train, no shared shafts.
Think again about how you calculated the number of steps per revolution. And be clear about which gear the steps are on and which gear is making the revolution.

 

[AC130]

I assume this is a simple gear train, no shared shafts.
Think again about how you calculated the number of steps per revolution. And be clear about which gear the steps are on and which gear is making the revolution.

Yes there aren't any shared shafts
I am quite unsure as to how I can calculate the number of steps per revolution from the information given.

I know that If I knew the step angle then I could just divide 360 by the step angle to find the steps per revolution

 

[haruspex]

Yes there aren't any shared shafts
I am quite unsure as to how I can calculate the number of steps per revolution from the information given.

I know that If I knew the step angle then I could just divide 360 by the step angle to find the steps per revolution

I realize I'm making an assumption which might not be correct, but if it is not correct then there is not enough information: I assume that one step of the stepper motor equals one tooth of the stepper motor gear.