Challenge #1: Big Bang Clock (Difficulty: Medium)

Introducing a new element to my store, product challenges! Occasionally, you will come across a product that has an associated challenge that can be solved! Sometimes I will issue random challenges via blog posts. The first challenge is attached to the "Infinite Gearing T-Shirt". Every calculation/solution style challenge will be set up so that you are "given" information, the hints of how to solve it will be in the "find" section, then "assume" so that there is no ambiguity with the problem to solve. Finally, the problem will be given a difficulty rating (Medium for this challenge).

Can you answer the following two questions ...

Questions

1. How many years would it take for one revolution of the last gear to occur?
2. Would the last gear have turned once if this gear system was turned on at the instant of the big bang?

The rules of the challenge are simple. By any means necessary, you must solve both questions of the challenge! As a reward for any solved challenge, you will receive a special one time discount code for XX% off any product of your choosing on the store. The discount code will depend on the difficulty rating of the problem. The information to solve this will be down below ...

Given

• Type of Gearing System: Compound Reverted Gear Train
• Number of Stages: 25
• Npinion = 7 teeth
• Ngear = 35 teeth
• Input Speed = π (~3.14) rads/s
  • * 2π radians = Full Circle *

Find

1. Gear Train, e
2. Output Speed of Last Gear, ω out
3. Time of Revolution of Last Gear, t out

Assume

 Assume No Backlash/Interference, assume everything properly supported!