wheel, we'll, weal

Wheel or wheel means the round things used to propel vehicles and other devices--
The garage has a machine to take the tire off of the wheel rim.
One wheel was loose; he could tell by the way the car shook.

We'll ( rhymes with wheel ) is a contraction ( short, informal form ) of "we will"--
We'll stop for pizza after the movie.
We'll be there about 9 o'clock.

Weal or weal ( rhymes with wheel ) means well-being or prosperity--
The politician made a series of speeches about taxes and the public weal.
We pay our taxes to contribute to the common weal.

Now that you know that, you can say--
"Then we'll raise taxes again to improve the public weal, like a hamster in a wheel."

Note--"well" ( no apostrophe, rhymes with bell ) means in a good way--
He does that well.
She plays well.
Well also means not ill or sick--
Get well soon.
Well is also a deep hole dug in the ground as a source of water--
He went to fetch some water from the well.
Note # 2--"common weal" ( two words, or rarely, one word, "commonweal"  ) means the common lot or level of prosperity--
Free public schools were meant to improve the common weal.
"Commonwealth" ( one word ) means a political entity, like a state or province--
I am a resident of the Commonwealth of Pennsylvania.
Canada is a member of the British Commonwealth of Nations.
Note # 3--"common wealth" as two words, could be used in a sentence--
They pooled their money, since with their common wealth they could afford to buy the car.