Solving 2 Rotating Discs Homework: Angular Velocities

[scottdave]

Alright. I finally think I have the answer... They both follow the format of $IΔω=F_{f}rt$ . I divided one by the other, leaving me with:

$\frac {r_{2}^4(ω_{2}-ω_{1})} {r_{1}^4ω_{1}}=-\frac {r_{2}} {r_{1}}$

. When simplifying and substituting the values for r1 and r2, it gave me:

$ω_{2}=\frac {ωr_{2}^2} {r_{1}^2+r_{2}^2}$
$ω_{1}=\frac {r_{2}^3ω} {r_{1}^3+r_{1}r_{2}^2}$

I arrived at the same answer, which I posted on his YouTube video, this morning. As of 3:30 PM central time today, he has not released it to the public view. So I'm going to assume it is probably correct.

 

[person123]

I arrived at the same answer, which I posted on his YouTube video, this morning. As of 3:30 PM central time today, he has not released it to the public view. So I'm going to assume it is probably correct.

At last! I'm just going to wait a while to make sure I got it, and then I'll close the thread.

 

[person123]

Well, I generalized it so that disc 1 could have any angular velocity as well:

https://www.desmos.com/calculator/discbz9gf1