Discussion
Honestly this is frightening, I started last weekend all "but y u intgrat tho 😭" and now I'm reading this all "oh of course, he never stipulates storing rotational speed of the wheel, he simply evaluates all forces in the moment, oh that's elegant, then you're more able to include components of fo-"
But I'm still stuck on dummy baby shit because I don't want to do that, and:
- I have torque
- I have a "rate the wheel is spinning" value
how do I... mush them together? What are the units of torque? What's a torque? How I torque the spinny variable? 😭
No one is explaining the baby shit! WHYYYYY
AH, there, ok, got an explanation, thanks all
In short, torque is to the rate of spin, as force is to velocity. So torque is the amount of change of the spin rate.
And I think there's a mass (moment of inertia) mixed up in there too, somewhere?
I feel like there's a delta_time too but, maybe not.
Linear: F = ma = m * (dv/dt)
Rotational has the exact analogy:
torque = mom_of_inertia * (d ang_vel/dt)
Where it gets tricky is that "moment of inertia" depends on the axis you're interested in, and it gets all ugly for the general case. But for a deliberately radially-symmetric wheel around a fixed axis it's all nice and simple.
@glassbottommeg Of course for bike physics now it's incredibly important to consider the angular momentum around other axes, because gyroscopic forces are what keeps the bike upright, and also how it turns corners.
All that being said, I wonder if I'm about to find out that modelling the wheel as a free-spinning disc just doesn't work, and that the reason nobody tracks the spin rate separately (and instead integrates to derive it frame to frame) is because this approach is flawed in some exciting way
and now I have 4 tabs
@glassbottommeg i misread that first one as "cat physics"
@[email protected] @[email protected] The cat bus from Totoro has friction too, you know
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