Quick physics question angular velocity

isn't the formula for the instantaneous angular velocity and for the average angular velocity the same thing?

I don't see the difference - both are diff in theta/diff in time

pls pls help

it's convention to use 'd' for infinitesimal amounts of change...
t₁ - t₀ might have been (but in this picture isn't) written as Δt... i.e. some measurable amount of time.

I'd say it's not really an important distinction unless you're using calculus

but the thing is that instantaneous angular velocity is a completely different thing to the average angular velocity especially when the acceleration is not zero. So surely they should have different formulas?
like if you had to work out the instantaneous angular velocity then how would you do it?

TBH it's a related thing. After all the units of average angular acceleration are the same as the units for instantaneous angular acceleration so it shouldn't be too much of a surprise.

I think you'll only have to worry about constant acceleration at A level BUT if you can get a formula giving angular velocity as a function of time you'd do differential calculus on it with respect to t to get the formula for angular acceleration.

FWIW this isn't unique to angular acceleration - instantaneous linear acceleration would be dv/dt and so on for anything that changes over time.

Hey thanks a lot! So i guess for a level i just ignore instantaneous angular velocity as its above the level iam required to know about?

it's convention to use 'd' for infinitesimal amounts of change...
t₁ - t₀ might have been (but in this picture isn't) written as Δt... i.e. some measurable amount of time.

I'd say it's not really an important distinction unless you're using calculus