Question

How τ, ω and f relate to each other?

Answer 1

τ ∝
`(1)/(\omega .f)`

Step-by-step explanation:

We know that Power, P =
`(2\pi. N.T)/(60)` -----(1)

where N is speed in rpm

T is torque

and

`\tau =(16.T)/(\pi .D^(3))` ---------(2)

where D is diameter

From (1) and (2) we get,

τ ∝ T

and T ∝ 1 / N

∴ τ ∝ 1 / N

Now we know, Angular velocity, ω =
`(2\pi . N)/(60)` -----(3)

and, ω = 2.π.f ---------------------------------(4)

where f is frequency

So from,(3) and (4), we get

ω ∝ N

and ω ∝ f

and since τ ∝ 1 / N

∴ τ ∝ 1 / ω

and τ ∝ 1 / f

Therefore, τ varies inversely to both ω and f