Question

How τ, ω and f relate to each other?

Answer 1

Answer:

τ ∝ $\frac{1}{\omega .f}$

Explanation:

We know that Power, P = $\frac{2\pi. N.T}{60}$  -----(1)

where N is speed in rpm

           T is torque

and

$\tau =\frac{16.T}{\pi .D^{3}}$   ---------(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 = $\frac{2\pi . N}{60}$   -----(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