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I'm trying to understand the equation P = 2(pi)TN/60, where T=torque, N=rpm...

So far I understand:

E = F.d = F.(2.pi.r)*(no. of revolutions) = 2T.pi.n
And
P = E/t = 2T.pi.n/t - but n/t is revolutions per second, so:
P = 2T.pi.f f = rev/second

This is where I'm having trouble, because
1 rev/sec = 60 rpm, so I'd say:
P = 2T.pi.60.N
but in the textbook and online it says P = 2(pi)TN/60 so I'm not sure what's going on...

Anyone know what's going on?

YellowPeril

1 rev/sec = 60 rpm
P = 2T.pi.f f = rev/second
f = N/60
P = 2(pi)TN/60

studiot

I'm glad you realise where your difficulty lies since your foregoing analysis is correct if somewhat roundabout.

However your intial data says the shaft is running at N rpm

By definition this is N/60 rps.

So your f = N/60 and you must substitute this for f in the equation you have developed, not the other way round.