I am stuck on the following question
A motor with a maximum running speed of 1000rpm and with a torque-speed characteristic given by
Tm= 200 - 0.76ωm Nm (ωm in rads-1)
is directly connected to a load with a torque-speed characteristic given by TL = 0.02ωL^2 Nm.
(a) Determine
the steady state running speed
(b)
If TL = 2ωL^2 Nm determine the steady state running (load) speed if a 5:1 reduction gearbox is used.
(c)
What value of gear ratio would be required if the motor was to be used to drive a load given by
TL = ωL^2 Nm at a (load) speed of 210 rpm?
I know how to do the first two parts of the question but I am unable to tackle the third part, i.e part C.
I only know that the first step is to convert the load speed from rpm to rad/s but after that, I dont know what to do.
I would greatly appreciate any help, it would also be great if you could provide links to some resources my lecture notes are not helpful and I am really having trouble understanding this topic.
Thanks a lot