A problem with finding torque and power associated with two flywheels

[TeaCup]

Homework Statement

The flywheel of a motor is connected to the flywheel of a pump by a drive belt (see image attached). The first Flywheel has a radius R₁, and the second a radius R₂. While the motor wheel is rotating at a constant angular velocity $$\omega$$₁, the tensions in the upper and the lower portion of the drive belt are T and T', respectively. Assume that the drive belt is massless.
a) What is the angular velocity of the pump wheel?
b) What is the torque of the drive belt on each wheel?
c) By taking the product of torque and angular velocity, calculate the power delivered by the motor to the drive belt, and the power removed by the pump from the drive belt. Are these powers equal?

Given:
T, T', R₁, R₂, $$\omega$$₁, R₁>R₂

Find:
$$\omega$$₂, $$\tau$$₁, $$\tau$$₂, P_in, P_out,

Homework Equations

$$\tau$$ = F$$\times$$R
v = $$\omega$$R
P = $$\tau$$$$\omega$$
W = $$\tau$$$$\Delta$$$$\phi$$

The Attempt at a Solution

I found the answer to part a, since the tangential velocity for both flywheels must be the same. But from the problem itself, it seems that T and T' are forces with different values. I don't really understand if they are different, how can the flywheels not have angular accelerations since the problem states that the flywheels each has its own constant angular velocities. Another thought was that the torque generated by the difference between tension forces from one flywheel is offset by that of the other flywheel. But that didn't exactly work out because I ended up with R₁ = -R₂. I finally thought maybe it's a trick question that T actually is equal to T' but then part c seems to suggest that a torque has to exist for each flywheel because otherwise, no power can be delivered for removed.

So here's my problem, can anyone please help me solve this? Thanks!:shy:

 

[rock.freak667]

If ω is constant then dω/dt = 0.

The velocity of the belt is the same. v=rω, so you can get ω of the other flywheel.

 

[TeaCup]

If ω is constant then dω/dt = 0.

The velocity of the belt is the same. v=rω, so you can get ω of the other flywheel.

Thanks, I forgot to say, part a is the only part I found the answer since the tangential velocity must be the same. But do you know how to find the answers for part b and c?

 

[rock.freak667]

For part b

Another thought was that the torque generated by the difference between tension forces

You already knew what to do

For part c, they told you that P=Tω, you just have two Ts, so it would be the difference between them.