The treadmill at Robert's gym is run by a belt and wheel system.
A motor spins wheel A which is attached by a belt to wheel B.
Wheel B is fixed by an axle to wheel C which spins the conveyor that Robert runs on.
The machine is set to run the conveyor at a pace of 1 mile every 8 minutes.
The figure is not to scale.
The radius of wheel A is 0.9 inches, the radius of wheel B is 0.75 inches, and the radius of wheel C is 3 inches.
At what angular speed is the motor rotating wheel A? Give your final answer in revolutios per minute.
This is what I know:
v=wr (This is the one I will use)
1) I know that it's a pace of 1 mile every 8 minutes, so 1/8 = 0.125
2) Thus, vC=0.125mi/min, now find wA
3) vC=wCrC -> 0.125mi/min=wc(3)
4) 7920in/min (converted miles to inches)
5) wC=2640(1rev/2pi)-420.169 = wB
Though I'm not really sure where the -420.169 came from, I had my teacher help me but I didn't quite understand, can someone explain it to me and what I should do next after this?
Answer is supposed to be 350.1409 rpm (from what my teacher said)