How does a gearbox work?

1. Dec 9, 2012

beyondlight

1. The problem statement, all variables and given/known data

Lets suppose i have two gears where the ratio between the rotational speed of the motor and the wheel is:

Motor/wheel 2:1 first gear
Motor/wheel 1:1 second gear

2. Relevant equations

P=Tω

3. The attempt at a solution

Now i guess that in the first gear following holds

$$P_m=ω_m*T_m=ω_w*T_w=P_w=2*ω_w*\frac{T_w}{2}$$

That means that the mechanical energy on the rotational axis is the same on both sides of the gearbox?

Is that correct?

2. Dec 9, 2012

CWatters

Yes. If you ignore losses in the gearbox then a gearbox doesn't change the power. It just trades torque and angular velocity.

You can also think of it in terms of the law of conservation of energy. A gearbox can't store or create energy so what goes in must come out (and at the same rate = power).