How Do Gear Ratios Affect Mechanical Energy in Gearboxes?

[beyondlight]

Homework Statement

This is related to my other thread https://www.physicsforums.com/showthread.php?t=657677

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

Homework Equations

P=Tω

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?

 

[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).