# Force = mass * acceleration. A question about gears.

1. May 28, 2014

### pletharoe

This question is about push bikes, but could be applied to anything with a versatile engine and a gearing mechanism.

My bike is propelled by pushing on the pedals. Whether I use a high or low gear, the force remains the same. If the force and mass remain constant, how come I can accelerate faster by starting in a low gear and working up in stead of just starting in in the high gear?

2. May 28, 2014

### Matterwave

When you pedal, you feel a constant force between a low gear and a high gear? I feel that the lower gears are harder to pedal...

3. May 29, 2014

### tduell

The force on your pedals may remain the same for any gear, but the torque applied to your wheel varies with the overall gear ratio.
Also, the rotational inertia of the driven wheel, as seen at the driving gear, varies with the gear ratio squared.
All this transpires to make it easier to accelerate faster in low gear.

Cheers,
Terry

4. May 29, 2014

### A.T.

Which force? What matters for the acceleration of you+bike are the external forces on you+bike, like the force between road and wheel. In lower gears the same internal force on the pedal creates a greater external force between road and wheel, and therefore more acceleration.