# Bike gear problem

1. Nov 8, 2006

### courtney1121

The rear wheel of a bicycle has a set of sprockets whcih vary in size. The chain hooks onto the sprockets, and when a pulling force is apply to the chain, the sprocket, hence the wheel turns. As any cyclist knows, when going up a hill, to maintain a constant velocity, it is better to use a lower gear, or larger sprocket. Why? In your answer, consider what the net torque is at constant velocity.

Ok so obviously, the larger the sprocket the easier it is to pedal, but I'm not quite sure why...I dont even know if that will apply here or not.

2. Nov 8, 2006

### courtney1121

Any suggestions?

3. Nov 8, 2006

### courtney1121

to explain in terms of torque...if the radius is increasing the force must decrease...causing there less force to be exerted on the pedals if the radius is large....soo should there be no net torque on the bike? how does this relate in terms of constant velocity?

4. Nov 8, 2006

### PhanthomJay

My ankles are weaker than my wrists. It is about torque, but not less force. When going uphill, gravity is trying to pull you back down; to counteract it and move at a steady pace, without slowing because of that hill, you've got to apply more torque to keep yourself moving ahead. The idea is to apply the same force, or not much more, as when riding level, but with the increase in radius, the torque will increase even at that same force, and this increase in torque will result in keeping you from slowing, i.e., moving at constant speed rather than decelerating.