- #1

UMath1

- 361

- 9

## Homework Statement

Given: Wheel radius is 20 CM, Gear radius is 5 CM, Coefficient of Static Friction is .2, Weight on rear wheel is 50 N.

What is the minimum force that must be applied to the pedal for the wheel to begin accelerating on a level surface?

## Homework Equations

Net T = I * a

T = R X F

Net F= m*a

## The Attempt at a Solution

I know that for the wheel to begin angularly accelerating a net torque must be present, meaning that the torque from the chain on the wheel must exceed the torque from static friction on the wheel. So I calculated the maximum possible torque from static friction. First, using

That all seems fine until you consider the case for translational acceleration. The only net force acting on the wheel is the force of static friction (the force of the chain is canceled out by the force of the axle). Then for the wheel to begin translationally accelerating even a force of 1 N on the pedal would be sufficient. Going through the process above in reverse, I would find that the 1 N force on the pedal would result in a force of 0.2 N from static friction. Since this would be the net force, the wheel should begin translationally accelerating prior to rotational acceleration.

But obviously this cannot be the case. I have never seen a bike slide before it rolls. How is it that rotational and translational acceleration coincide?