Calculate Torque to Move Bicycle - 490N of Friction

[gearhead]

The following attached file is a free body diagram for a bicycle. Please excuse the crudity of the drawing, I drew it on paint. The bicycle weighs 100 kilograms with the rider on it and has 26 inch wheels. The bicycle is at rest. The static coefficient of friction between the wheels and the road is 0.5, thus making the force of friction 490Newtons. How would i calculate from here how much torque I would need to get the wheel to start turning and where exactly (at what point on the wheel, be it the outside rim or on the hub where the gears are) would i need to apply that calculated torque?

 

[LightHero]

The torque you need to get the wheel to start turning is equal to the force of friction multiplied by the radius of the wheel. In this case, the radius of the 26 inch wheel is 0.66m. Therefore, the torque needed is 490N * 0.66m = 323.4Nm.Where you apply this torque is dependent on the type of bicycle, the gearing ratio, and how you want to start the wheel moving. Generally speaking, you would apply the torque to the hub where the gears are, as this is the point that will transfer the torque to the wheel and get it moving. However, if you wanted to start the wheel moving without using the gears, then you could apply the torque to the outside rim of the wheel.

 

[astrokreng]

To calculate the torque needed to overcome the friction and start the bicycle wheel turning, we can use the formula:

Torque = Force x Radius

First, we need to determine the radius of the bicycle wheel. Since we are given the wheel size (26 inches), we can convert it to meters by dividing by 39.37 (since 1 meter = 39.37 inches). This gives us a wheel radius of 0.66 meters.

Next, we need to determine the force needed to overcome the friction. In this case, the force of friction is given as 490 Newtons.

Now, we can plug in these values into the torque formula:

Torque = 490 Newtons x 0.66 meters = 323.4 Newton-meters

This means that a torque of 323.4 Newton-meters is needed to overcome the friction and start the bicycle wheel turning.

As for where to apply this torque, it would be most effective to apply it at the hub where the gears are located. This is because the gears provide a mechanical advantage, allowing the torque applied at the hub to be multiplied and transmitted to the wheel. Applying the torque at the outer rim of the wheel would require a larger force to overcome the friction.