I've noticed that when I apply the front brakes on my bike it stops quite quickly. If I apply the back brakes at the same speed, it skids rather than stopping quickly. Why?
Answer
Using the brakes on the front of the bike causes your weight to shift forward. Additional weight allows more force before the tire will slip (skid). If you brake hard enough the back tire of your bike will lift up and at that point all of the mass is distributed on the front tire.
Remember the maximum force is $F_{max} = \mu F_{normal}$ and $F_{normal}$ is proportional to the distribution of weight on the tire so as weight shifts forward $F_{normal}$ increases and therefor the maximum stopping force $F_{max}$ increases.
Braking with your back tire doesn't shift weight onto the back tire so its stopping power doesn't increase.
Wikipedia explains this in great detail in the Bicycle and motorcycle dynamics article.
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