Q: Why is there a g*sin(theta) correction and not a g*cos(theta) term?
REV 7.05

A: Think of the incline free body diagram from your college text book. The incline is the roll or pitch in our case. In the free body diagram it is just theta.

What we are trying to find is the change from one position to the next. First, we should look at the mean (position 0). Lets assume theta0 = 0. So, the equations are:

F0 = W*sin(theta0) = W*sin(0) = 0 N0 = W*cos(theta0) = W*cos(0) = W

At position 1, the equations are:

F1 = W*sin(theta) N1 = W*cos(theta)

Let's look at the change in friction force. So, dF = F1 - F0 = W*sin(theta) - 0 = W*sin(theta)

With the assumption of a small theta, sin(theta) -> theta. Therefore, dF = W * theta

or

dF = W * roll

Now, let's look at the change in the normal force. dN = N1 - N0 = W*cos(theta) - W = W*(cos(theta) - 1)

for a small theta, cos(theta) -> 1. therefore,

dN = W*(1 - 1) = 0

So, there is a g*sin(theta) correction, but the g*cos(theta) term cancels out.

The same works for pitch.