Cross/Dot Products in Physics: Work, Torque & Impulse

[danyo]

Hello, I was thinking about the definition of Work to equal Fdcos(theta) , where F is force and d is the distance traveled; and that torque is rFsin(theta) whereas r is radius, and F is the force applied, and theta is the angle that the force vector makes with the object. I understand the geometric reasoning to the equation for torque above, but not as for work. Could you help me with some insight on the theory behind this? (Also I'm interested as to how Impulse is the integral of Work done). And what other things in mechanics or any branch of physics involve these cross products or dot products?

Thanks in advance, and my apologies for the very basic questions; I'm relatively new to physics, but I'm excited to familiarize myself with what goes on behind the problems I solve and the equations I use on my homework problems. Cheers, Daniel. =)

 

[Born2bwire]

\theta is the angle between the direction of the applied force and the path of motion of the object (not the angle that the force makes with the object). Work is defined as the amount of force applied over the path of motion. So we take the dot product of force and the path of motion (and integrate over the path to find work) to find the component of the force that was actually applied along the path. In scalar form, this is equal to F*\cos(\theta).