3.1 Work as Energy Transfer

For displacement along a line, work by a constant force depends on the component of force parallel to displacement. That is why the angle term appears in W = Fs cos(theta): only the aligned part of the force contributes to transfer along that motion segment.

If the force points partly in the displacement direction, work is positive and the body’s kinetic energy can increase. If it points opposite displacement, work is negative and kinetic energy tends to decrease. If force and displacement are perpendicular, that force does no work on the body over that segment.

When force changes with position, split the path into tiny intervals where force is approximately constant. Summing those tiny contributions leads to the area under the force-position graph. That area interpretation is often faster and less error-prone than computing each interval separately.

This graph method also clarifies sign. Area above the axis corresponds to positive work and area below corresponds to negative work. The net work is the signed area sum, not just a geometric area magnitude.

In uniform circular motion, instantaneous displacement is tangential while centripetal force is radial. Their angle is 90° at every instant, so the centripetal force changes direction of velocity but not speed. That is a pure direction change with zero work by the centripetal force.

This is a useful separation: a force can be essential for shaping a path while doing no work. Work is about transfer along displacement, not merely about the existence of force.