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Work done by forces at an angle

There is no work done by a force when an object does not move or moves in a direction which is perpendicular to the direction of the force.

The force which acts on an object that moves in circular motion does no work as the force is always perpendicular to the motion of the object.

If the direction of the force is at an angle $$\theta$$ to the displacement of the object, the work done on the object is the product of the component of the force along the direction of motion of the object (i.e. the direction of the displacement $$\vecphy{s}$$ of the object) and the magnitude of displacement: $$$W=Fs\cos\theta$$$

Note that $$\theta=0$$ corresponds to the force pointing in the same direction as the displacement and $$\theta=\pi$$ indicating that the force and displacement point in opposite directions.

$$F=$$force; $$s=$$displacement in the direction of the force.