Why does friction do no work

If you consider the motion of a point on the rolling object its path is a cycloid. The image below is taken from the Wikipedia article on the cycloid and I need you to imagine that the black line at the bottom is inclined to the horizontal and thus representing the inclined plane. This means that the direction of motion of the point of contact is perpendicular to the frictional force and so the frictional force does no work on the object.

Yep you're right. Consider the case of a cylinder rolling down a hill, starting from rest. Friction does provide a torque and definitely does work on the cylinder. However, in the case of pure rolling motion, i. It therefore appears based on that conservation statement that the frictional force does no work. If you have a solid wheel rolling on a perfectly smooth plane and the material of the wheel and the surface have zero elasticity, no work is done. If you have a perfectly spherical cow of uniform density and zero elasticity rolling on a smooth, flat, perfectly rigid plane in a vacuum, and no external force, then no work is done.

In your question, adding an external force changes the equation, such that the linear acceleration applied by that external force is partially but negligibly countered by the change in rotational speed, due to friction applying torque. As with most spherical cow analogies, the calculations are good enough in most circumstances. A baseball's flight can be predicted fairly accurately by taking just a point-object ballistic trajectory through a vacuum most of the time.

Throwing a crumpled ball of paper, though, you'll need to take drag into account. The same with rolling objects.

For most calculations, you can ignore friction, because it will be negligible compared to other forces, such as slope.

If you reduce the rigidity of either the object or the plane it's rolling in, or add other external forces though, then friction starts to matter. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How can friction do no work in case of pure rolling? Ask Question. Asked 2 years, 8 months ago.

Active 4 months ago. Viewed 4k times. There is no force, no torque and therefore no work done. The more interesting case is that where the object is rolling under an external force, say down an inclined plane. See the diagram below. Now, you can analyze it in two ways. One is similar to Farcher's answer where the point of contact moves perpendicular to the frictional force and hence, there is no work done.

But you were interested in it from the point of view of torques where we consider the whole wheel, not just the point of contact so let's do that. Friction does two things to the wheel as a whole. It does negative work when you look at the linear motion of the wheel.

Next, the friction provides a torque about the center of the wheel and the wheel has angular displacement. Hence, it does positive rotational work i. As an example consider an object rolling, without slipping, down an inclined plane. Then we have:. Plugging this into the first equation gives. Conservation of energy then gives:. Of the three forces in the system, two act at that point, so they have no lever arm. Solution There are at least three ways to tackle this problem.

Method 1: Forces and torques.