# Friction in case of pure rolling [closed]

I know that friction in pure rolling is zero.But in some questions friction is included such as on an inclined plane while in others friction is not included . I am very much confused with friction in pure rolling. Can anybody clarify me what actually happens and where I am going wrong?

Should we include friction or not and if yes then in which cases?

I have one more doubt that what if any external force is present in case of rolling down for rough and smooth inclined plane? I believe that in smooth incline plane the force will provide the torque and the object will roll down but what in case of rough inclined plane. Also can it perform pure rolling motion without slipping?

• If you could give a couple of examples where you are confused, that would help enormously. At present, your question is so broad that it's difficult to know how to answer it. May 2, 2020 at 22:05

Frictional force is not zero in a rolling motion An object is able to roll only because friction prevents the bottom part from slipping. Else the body would simply slip through the floor. It is true for all kinds of surface-flat, inclined, cicular...

Work Done by frictional force, during a pure rolling motion is zero

Referring to the animation, we see that the bottom most point, which is in contact with the ground lifts up perpendicular to the direction of force of friction. Thus, No work is done by friction and no energy losses occur during rolling.

When to consider rolling friction and when to not If you are dealing with problems involving conservation of enrgy, work energy theorem, etc you should not consider work done by friction (since no work. is done) but you should not forget that force of friction do exist. When you are to find the acceleration of a body, or forces on a rolling body, you have to consider the frictional force.

A problem can be solved in both ways-using work energy theorem or using forces. In general, If your approach is using energy conservation, No frictional losses. If your approach is using force-acceleration, consider the frictional force. I am attaching a problem solved in both ways for a clearer understanding.

• Here I have considered the force $F$ to be constant since we know it. You may also differentiate both sides to get the same result... the term $\frac{dh}{ds}$ would give $sin\theta$ May 3, 2020 at 5:23
• Thanks for your answer. I have read that if any external force is present then static friction acts and if external force is absent then the static friction is zero. Is this statement correct? If yes what is static friction in case of rolling? May 3, 2020 at 7:15
• The statement is partially correct. "If a net external force is present, and the body is not moving, then it is static friction and if external force is absent, friction is zero" is a better statement. And in case of rolling, since the bottom most point is not moving, the frictional force acting our there is static friction. It prevents the wheel from slipping. A detailed explaination is not possible here. You may ask that as another question May 3, 2020 at 11:43
• I have edited the question. Now can you please provide the answer to my query by editing your answer. I am very much confused in this thing. It would be great if you could provide it here only. May 3, 2020 at 13:26

I think your confusion is due to the fact that there are two types of friction.

• One is always zero. That is kinetic friction (it only appears when something slides, which isn't the case for rolling).
• The other is not always zero. That is static friction (it appears to prevent sliding, so it holds on to the contact point whenever there is a tendency to slide).

When you accelerate or brake with your car, the wheels rolling over the surface feel a static friction force. If not, then the wheels would slide over the surface, because they are being slowed down by the engine (via the axle) but nothing is slowing down the car as a whole and so, the wheels will slide over the asphalt.

Also, as in your example, if you roll anything uphill or downhill, gravity pulls downwards and tries to make the contact point slide. Static friction then appears to prevent that sliding. It must thus pull up along the incline (regardless of rolling direction).

I have one more doubt that what if any external force is present in case of rolling down for rough and smooth inclined plane? I believe that in smooth incline plane the force will provide the torque and the object will roll down but what in case of rough inclined plane.

An external force could for instance be gravity, I guess, unless you are thinking of something specific. But gravity sums up to be pulling in the centre of the wheel. It causes no rotational torque about the centre. So, gravity can't be the thing that causes the rotation.

Rather, static friction at the contact point makes the wheel rotate.

• Is the incline completely smooth, then no static friction is possible. Then no rotation happens and the wheel will simply slide down the incline without ever beginning to spin around.
• Is the incline rough, then a static friction force is possible, and now this static friction causes a torque that makes the wheel rotate.

In other words, a rough surface is a requirement for pure rolling (or rolling without slipping/sliding) to be possible in such scenario.

• Thanks for your answer!!! I was actually talking about any specific force that would act tangentially to the rolling object. So in this case can we say that both friction (in case of rough inclined plane) and that force will provide a net torque, which could cancel out each other or may give a net torque which will cause Pure Rolling Motion? May 3, 2020 at 20:45
• @Guest2020 I'm sorry, I do not fully understand your question. What other force are we taking about? May 4, 2020 at 21:31
• Tangential force May 5, 2020 at 9:47
• @Guest2020 Okay, so a scenario where another tangential force is present as well as static friction. In such scenario, the static friction force will adjust to fit. All static friction cares about is to avoid that the contact point starts sliding. For instance, if there is another force already causing a fitting rotation, so that the periphery speed matches the relative surface speed, so they won't move relative to each other, then no static friction is needed (since there is no tendency to sliding) and so it would be present. May 5, 2020 at 9:52

Sometimes, one point of confusion is due to the difference between friction as a Force and friction as a source for energy losses. In rolling without slipping, friction can exist, but it does not do any work. Therefore, it would not do any work, and it would not cause any energy to be lost.

However, friction is required to induce any changes in the angular velocity of the object. If an object is rolling along on a plane, there does not need to be any frictional force. However, if there was no friction (or any other forces), there can not be a torque, and there cannot be a change in angular velocity. If we let a cylinder roll without slipping down an incline plane, its angular velocity must be increasing, as its linear velocity is increasing. Therefore, there must be some torque that causes this. Typically in problems this is due to friction.

This friction is also referred to as traction in rolling type motion. Traction is required to move forward in a car (if you accelerate in a car on frictionless ice, you would skid, and not move forward), but as long as you are not slipping, it does not induce any energy losses, since the point of contact does not slide.

• So if I consider a smooth and a rough surface on an inclined plane then I can say that the friction on the smooth surface is zero and hence the object will not perform rolling motion and just slide down the incline plane and in case of rough surface the object will perform a rolling motion because of the torque of friction.Right? May 3, 2020 at 6:50
• Yes, thats correct. It would be the same as a block sliding down a frictionless incline. There is nothing to produce a rolling motion. Similarly, a ball can "roll" in place with the center of mass not moving on a flat frictionless surface. However, these do not count as rolling without slipping. May 3, 2020 at 6:56
• Thanks for your answer!!! I want to ask one more thing that what happens in case if any external force is present in case of rolling down for rough and smooth inclined plane? I believe that in smooth incline plane the force will provide the torque and the object will roll down but what in case of rough inclined plane. Will there be both friction as well as external force ? And then also can it perform pure rolling motion without slipping? May 3, 2020 at 7:22

Friction works to ensure pure rolling motion. When an object is not undergoing pure rolling friction, it will adjust its direction to ensure pure rolling and once it has been achieved it will no more be present so it's sole purpose is to make object roll without slipping. In the case of inclined plane friction, it is necessary because no other force is present about center of mass whose torque can make the object roll purely.

• Thanks for your explanation. I have one more doubt that what if any external force is present in case of rolling down for rough and smooth inclined plane? I believe that in smooth incline plane the force will provide the torque and the object will roll down but what in case of rough inclined plane. Also can it perform pure rolling motion without slipping? Please elaborate the rolling motion if an external force is also present. May 3, 2020 at 11:05