# Quesiton on applied force on a rolling object

Hi guys, I thought of something when I was rolling something.

In a nut shell, why is it easier to roll an object once it started rolling, and what would be the force required to keep the object rolling?

Let's use a car as an example, when you push the car, it will only start rolling once you apply more force than the static friction force. But once the car start rolling, it becomes increasingly easier for you to keep the car rolling (hence need less apply force). I think the reason for this is because the car will have more and more momentum as it roll faster and faster, thus the faster the car is rolling, the less force is needed for you to keep it rolling. But then that would lead me to think that there must be an equation which relate the force, momentum and static friction. Does anyone know what that equation is, and is my reason for less force required to roll an object already in motion correct?

Thank you!

Hi guys, I thought of something when I was rolling something.

In a nut shell, why is it easier to roll an object once it started rolling, and what would be the force required to keep the object rolling?

Let's use a car as an example, when you push the car, it will only start rolling once you apply more force than the static friction force. But once the car start rolling, it becomes increasingly easier for you to keep the car rolling (hence need less apply force). I think the reason for this is because the car will have more and more momentum as it roll faster and faster, thus the faster the car is rolling, the less force is needed for you to keep it rolling. But then that would lead me to think that there must be an equation which relate the force, momentum and static friction. Does anyone know what that equation is, and is my reason for less force required to roll an object already in motion correct?

Thank you!

First of all, it's important to not confuse the force needed to accelerate an object with the force needed to keep it at a constant speed. For a car, the first one will usually be bigger because the inertia of the car is so large. You need to add kinetic energy to accelerate the object, in addition to overcome the friction. To keep the speed constant, you only need to overcome the friction, not add kinetic energy.

If the car had rigid tires and rolling surface, i.e. made of diamond, it would be just as easy to accelerate the car from rest as it is when it is moving (i.e. same amount of force needed to increase speed by a given amount). It would then continue to roll at a constant speed without any force pushing on it.

As regards static and dynamic friction. For a block of wood sliding on some surface, the static friction will be higher than the dynamic/sliding friction. The reason is that the wood will "attach" itself better to the surface when it is allowed to come to rest.

For a car with rubber tires, I think the difference will be less. Resistance to acceleration from rest will maybe be slightly larger than resistance towards acceleration from some nonero velocity, but it would be related to the deformation properties of the tire rubber. It depends on how much power is needed to deform the tire rubber at different rates. If less than twice the power is needed to deform the rubber twice as fast, then the rolling friction will be less than the static friction.

Torquil

For automobiles, the biggest rolling resistance at low speeds is due to the tire flexing. Tires have a rolling resistance coefficient (RRC), which is nearly independent of wheel RPM. See table in
http://en.wikipedia.org/wiki/Rolling_resistance
If a car has a mass M, and a weight M·g, then the force to push a car is RRC·M·g. For a typical tire, RRC ~0.01, so with M=1000 kilograms, the required pushing force is ~98 Newtons. Some tires develop flat spots if the car is parked overnight, so pushing it is harder in the morning.

Bob S