# In which direction does the friction act in a circular motion?

I want to know how a body moves on a circular track. Suppose a car enters a circular path. If I don't turn my steering wheel, then the car would travel in straight line and perpendicular to the radius of the circular park. In the second case I turn my steering wheel to enter into the circular path at that very moment. I think the tires would have pushed the ground and the ground would have pushed the tires back (friction force) to enter into the path. Now I must keep the steering wheel at that position to be in the circle, but on the contrary from every person I ask about the direction of friction, they tell me its towards the center. Why is only part of friction in the 'play' is that it gives reaction to action. So Why is the frictional force acting towards center.

• Do they mean directly towards the centre, or just more towards the centre than a straight path?
– JMac
Commented Aug 22, 2017 at 17:16
• This discussion usually assumes that you are using the accelerator to balance out any contribution from rolling friction and areodynamic drag along the direction of motion. Commented Aug 22, 2017 at 18:02

Think of this:

The car wants to just continue straight. When you turn the wheels to the left, they can't roll along with the car motion. Which way would the friction act, if the car still continued straight ahead so that the turned wheels would be sliding aber the asphalt?

The friction is of course backwards. To stop the motion. There is a friction component perpendicular to the turned wheels. And it is not balanced. This is a force that pushes inwards on the circle that is about to be formed.

Now, if you only turn your wheels gradually, sliding will never occur. The perpendicular component will appear when slight turning starts, and it will be static friction. Turning the wheels gradually and not too fast makes it possible to keep this static friction. It is still perpendicular. And thus the car is turned.

This is inwards friction. Static friction. If your wheels roll rather than sliding, then there is no parallel friction any more. Only the perpendicular component is present and it causes the constant direction change - the turning.

• But it is said that “friction opposes relative motion”. The car at any instant will have its velocity tangential to the circle. So as per the above statement shouldn’t it always be tangential? I understand that only friction can provide centripetal force, but why is my argument wrong? Commented Mar 9, 2023 at 9:33
• @Amsterdam6483 Think of "relative motion" as sliding. When a car moves, then it has rolling wheels that do not slide. The contact points of all wheels on the ground is momentarily stationary. So there is nothing for friction to hold back against in this tangential direction even though the car as a whole is indeed moving tangentially. Since there is a tendency to slide sideways, though, when turning the wheels, then static friction appears in order to prevent such sideways sliding. And that static friction thus is inwards and causes the turning. Commented Mar 9, 2023 at 9:40
• Yes, talking about the tyre made the tangential part crystal clear. But why is it that the wheel (to be precise, the point of contact) has a tendency to move outward? Isn’t velocity the only indicator of the tendency of movement? We just agreed that the point is momentarily at rest. Commented Mar 12, 2023 at 4:23
• @Amsterdam6483 That would be due to inertia. If the car is in motion forwards with the wheels straight and rolling and you then suddenly turn the steering wheel violently so the wheels turn 90 degrees, then the inertia og the already moving car is forcing the now perpendicular wheels to slide. This is what happens on a more miniscule level when you turn the wheels just a bit. Commented Mar 12, 2023 at 9:09
• @Amsterdam6483 Yes, you are correct, it is the current (momentary) velocity vector which indicates what I call "tendency to move". In the example I gave with a car moving forwards where the driver suddenly turns the steering wheel, then the "tendency to move" is forwards, because that is the direction of the velocity vector in that moment. It sounds like you aren't fully convinced about this from my attempts of explanations here - can you point out where the confusion arises more accurately? Commented Mar 12, 2023 at 17:46

Friction is always opposite to the direction of motion. So, you are correct. Friction will be in the direction of the tires opposing there car's motion.

It is the centripetal acceleration which is towards the center. So, to stay in circular motion at constant speed, you would need to turn the steering wheel in towards the center of the track and accelerate the car towards the center of the circle.

So why do we only need to turn the steering wheel slightly inwards to stay on the circular track? Actually, the centripetal acceleration towards the center would be a combination of the acceleration of the car in the direction of the front wheels and the deceleration of the car by friction. To get the acceleration towards the center then requires the wheels turned only slightly inwards.

After reviewing the comments and investigating other similar questions I have surmised the following edit:

The thrust of the car, produced by the engine, and then redirected by the front wheels ( regardless of whether it is front wheel or rear wheel drive ) is converted to rotational motion in the wheels. This energy pushes the ground backwards ( unsuccessfully of course because of the large mass of the earth ) but results in a forward equal and opposite reactive force of friction which propels the car forward. This frictional force is opposing the backwards thrust on the earth which gives a forward motion to the car. And by forward, I mean in the direction that the front wheels are pointing. The resultant combination of the reacting friction force which propels the car and the more normal frictional force which opposes the motion of the car produces an acceleration towards the center of the circle.

It should be noted that friction is not a fundamental force. It is actually a result of electrostatic forces by outer electrons opposing each other in two different materials. So, when we say that friction is responsible for the forward acceleration of the car, this is a bit subjective because the force is also caused by the thrust of the engine pushing the earth backwards. The engine cannot thrust the car forward without the friction of the tires to the road, but conversely the friction cannot thrust the car forward without the engine's thrust. When we say that the acceleration towards the center of the circle ( responsible for circular motion ) is caused by friction, this is misleading because it is the combination of two separate frictional forces. One of those frictional forces being the reaction force caused by the action of the engine. In my opinion, I think it is more clear to view the centripetal acceleration as a resultant force of the thrust of the car in the direction of the steering wheels and the friction opposing the cars tangential motion.

• The acceleration of the car in the direction of the front wheels is exactly balanced by the deceleration of the car by friction. That doesn't contribute to the resulting force which points to the center. Commented Aug 22, 2017 at 17:40
• The front tires are not pointing in the same direction as the car's motion when the car is turning, so they do not cancel. see the diagram that I added to explain the vector addition of the forces involved Commented Aug 22, 2017 at 18:00
• Hmmm ... this diagram is more correct for a front-wheel drive car than for a rear-wheel drive where the thrust is along the body axis and it really is friction on the tires that provides the centripetal force. Commented Aug 22, 2017 at 18:04
• Yes, I should have written "in the direction tangential to the radius". Commented Aug 22, 2017 at 18:05
• @dmckee True that the rule for direction of friction applies to kinetic friction and not specifically to static friction, but there is a very good reason for that. Static friction can occur when an object is at rest and yet the friction still has a direction. The direction is nevertheless opposite to the intended direction of force,even when static rolling friction is involved. Do a thought experiment of a wheel rolling down a road. Which direction is the static friction? It is definitely never tangential to the direction of motion of the wheel. Commented Aug 22, 2017 at 19:10

The direction of friction in circular motion varies depending on what type of circle is formed. For example in a horizontal circle, the one that you have defined with a car entering a track, friction is the provider of the centripetal force, therefore acts towards the centre of the track. The reason for this is due to the direction of motion of the wheels on the car.

In a vertical circle the direction depends on the position of the object in the circle. For example in a loop de loop.

The frictional force actually plays two roles in this situation:

1) It maintains the speed of the car. This also happenes when you are driving in a straight line: The engine works to push the car against the road in order to maintain its speed.

2) It maintains the circular path of the car. This is what actually interests you. To understand why the force acts towards the center, try drawing the car in one instant of time and then a moment later. Draw the velocity vectors at each instant. Now, since acceleration is the change in velocity over time, subtract $\vec v_1$ from $\vec v_2$. You will see that the resulting vector is pointing towards the center of the circle. That means that the acceleration is directed towards the center of the circle, and hence the force required to maintain the path must also point towards the center.

• Net acceleration of the object is not the same as the friction forces. You've shown that the total acceleration is directed at the middle; but you've neglected what was mentioned in point 1, that the engine also requires a force to act in the direction of motion, which also comes from friction.
– JMac
Commented Aug 22, 2017 at 17:22
• The force from the engine is exactly balanced by the friction from the road in the direction tangential to the radius, that's why the speed doesn't change, only the direction of the velocity. Commented Aug 22, 2017 at 17:25
• I would say it actually depends on the type of the car, as dmckee wrote above. Commented Aug 22, 2017 at 18:19

In order to keep the car in a circular motion, the velocity of your car needs to be bent towards the center of the track all the time. This change in your movement direction requires a force, and only force can do that in your situation is the friction.