Physics Help Forum Centripetal Force

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Sep 21st 2017, 05:00 AM #1 Junior Member   Join Date: Sep 2017 Posts: 5 Centripetal Force Hi, in my homework it is asked what provides the centripetal force for: a) a car turning a corner b) the icy rocks in Saturn's rings c) the rim of a bicycle wheel So b is the gravitational force of Saturn I think. But I'm not sure abut a and c. Could it be the spokes of the bicycle for c? An then a... I would stay turning the steering wheel, but that is probably not right, because it should be the result of that. Is it the friction between the wheels and the road? But if so, how, because this friction is also there when the car is going straight. Can someone explain? Please. Thank you so much.
 Sep 21st 2017, 06:03 AM #2 Senior Member     Join Date: Jun 2016 Location: England Posts: 590 I would say you are on the correct path. The key with the friction of the car wheels is that the friction force is not aligned with the direction of travel. When traveling in a straight line the friction is working in exactly the opposite direction to the direction of travel. When the steering wheel turns the front wheels of the car, they start generating friction at an angle to the direction of travel, which then turns the car. __________________ ~\o/~
 Sep 21st 2017, 06:08 AM #3 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 987 Hi Max A good question and good thinking on your part, you have all three sources correct. It is useful to note that the centripetal force is always a real force that you would include in any free body diagram (Have you done those?) that must be present when curving or circular motion occurs. It is just a name for those forces which act towards a centre or central forces. This is the force that pulls the body off its intended straight line motion and always has an ordinary everyday source, like gravity, the tension in the spokes, friction etc. All forces act along a stright line they do not act round curves. OK so how do friction work? Well Newton's First Law tells us that a body left to its own devices continues in straight line motion (or rest). So yes when driving in a straight line friction is present or the wheels would just spin on the road. But friction always acts in the opposite direction to the intended motion. So in a straight line the friction is purely backwards. But when the steering wheels are set at an angle to the straight direction, there is also a sideways force between the road and the pad of tyre that is contacting the road. The sideways componenet is the friction that is called the centripetal force. It is also worth noting that the normal reaction of the road on the tyre can provide some of the centripetal force if the road is correctly banked so the normal reaction is not vertical but also has a horizontal (sideways) component.
 Sep 21st 2017, 06:49 AM #4 Junior Member   Join Date: Sep 2017 Posts: 5 Ah I see! Thank you very much. It is good to know I was already on the right track and now I think I fully understand it. Thanks so much for your help!
Sep 21st 2017, 07:11 AM   #5
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 Originally Posted by Woody The key with the friction of the car wheels is that the friction force is not aligned with the direction of travel.
Friction always works in the direction opposite to acceleration unless there is an opposing force in which case it acts in the direction opposite to that force ... I think.

 Sep 21st 2017, 07:49 AM #6 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 987 Friction and forces more generally still act when there is no acceleration.
Sep 21st 2017, 08:11 AM   #7
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 Originally Posted by Pmb Friction always works in the direction opposite to acceleration unless there is an opposing force in which case it acts in the direction opposite to that force ... I think.
Sorry, but this is not correct. Friction between two bodies works in the direction opposite the motion of each body relative to the other. It is not dependent on acceleration, but rather relative motion. For example if you slide a book across a table at constant velocity acceleration = 0, which means the sum of forces acting in the book is zero, which means the friction force acting on the book is opposite in direction to the pushing force your hand is applying to the book (and also opposite the book's direction of motion).

For a car turning in a circle the acceleration of the car is directed towards the center of the turn, which means the friction force acting on tires is towards the center of the turn (i.e. aligned with it's acceleration - this from $\displaystyle \vec F = m \vec a$). The source of that friction is the slip angle between the tire and the road surface - if you turn the wheel, say, 10 degrees to the left, the car actually turns at about 9 degrees; the 1 degree difference is the "slip angle" between tire and road surface and is what causes a force between road and tire towards the center of the turn.

Sep 21st 2017, 10:22 AM   #8
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 Originally Posted by ChipB Sorry, but this is not correct. Friction between two bodies works in the direction opposite the motion of each body relative to the other.
Well, I did say "I think." But I disagree with you 100% since its not always in the direction opposite to the motion. In fact you yourself gave a counter example, the same one used here, of the car which is accelerating perpendicular to the direction of motion. In this case the force of friction is in the direction of the cars acceleration. I made the mistake of saying opposite. Oops.

 Originally Posted by ChipB For example if you slide a book across a table at constant velocity acceleration = 0, which means the sum of forces acting in the book is zero, which means the friction force acting on the book is opposite in direction to the pushing force your hand is applying to the book (and also opposite the book's direction of motion).
Ummm ..... you read what I wrote closely enough. I said unless there is an opposing force in which case it acts in the direction opposite to that force. My mother did raise a fool, but it was my brother, not I.

 Originally Posted by ChipB For a car turning in a circle the acceleration of the car is directed towards the center of the turn, which means the friction force acting on tires is towards the center of the turn (i.e. aligned with it's acceleration - this from $\displaystyle \vec F = m \vec a$).
Yep. That is indeed what we were talking about. I don't see what the problem you're having is. You said "in the direction of motion" and I said (with the exception I stated above) in the direction of acceleration. The force of friction in this case is in the direction of acceleration, i.e. towards the center just like the direction of the force of friction.

Last edited by Pmb; Sep 21st 2017 at 10:32 AM.

Sep 21st 2017, 12:46 PM   #9
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 Originally Posted by Pmb Well, I did say "I think." But I disagree with you 100% since its not always in the direction opposite to the motion. In fact you yourself gave a counter example, the same one used here, of the car which is accelerating perpendicular to the direction of motion. In this case the force of friction is in the direction of the cars acceleration.
It's a subtle point, but worth belaboring. Think about the relative motion of the portion of tire tread that is in contact with road to the road itself - the tire patch. If a car is coasting in a straight line that relative motion is zero, and there is essentially no friction acting between road and tire, and the car simply coasts. If the brakes are applied, the tire slows its rotation so that it the tire patch is actually moving forward relatve to the road (i.e. the tire is skidding), and friction acts to the rear so that the car slows. Conversely, if you press on the accelerator the engine causes the tires to speed up relative to the road, which means the tire spins and the tir patch is moving rearward, and the car is propelled forward. It may be a bit hard to visualize; I could draw a diagram if it would help.

Now let's consider a car that is turning, let's say at constant speed. With the tire angled relative to the diection of travel there are two components of motion to consider. First is motion of thentire patch in the direction parallel to the tire - as before there is no relative motion of tire patch and road surface, so no friction acting in that direction. Second is the component of motion perpendicular to to the tire - this component of motion is due to the slip angle of tire relative to the road that I mentioned earlier. It acts perpendicular to the direction the car, in a an outward direction, causing friction between tire patch and road toward the center of the turn. Hence the car turns, according to $\displaystyle \vec = m \vec a$. So yes, even in this case friction acts counter to the relative direction of motion of tire patch to road surface.

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