# In circular motion - centripetal acceleration is never there

• ela12aj

#### ela12aj

So far what we know about the circular motion is that an object moving in a circle experiences a force towards the center of the circle and as a result accelerates towards this center.

But we also know that an object always moves in the direction of resultant force - if two tractors moving at an angle of 45 from each other and pulling a mass , the mass will move forward at an angle 22.5 to either of them.

Now when a car is moving in a straight line, the resultant force is that of engine E in forward direction (imagine the car is not moving with constant velocity). But as soon as we turn the steering wheel, the friction force F starts to act at 90 to the E. F is not equal to E but relatively small and dependent on tires etc. so when F & E are added, we get resultant force (say) G which acts on the car at some angle lesser than 90 with F and the car moves in its direction. So we can say that the car is accelerating in the direction of this resultant force G and not towards the center of circle of the bank of the road.
Agree or not, but please can all arguments be concise and with examples.

• Delta2

But we also know that an object always moves in the direction of resultant force ...
Sorry, we don't know that. When a soccer player kicks a ball, the direction of motion changes continuously, yet the resultant force (gravity) is straight down. That's neglecting air resistance. With air resistance the resultant is mostly straight down but still not in the direction of motion.

• vanhees71, Chestermiller and russ_watters
An object accelerates in the direction of the force. If it is already moving, in a different direction, the velocity changes, and the change is in the direction of the force, but the resultant velocity is not in the direction of the force.

It was one of the great advances in classical physics when people like Galileo realized that force does not cause motion, it causes acceleration.

An object in circular motion is accelerated towards the centre; its direction of motion is constantly changing, but its tangential velocity means that it keeps going round the centre rather than moving towards it. An object in Earth orbit is in free fall around the Earth.

• vanhees71 and sophiecentaur
But we also know that an object always moves in the direction of resultant force
This is not true. The only time this is true is if the resultant force is constant and has remained constant since the object was at rest (or by coincidence).

At terminal velocity the resultant force is zero and the object is moving downwards. In orbit the resultant force is down and the object is moving in an orbit. When braking in a car the resultant force is backwards and the motion is forwards.

• vanhees71 and russ_watters
Now when a car is moving in a straight line, the resultant force is that of engine E in forward direction (imagine the car is not moving with constant velocity). But as soon as we turn the steering wheel, the friction force F starts to act at 90 to the E. F is not equal to E but relatively small and dependent on tires etc. so when F & E are added, we get resultant force (say) G which acts on the car at some angle lesser than 90 with F and the car moves in its direction. So we can say that the car is accelerating in the direction of this resultant force G and not towards the center of circle of the bank of the road.
You seem to be making this more complicated than necessary. Acceleration is a vector. The component parallel to the motion changes the speed, the component perpendicular to the motion changes the direction. For the case of uniform circular motion the component parallel to the motion is zero. For the case of rectilinear motion the component perpendicular to the motion is zero. Introductory courses tend to focus on these two special cases, but most cases involve both components being nonzero.

Agree or not...
Of course it is true that if you apply two forces to an object the resulting acceleration will be in the direction of the vector sum of the two forces. So what? This is trivially obvious. What is the point?

[caveat about confusing motion and acceleration]

• Dale
Now when a car is moving in a straight line, the resultant force is that of engine E in forward direction (imagine the car is not moving with constant velocity). But as soon as we turn the steering wheel, the friction force F starts to act at 90 to the E. F is not equal to E but relatively small and dependent on tires etc. so when F & E are added, we get resultant force (say) G which acts on the car at some angle lesser than 90 with F and the car moves in its direction. So we can say that the car is accelerating in the direction of this resultant force G and not towards the center of circle of the bank of the road.
Agree or not, but please can all arguments be concise and with examples.
Hi ela12aj. Welcome to PF!

You have to be careful in applying Newton's laws. Assuming the road is flat, there are two horizontal forces acting on the car when it is moving in a straight horizontal line. There is the forward force that the engine applies to the car tires to push against the road and opposing forces of rolling friction and air resistance. Direction is not changing so if the car is not changing its speed there is no change in momentum so there is no net force. We know this from Newton's first law. So if the car is then subjected to a net force perpendicular to its direction of motion, there will be acceleration only in the direction of the net force - i.e. perpendicular to its direction of motion.

If the car engine is causing the car to increase its forward speed when the steering wheel is turned and this increase in speed continues after the wheel is turned, then there will be a net acceleration that is the vector sum of both accelerations. Then "we get resultant force (say) G which acts on the car at some angle lesser than 90 with F and the car moves in its direction. So we can say that the car is accelerating in the direction of this resultant force G and not towards the center of circle of the bank of the road."

AM

• ela12aj
Hi ela12aj. Welcome to PF!

You have to be careful in applying Newton's laws. Assuming the road is flat, there are two horizontal forces acting on the car when it is moving in a straight horizontal line. There is the forward force that the engine applies to the car tires to push against the road and opposing forces of rolling friction and air resistance. Direction is not changing so if the car is not changing its speed there is no change in momentum so there is no net force. We know this from Newton's first law. So if the car is then subjected to a net force perpendicular to its direction of motion, there will be acceleration only in the direction of the net force - i.e. perpendicular to its direction of motion.

If the car engine is causing the car to increase its forward speed when the steering wheel is turned and this increase in speed continues after the wheel is turned, then there will be a net acceleration that is the vector sum of both accelerations. Then "we get resultant force (say) G which acts on the car at some angle lesser than 90 with F and the car moves in its direction. So we can say that the car is accelerating in the direction of this resultant force G and not towards the center of circle of the bank of the road."

AM
Hi, many thanks for a calm and meaningful explanation (seldom found). So now we are dividing the circular motion in two cases - with and without constant velocity.
Now, in case of car accelerating forward and wheel is turned, you agree to what I said - the acceleration is NOT DIRECTED TOWARDS THE CENTER. so this case is closed but perhaps we might want to update our textbooks.
Now in the other case where car is moving with constant velocity and just the wheel is turned (engine force is not increased), I think it’s worth doing a practical investigation of whether the car will decelerate or not. But my view or perhaps imagination is it will. I support this with the arguments about the nature of friction- being a force that attempts to impede motion. So when we turn the wheel, the friction between tires and road impedes the constant velocity of car and either the speedometer goes back (if car is very fast) or engine requires reving.

Now in the other case where car is moving with constant velocity...
In uniform circular motion the velocity is not constant, just its magnitude (speed).

... and just the wheel is turned (engine force is not increased), I think it’s worth doing a practical investigation of whether the car will decelerate or not. But my view or perhaps imagination is it will. I support this with the arguments about the nature of friction- being a force that attempts to impede motion. So when we turn the wheel, the friction between tires and road impedes the constant velocity of car and either the speedometer goes back (if car is very fast) or engine requires reving.
All you do here is arguing against your own ill defined premises.

• russ_watters
In uniform circular motion the velocity is not constant, just its magnitude (speed).
.

All you do here is arguing against your own ill defined premises.

I am referring to the motion in straight line which becomes circular upon the turning of steering wheel

And all you have done is shown a complete lack of appreciation of the depth of matter.

• And all you have done is shown a complete lack of appreciation of the depth of matter.

What depth ? Accelerations are additive... is there a reason they shouldn't be ?

If I'm zooming across the tundra on my rocket-toboggan, which main motor is providing an acceleration of 4 straight forward, and I turn on my side-facing motor which provides an acceleration of 3 to the right or left, then I end up going diagonally at an acceleration of 5.

Last edited:
• russ_watters
Now, in case of car accelerating forward and wheel is turned, you agree to what I said - the acceleration is NOT DIRECTED TOWARDS THE CENTER. so this case is closed but perhaps we might want to update our textbooks.
There is nothing to update in the textbooks - it is already quite well understood that accelerations can be added vectorially.
Now in the other case where car is moving with constant velocity and just the wheel is turned (engine force is not increased), I think it’s worth doing a practical investigation of whether the car will decelerate or not.
I suggest you download an accelerometer app for your phone and use that for this experiment (I just tried this on my phone/car and it works). It will show the effects of multiple simultaneous acceleration components clearly.

What depth ? Accelerations are additive... is there a reason they shouldn't be ?

If I'm rocketing across the tundra on my rocket-toboggan, which main motor is providing an acceleration of 4 straight forward, and I turn on my side-facing motor which provides an acceleration of 3 to the right or left, then I end up going diagonally at an acceleration of 5.
OMG you have said what I have been saying all the time! why you are getting 5 in the diagonal? Only because that’s the resultant of 4&3 (using Pythagoras) and this resultant is directed towards the diagonal not the center of circle
There is nothing to update in the textbooks - it is already quite well understood that accelerations can be added vectorially.

I suggest you download an accelerometer app for your phone and use that for this experiment (I just tried this on my phone/car and it works). It will show the effects of multiple simultaneous acceleration components clearly.
i think someone has just done it.

I am referring to the motion in straight line which becomes circular upon the turning of steering wheel

And all you have done is shown a complete lack of appreciation of the depth of matter.
Sorry, not hurting anyone but it’s just the curiosity

• weirdoguy
Now, in case of car accelerating forward and wheel is turned, you agree to what I said - the acceleration is NOT DIRECTED TOWARDS THE CENTER. so this case is closed but perhaps we might want to update our textbooks.
Take another look at the textbooks. The acceleration is not depicted as pointing towards the center except in some special cases. Uniform circular motion is one of those special cases.

• Ibix
I think it’s worth doing a practical investigation of whether the car will decelerate or not. But my view or perhaps imagination is it will. I support this with the arguments about the nature of friction- being a force that attempts to impede motion. So when we turn the wheel, the friction between tires and road impedes the constant velocity of car and either the speedometer goes back (if car is very fast) or engine requires reving.
Practical problems mean that this experiment may not demonstrate what you wish it to demonstrate.

Automobile tires do not behave strictly in accordance with the rules of static and kinetic friction. When a rolling tire provides a frictional force, some slip occurs. When a car is in a turn, slip also occurs. The greater the force, the greater the slip rate. Slippage like this means that there is a loss of mechanical energy. If you turn the car, you lose mechanical energy in this manner.

Not because of some physical principle of acceleration -- but because of the behavior of rubber on pavement.

Sorry, not hurting anyone but it’s just the curiosity
Here is another way of looking at it... if you traveling in a circle, I think we all agree that the change in velocity is acceleration. however the velocity (having a magnitude and direction) is only changing in direction , as magnitude is not changing... so when you change direction, this results in a 90dgree apposed force. (inward, perpendicular to the tangent at any point in the path around the circle) this force is called centripetal force or acceleration. as was said by others, the acceleration is toward the center, but the path is circular.

OMG you have said what I have been saying all the time!
Yeah, but I said it eleganter.

Just following up : the problem you seemed to be having is with the statement in most books "circular motion causes acceleration towards the centre of the circle" (or something like that). That's true.

In keeping with the winter theme of my last post...
If I'm traversing the ice in my (unpowered) bobsled, and I steer into a circle. Is there acceleration ? In which direction ?

Last edited: