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Centripetal force velocity

Is it compulsory for the speed to remain constant for an object to move in a circle?
Original post by Aaradhana
Is it compulsory for the speed to remain constant for an object to move in a circle?


No. To move in a circle all you have to do is move in a circle.

But I suspect this isn't your real question if you are thinking about centripetal force.
What is your real question. :smile:
Reply 2
Original post by Stonebridge
No. To move in a circle all you have to do is move in a circle.

But I suspect this isn't your real question if you are thinking about centripetal force.
What is your real question. :smile:

Yes I had something else on mind, but now that I think of it it doesn't make sense. But I really just don't get the essence of centripetal force in general.

Ok so for example, when you're spinning a bob, when you increase the speed a lot, why doesn't the bob simply fall to the center? Why does it keep spinning as it's speed keeps increasing? I know science is about the 'how' and not the 'why' but, I don't know, something just sounds wrong.

And I get that centrifugal force is imaginary but it really doesn't make sense to me.
(edited 10 years ago)
The essence of centripetal force is that, according to Newton an object will move in a straight line with constant speed unless you apply an external resultant force on it. To make an object move in a curve (it doesn't have to be a circle) you need the force acting sideways on it. If that curve happens to be a circle, the sideways force acts exactly in the direction of the center of the circle. (This can be proved mathematically.)
That's all it is. You then need to find something to provide that force. If it's a planet in orbit the force is gravity. If it's a mass on the end of a string it's the tension in the string. If it's a car going round a corner it's the friction between the road and the tyres. If it's a train its the force of the rails on the wheels.
Reply 4
Original post by Stonebridge
The essence of centripetal force is that, according to Newton an object will move in a straight line with constant speed unless you apply an external resultant force on it. To make an object move in a curve (it doesn't have to be a circle) you need the force acting sideways on it. If that curve happens to be a circle, the sideways force acts exactly in the direction of the center of the circle. (This can be proved mathematically.)
That's all it is. You then need to find something to provide that force. If it's a planet in orbit the force is gravity. If it's a mass on the end of a string it's the tension in the string. If it's a car going round a corner it's the friction between the road and the tyres. If it's a train its the force of the rails on the wheels.


Yes I completely get all of that but what is it that keeps the object from coming towards the center as the force increases?
Original post by Aaradhana
Yes I completely get all of that but what is it that keeps the object from coming towards the center as the force increases?


In what example does the force increase? Why should it? And is that "resultant" force.
Reply 6
Original post by Stonebridge
In what example does the force increase? Why should it? And is that "resultant" force.


For e.g. when you're spinning a pendulum and you increase the force on it, the velocity of the pendulum increases but it never falls to the center.

Well, and is that the resultant force? I think it should be because it shows a clear change in momentum as the velocity increases.
Original post by Aaradhana
For e.g. when you're spinning a pendulum and you increase the force on it, the velocity of the pendulum increases but it never falls to the center.


Exactly. If you increase the speed, you have to increase the force.
This follows from the equation for centripetal force.

F=mv2rF = \frac{mv^2}{r}

If the object is on a string the radus r is kept constant. Assuming the mass is also constant then F is proportional to v2
If the object moved closer to the centre (r decreased) then the string would go slack and the force would be reduced. This would cause the object to move further away again. So there is an equilibrium here with the value of F providing the centripetal force for the radius r and speed v.
By the way.
The object actually is falling towards the centre, but because it is also moving at right angles to the force, it doesn't ever reach the centre, it keeps going round in a circle. That's what circular motion is.
Have you studied the equation above and how it is derived?
v2/r is the acceleration towards the centre.
(edited 10 years ago)
Reply 8
Original post by Stonebridge
Exactly. If you increase the speed, you have to increase the force.
This follows from the equation for centripetal force.

F=mv2rF = \frac{mv^2}{r}

If the object is on a string the radus r is kept constant. Assuming the mass is also constant then F is proportional to v2
If the object moved closer to the centre (r decreased) then the string would go slack and the force would be reduced. This would cause the object to move further away again. So there is an equilibrium here with the value of F providing the centripetal force for the radius r and speed v.
By the way.
The object actually is falling towards the centre, but because it is also moving at right angles to the force, it doesn't ever reach the centre, it keeps going round in a circle. That's what circular motion is.
Have you studied the equation above and how it is derived?
v2/r is the acceleration towards the centre.


I just looked at the derivation. At least mathematically it makes more sense now.

As for the theoretical part, I think I get your point--the very nature of the force is such that it acts at right angles to the object. Like, in general, forces act in the direction that they are applied but centripetal forces act at right angles. It's like they are balancing some other force to reach an equilibrium at right angles. So for e.g. the initial condition of the object is to move in a straight line, however centripetal forces disrupt this and they reach a kind of agreement where the object is neither travelling in the same straight line as before nor getting pulled towards the object of centripetal force. It is just at right angles- in between.

Is that way of thinking right?
Original post by Aaradhana
I just looked at the derivation. At least mathematically it makes more sense now.

As for the theoretical part, I think I get your point--the very nature of the force is such that it acts at right angles to the object. Like, in general, forces act in the direction that they are applied but centripetal forces act at right angles. It's like they are balancing some other force to reach an equilibrium at right angles. So for e.g. the initial condition of the object is to move in a straight line, however centripetal forces disrupt this and they reach a kind of agreement where the object is neither travelling in the same straight line as before nor getting pulled towards the object of centripetal force. It is just at right angles- in between.

Is that way of thinking right?


Yes. You have to think of it in whatever way makes sense to you.
Always start from Newton's Laws and say to yourself
This object is not moving in a straight line.
Therefore there must be a resultant force acting on it.
The force isn't making the object's actual speed get larger, so it is not a force acting in the direction of motion. It is a "sideways" force.
If the motion is a circle (a special case of non-linear motion) this resultant force acts sideways at right angles to the direction of motion.
This is the centripetal force.
Now, can I identify this force. What is producing it?

Hope this helps.
Reply 10
Original post by Stonebridge
Yes. You have to think of it in whatever way makes sense to you.
Always start from Newton's Laws and say to yourself
This object is not moving in a straight line.
Therefore there must be a resultant force acting on it.
The force isn't making the object's actual speed get larger, so it is not a force acting in the direction of motion. It is a "sideways" force.
If the motion is a circle (a special case of non-linear motion) this resultant force acts sideways at right angles to the direction of motion.
This is the centripetal force.
Now, can I identify this force. What is producing it?

Hope this helps.


Yes. That was very very helpful. Thanks a lot.
PRSOM.

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