# Perceived gravity in circular motion

• Abdullah Wahid
In summary: The object is at rest with respect to the space station, not accelerating with respect to the rotating frame, so the object is... stationary.In summary, there is inertial centrifugal force which exists only when you analyse the situation in a rotating reference frame. When you use the co-rotating frame, the object does move in a straight line just as you would expect when the fictitious force of perceived gravity cancels with the real centripetal force.
Abdullah Wahid
Is there any thing like perceived gravity in circular motion??
If I consider that it is in opposite direction to centripetal force, then both perceived gravity and centripetal should cancel each other and object should move in a straight line. Why does it nit happen?

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Abdullah Wahid said:
Is there any thing like perceived gravity in circular motion??
Yes.
If I consider that it is in opposite direction to centripetal force, then both perceived gravity and centripetal should cancel each other and object should move in a straight line. Why does it nit happen?
If the object moves in a straight line there is no centripetal component.

A situation where centripetal acceleration is balanced against gravity is an orbit.

FactChecker
Abdullah Wahid said:
Is there any thing like perceived gravity in circular motion??
Not in circular motion, but in a rotating frame of reference

Abdullah Wahid said:
If I consider that it is in opposite direction to centripetal force, then both perceived gravity and centripetal should cancel each other and object should move in a straight line. Why does it nit happen?
In the rotating frame of reference the object can be at rest, consistent with zero net force.

In the most common examples, like the moon orbiting the earth, the gravity is the centripetal force. Centripetal force is just a force applied to an object where the resulting motion is circular, there's nothing different or special about it.
I'm not sure I understand, can you provide a sketch showing the forces you are asking about?

russ_watters said:
Yes.

If the object moves in a straight line there is no centripetal component.

A situation where centripetal acceleration is balanced against gravity is an orbit.
But if centripital force is balanced by gravity, object must travel in straight line as there is no resultant force to cause acceleration

Abdullah Wahid said:
But if centripital force is balanced by gravity,
No, the centripital force is provided by gravity. They are the same thing in this case.

DaveE said:
In the most common examples, like the moon orbiting the earth, the gravity is the centripetal force. Centripetal force is just a force applied to an object where the resulting motion is circular, there's nothing different or special about it.
I'm not sure I understand, can you provide a sketch showing the forces you are asking about?
DaveE said:
In the most common examples, like the moon orbiting the earth, the gravity is the centripetal force. Centripetal force is just a force applied to an object where the resulting motion is circular, there's nothing different or special about it.
I'm not sure I understand, can you provide a sketch showing the forces you are asking about?

My teacher told me that this perceived gravity acts opposite to the centripital force and this perceived gravity is the force which keeps water in the bucket when bucket is upside down.
My question is that if both forces are in opposite direction, why aren't they cancel each others effect so that bucket has no resultant force and why isn't the bucket moving in a straight path?

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A.T. said:
No, the centripital force is provided by gravity. They are the same thing in this case.
Have a look at this diagram where bucket is in circular motion. Why aren't perceived gravity and centripital force cancelling out each other as they both are in opposite direction?

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Abdullah Wahid said:
Have a look at this diagram where bucket is in circular motion. Why aren't perceived gravity and centripital force cancelling out each other as they both are in opposite direction?
Have a look at post #3. The "perceived gravity" is called inertial centrifugal force, and exists only when you analyse the situation in a rotating reference frame. In the co-rotating frame the inertial centrifugal force does cancel the centripetal force, which is consistent with the bucket being at rest (having no acceleration) in that frame.

https://en.wikipedia.org/wiki/Centrifugal_force

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DaveE
Got it. Thank you for helping

A.T. said:
Have a look at post #3. The "perceived gravity" is called inertial centrifugal force, and exists only when you analyse the situation in a rotating reference frame.
+1

Note that, when you use the co-rotating frame, the object does move in a straight line (it stays stationary) just as you would expect when the fictitious force of perceived gravity cancels with the real centripetal force. Carnival rides such as the rotor or gravitron use this effect.

I'm adding what I consider a clarification. Say you have a rotating space station and an object on the floor of the space station. From an inertial (non-rotating, non-accelerating) frame of reference, you have a Newton third law pair of forces, the floor exerts an inwards centripetal force onto the object, and the object exerts an outwards force in reaction to the centripetal force (sometimes called reactive centrifugal force). The point here is that the object experiences a net inwards centripetal force from the floor.

Using the space station itself as a rotating frame of reference, the object is at rest with respect to the space station, not accelerating with respect to the rotating frame, so the object is experiencing zero net force. In a rotating fame, the forces acting on the object are the real inwards (centripetal) force from the floor, and the fictitious outwards centrifugal force due to the rotating frame of reference (it's not considered as a reactive force to acceleration, because the object is not accelerating with respect to the rotating frame). This is not a Newton third law pair of forces because both forces are acting on the same object.

Abdullah Wahid said:
But if centripital force is balanced by gravity, object must travel in straight line as there is no resultant force to cause acceleration
In an orbit, there is only one force being applied, and it causes the acceleration inward. Gravity *is* the centripetal force. The opposing force is due to the object's inertia and acceleration.

russ_watters said:
The opposing force is due to the object's inertia and acceleration.
Key is: In the inertial frame there is no opposing force.

russ_watters
A.T. said:
Key is: In the inertial frame there is no opposing force.
Agreed.

Maybe to make it more clear for the OP: what he's suggesting is like saying the "ma" in f=ma is a second applied force that cancels the "f" and results in the acceleration. But no, the ma is just the other half of the force pair resulting from the acceleration; it's the reaction force.

https://en.m.wikipedia.org/wiki/Fictitious_force

russ_watters said:
ma is just the other half of the force pair resulting from the acceleration; it's the reaction force.

https://en.m.wikipedia.org/wiki/Fictitious_force
Fictitious forces do not have third-law partners. The "centrifugal reaction force" is a real force that is the third law partner of the real centripetal force.

We are talking 2nd law here.

$$F_{real}=ma_{real}$$
$$F_{real}=m(a_{real}-a_{frame} + a_{frame})$$
$$F_{real}=m(a_{real}-a_{frame}) + ma_{frame}$$
$$F_{real}=ma_{relative} + ma_{frame}$$
$$F_{real}-ma_{frame}=ma_{relative}$$
$$F_{real}+F_{pseudo-gravity}=ma_{relative}$$

[Adopt a sign convention so that pseudo-gravity is a negative (downward-pointing) vector for a positive (upward-pointing) frame acceleration]

The mass of an object times the acceleration of the non-inertial frame of reference one is adopting manifests as a term that looks just like a force. It can be called "pseudo-gravity" if you like. But it is not a "reaction force".

hutchphd, nasu and russ_watters
russ_watters said:
In an orbit, there is only one force being applied, and it causes the acceleration inward. Gravity *is* the centripetal force. The opposing force is due to the object's inertia and acceleration.
Consider a two body system, where two objects orbit about a common center of mass, there is no "opposing" reaction force, both objects are in "free fall". The Newton third law pair is the gravity each object experiences due to the gravitational field from the "other" object.

Abdullah Wahid said:
My teacher told me that this perceived gravity acts opposite to the centripital force and this perceived gravity is the force which keeps water in the bucket when bucket is upside down.
My question is that if both forces are in opposite direction, why aren't they cancel each others effect so that bucket has no resultant force and why isn't the bucket moving in a straight path?
I think you are hopping from one frame to another in your mind and that is giving you an apparent paradox. You can explain the situation in one frame by sticking to that frame - likewise for a different frame.

jbriggs444
jbriggs444 said:
looks just like a force. It can be called "pseudo-gravity" if you like. But it is not a "reaction force".
In that frame, there is a 'pseudo gravity' and the reaction pair are the forces against your feet and against the ground. The would both disappear if the floor gave way.

I like this type of PF thread because it's a bit like the whole 'PF brain' mulling over a topic - much the same as one does on one's own. No-one is getting their feathers ruffled about the differences in how we are looking at things. We are just examining the thing from all the different possible directions.

## 1. What is perceived gravity in circular motion?

Perceived gravity in circular motion is the sensation of a force pulling an object towards the center of a circular path. This is often experienced in amusement park rides or when driving around a curved road.

## 2. How is perceived gravity different from actual gravity?

Perceived gravity is a subjective experience, while actual gravity is a physical force that exists in the universe. Perceived gravity is influenced by factors such as motion, acceleration, and the position of the observer, while actual gravity is a constant force that is always present.

## 3. What causes perceived gravity in circular motion?

Perceived gravity in circular motion is caused by the centripetal force, which is the force that keeps an object moving in a circular path. This force is directed towards the center of the circle and is responsible for the sensation of being pulled towards the center.

## 4. How does perceived gravity change with different speeds and radii?

The strength of perceived gravity in circular motion is directly proportional to the speed of the object and inversely proportional to the radius of the circular path. This means that the faster an object moves or the smaller the radius of the circle, the stronger the perceived gravity will be.

## 5. Can perceived gravity in circular motion be dangerous?

In most cases, perceived gravity in circular motion is not dangerous. However, if the forces involved are too strong, it can cause discomfort or even injuries. It is important to follow safety guidelines and ride within your comfort level to avoid any potential risks.

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