# COnstant centripetal force to move in a circle?

• jsmith613
In summary, the conversation discusses the concept of centripetal force and its relationship to the speed and radius of an object moving in a circular path. It is determined that the force needed to keep an object on a circular path depends on both the speed and the radius, and that increasing one variable will require a corresponding change in the other to maintain the same force. The conversation also considers the application of these concepts to real-life situations, such as orbits and magnetic fields, and the use of mathematical expressions to calculate the required force.
jsmith613
An interesting thought just struck me and I wanted to confirm if it is correct.
Do all objects (of fixed mass) need a particular magnitude of force to keep them moving in a circle,
e.g: a ball will ALWAYS need a force of 10N to keep it moving in a circle
If the speed increases then the radius must ALSO increase to accommodate for the change in speed so as to ensure the centripetal force required is CONSTANT?

is this idea correct?

No, it's not correct.

jsmith613 said:
An interesting thought just struck me and I wanted to confirm if it is correct.
Do all objects (of fixed mass) need a particular magnitude of force to keep them moving in a circle,
e.g: a ball will ALWAYS need a force of 10N to keep it moving in a circle
If the speed increases then the radius must ALSO increase to accommodate for the change in speed so as to ensure the centripetal force required is CONSTANT?

is this idea correct?

If you had a way of generating a constant centripetal force, yes. That's how satallites get to higher orbits. (I think).

Doc Al said:
No, it's not correct.

It would seem sensible though.
Imagine a CD spinning. the dust particles collect around the centre as all the dust particles are of similar/identical mass and thus ALL require the same force to keep them moving in a circle.

If the CD span faster, I presume that they would move further out on the CD as the force provided there is sufficent to keep them moving in a circle as the centripetal force required is matched?

jetwaterluffy said:
If you had a way of generating a constant centripetal force, yes. That's how satallites get to higher orbits. (I think).

Do you imply that the centripetal force in the higher orbit is the same as in the lower one?

nasu said:
Do you imply that the centripetal force in the higher orbit is the same as in the lower one?

well in the lower one, surely the speed is less too! so yes! (and it depends on mass of the object)

jsmith613 said:
well in the lower one, surely the speed is less too! so yes! (and it depends on mass of the object)
Going from lower orbit to higher orbit is not so simple so the discussion about speeds depends on what kind of orbits you have and what do you call "speed" in case you have elliptical orbits. For stable circular orbits however the speed is higher in the lower orbit.
The centripetal force ("provided" by gravity) is lower for the higher orbit (see Newton's law of gravity).

jsmith613 said:
An interesting thought just struck me and I wanted to confirm if it is correct.
Do all objects (of fixed mass) need a particular magnitude of force to keep them moving in a circle,
e.g: a ball will ALWAYS need a force of 10N to keep it moving in a circle
If the speed increases then the radius must ALSO increase to accommodate for the change in speed so as to ensure the centripetal force required is CONSTANT?

is this idea correct?
To expand on my previous answer: Twirl a ball at the end of a string in a circle. What stops you from twirling it as fast as you want? The tension in the string will just increase, since the required force is greater. (Until it breaks of course.)

You're statement that all objects of fixed mass need the same centripetal force is clearly wrong. It depends on how fast they are moving and at what radius. (Sure, you might conceive of situations where the force remains constant and the radius changes just right to keep it moving in a circle, but that's not true in general.)

nasu said:
Do you imply that the centripetal force in the higher orbit is the same as in the lower one?

If the difference in height isn't too big, yes. But I see your point.

another example similar to Doc Al's is imagine a charged particle with some velocity. Then imagine a magnetic field is turned on, and its direction is perpendicular to the particle's velocity.

The velocity of the particle will remain constant, and it will go in a circle. If the strength of the magnetic field is increased, then the force on the particle will increase, and the radius of the circle traveled by the particle will decrease.

Hi guys, i am having a nightmare with the l3 btec in mechanical engineering and wondered if anyone could help.

I need to find out how to calculate the minimum speed required for an object to travel in a vertical circle of 1.5m,

The 1.5m is that the radius and if so does this look right?

centripetal force = weight
mv2/r = mg
thus v2 = rg
v2 = 1.5 * 9.81
v = 3.836 ms-1

I know that some people just HATE the idea of using or accepting Maths in an explanation but one simple Maths expression says it all.
The (centripetal) force needed to keep a mass m (kg) on a circular path of radius r (m) at as speed of v (m/s) is

F= mv2/r (N)

That shows you that, if you want to increase the speed, the force needs to increase but, if you want to increase the radius, the force gets less.

If you are discussing Orbits, then the gravitational force will decrease as the radius increases so the sums get a bit more complicated and you can't just assume an unstretchable 'piece of string' is keeping the mass on its path.

wilko2008 said:
Hi guys, i am having a nightmare with the l3 btec in mechanical engineering and wondered if anyone could help.

I need to find out how to calculate the minimum speed required for an object to travel in a vertical circle of 1.5m,

The 1.5m is that the radius and if so does this look right?

centripetal force = weight
mv2/r = mg
thus v2 = rg
v2 = 1.5 * 9.81
v = 3.836 ms-1

You are right that the weight of the mass is enough to keep it on track when at the top of the circle but you haven't actually said why.
I think you probably mean the speed at the top? Looks right to me.
Of course, the speed -on a string, say - wouldn't be constant in this model. (See title of thread)

sophiecentaur said:
You are right that the weight of the mass is enough to keep it on track when at the top of the circle but you haven't actually said why.
I think you probably mean the speed at the top? Looks right to me.
Of course, the speed -on a string, say - wouldn't be constant in this model. (See title of thread)

Ok thanks for your help. appreciate it

## 1. What is a constant centripetal force?

A constant centripetal force is a force that is always directed towards the center of a circular path, and is required to keep an object moving in a circular motion.

## 2. How is centripetal force related to circular motion?

Centripetal force is the force that keeps an object moving in a circular motion. It acts as a centripetal acceleration, constantly changing the direction of the object's velocity.

## 3. What factors affect the amount of centripetal force needed for an object to move in a circle?

The amount of centripetal force needed is affected by the mass of the object, the speed of the object, and the radius of the circle.

## 4. Why is a constant centripetal force necessary for circular motion?

A constant centripetal force is necessary to prevent an object from moving in a straight line and to keep it moving in a circular path. Without it, the object would move in a straight line tangent to the circle.

## 5. How can we calculate the amount of centripetal force needed for an object to move in a circle?

The amount of centripetal force can be calculated using the formula Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circle.

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