COnstant centripetal force to move in a circle?

Click For Summary

Discussion Overview

The discussion revolves around the concept of centripetal force and its relationship with mass, speed, and radius when an object moves in a circular path. Participants explore whether a constant force is necessary for circular motion and how changes in speed and radius affect the required centripetal force.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Some participants propose that a fixed mass requires a specific magnitude of force to maintain circular motion, suggesting that if speed increases, the radius must also increase to keep the centripetal force constant.
  • Others argue that this idea is incorrect, noting that the required centripetal force depends on both speed and radius, and that a constant force is not a general requirement for all scenarios.
  • A participant mentions that in the case of satellites, a constant centripetal force can be generated to achieve higher orbits, but questions arise about the differences in centripetal force between orbits.
  • Another participant discusses the dynamics of a spinning CD, suggesting that as speed increases, particles move outward, which raises questions about the nature of centripetal force in practical examples.
  • Mathematical expressions are introduced to illustrate the relationship between centripetal force, mass, speed, and radius, emphasizing that increasing speed requires greater force, while increasing radius reduces the required force.
  • A participant seeks help with calculating the minimum speed for an object in a vertical circle, leading to further discussion about the role of weight and speed at different points in the circular path.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the necessity of constant centripetal force and the relationships between speed, radius, and force. The discussion remains unresolved, with no consensus on the initial proposition.

Contextual Notes

Some participants highlight the complexity of orbits and the influence of gravitational force, indicating that assumptions about constant force may not hold in all cases. The discussion also touches on the implications of using mathematical models to describe physical phenomena.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics, particularly those interested in circular motion, centripetal force, and the mathematical relationships governing these concepts.

jsmith613
Messages
609
Reaction score
0
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?
 
Physics news on Phys.org
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.
 
  • #10
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.
 
  • #11
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
 
  • #12
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.
 
  • #13
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)
 
  • #14
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
 

Similar threads

Undergrad Where is the centripetal force acting on mass M?
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad Origin of Centripetal force when the net force toward the center is 0?
  • · Replies 8 ·
Replies
8
Views
3K
High School Why is speed constant when centripetal acceleration is constant?
  • · Replies 24 ·
Replies
24
Views
4K
Undergrad Why Does Friction Provide Centripetal Acceleration in Circular Motion?
  • · Replies 37 ·
2
Replies
37
Views
5K
Undergrad How Does Centrifugal Force Affect Objects on a Rotating Disk?
  • · Replies 18 ·
Replies
18
Views
3K
High School Confusion while trying to build intuition of centripetal force
  • · Replies 15 ·
Replies
15
Views
4K
High School A scenario of non-uniform circular motion
  • · Replies 4 ·
Replies
4
Views
846
Undergrad Angular momentum and centripetal force
  • · Replies 5 ·
Replies
5
Views
7K
Undergrad Direction of friction of each wheel and total moment when a car turns
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Trajectory collision calculation
  • · Replies 6 ·
Replies
6
Views
2K