Normal reaction of a circulating object on a planet

[Janiceleong26]

Why is the normal reaction of an object circulating a planet, equals to the gravitational force minus the centripetal force? I thought both gravitational force and centripetal force are directed towards the centre of the circular path i.e. in the same direction, therefore having, normal reaction = gravitational force + centripetal force. But instead, it's minus. Why?

 

[Bandersnatch]

Hi Janiceleong26

Frankly, I can't make heads nor tails of it, either way. Some context would be useful.
Can you show us an example of where you saw that formulation? Maybe a full question or paragraph?

 

[Doc Al]

Why is the normal reaction of an object circulating a planet,

I assume you mean an object resting on the surface of a rotating planet.

I thought both gravitational force and centripetal force are directed towards the centre of the circular path i.e. in the same direction, therefore having, normal reaction = gravitational force + centripetal force. But instead, it's minus. Why?

Newton's 2nd law: ΣF = ma

Since the acceleration is centripetal, we call the net force the "centripetal force". The only forces acting are the normal force (which acts outward) and the gravitational force (which acts centripetally). ("centripetal force" is not a separate force.) Taking the radially inward direction as positive: ΣF = Weight - Normal = m a_centripetal.

 

[Janiceleong26]

Hi Janiceleong26

Frankly, I can't make heads nor tails of it, either way. Some context would be useful.
Can you show us an example of where you saw that formulation? Maybe a full question or paragraph?

Here it is :
Q1iii)

This is the answer :

Normal reaction = GMm/R^2 - mRω^2
I know that GMm/R^2 is the gravitational force between the planet and the object, and mRω^2 is the centripetal force required for the circular motion of the small mass, but why normal reaction exerted by the planet on the mass is the difference between the gravitational force and the centripetal force ? I thought gravitational force and centripetal force are both acting at the same direction , so both having the same sign. Instead one is negative and the other positive. So sorry for not showing an example at my earlier post, my bad. Thanks for the reply too

 

[Doc Al]

I know that GMm/R^2 is the gravitational force between the planet and the object, and mRω^2 is the centripetal force required for the circular motion of the small mass, but why normal reaction exerted by the planet on the mass is the difference between the gravitational force and the centripetal force ? I thought gravitational force and centripetal force are both acting at the same direction , so both having the same sign. Instead one is negative and the other positive.

Please review my reply above.

 

[Janiceleong26]

I assume you mean an object resting on the surface of a rotating planet.Newton's 2nd law: ΣF = ma

Since the acceleration is centripetal, we call the net force the "centripetal force". The only forces acting are the normal force (which acts outward) and the gravitational force (which acts centripetally). ("centripetal force" is not a separate force.) Taking the radially inward direction as positive: ΣF = Weight - Normal = m a_centripetal.

Yeah , it's on the surface of the planet. And thanks so much, I got it now. But why is the centripetal force, the net force?

 

[Bandersnatch]

But why is the centripetal force, the net force?

It's the other way around. For an object to move in circles, the net force must be equal to the centripetal force.

 

[Doc Al]

But why is the centripetal force, the net force?

Don't think of "centripetal force" as a force. It's just the name we give to the net force in the case of centripetal acceleration. If you were asked to list all the forces acting on the object, you would not list "centripetal force" (or at least you'd better not!). Best to think in terms of ΣF = ma, where a = a_centripetal.

 

[Janiceleong26]

It's the other way around. For an object to move in circles, the net force must be equal to the centripetal force.

I see, thanks. So centripetal force isn't a force that acts on the mass ? It's the resultant force of the two forces acting on it, the gravitational force and the normal reaction force ? Why is it a separate force?

 

[Janiceleong26]

Don't think of "centripetal force" as a force. It's just the name we give to the net force in the case of centripetal acceleration. If you were asked to list all the forces acting on the object, you would not list "centripetal force" (or at least you'd better not!). Best to think in terms of ΣF = ma, where a = a_centripetal.

Wow, I see I see. Thanks, it was clear. :)

 

[Doc Al]

So centripetal force isn't a force that acts on the mass ? It's the resultant force of the two forces acting on it, the gravitational force and the normal reaction force ?

Right.

Why is it a separate force?

It's not a separate force!

The only forces acting on the object (in your example) are the normal force and gravity. That's it!

 

[Janiceleong26]

Right.It's not a separate force!

The only forces acting on the object (in your example) are the normal force and gravity. That's it!

Oh ok, understood. Thanks so much !

 

[sophiecentaur]

Imo, it could be worth thinking in terms of the Centripetal force being 'Provided By' Gravity. If it's in a circular orbit, the mg force is 'just right' and so are the velocity and the radius When the orbit is not circular, the Centripetal component of g will sometimes be greater and sometimes less than the required value of centripetal force to give circular motion. "Centripetal" only means 'towards the centre' and is, perhaps, an easier concept for rigid spinning objects.