Two identical objects are rotating in a uniform circle about the earth. One object is twice the distance from the center of the earth as the other. What is the ratio of the centripetal forces acting on the objects?

That's what I thought too. This is a Q from a TBR FL, and they say the answer is 1/4. Because the centripetal force is supplied by gravity, they equate the centripetal force with the gravitational force. Therefore the force is proportional to 1/r^2, not 1/r.

That's what I thought too. This is a Q from a TBR FL, and they say the answer is 1/4. Because the centripetal force is supplied by gravity, they equate the centripetal force with the gravitational force. Therefore the force is proportional to 1/r^2, not 1/r.

They have a very good point. What I wrote would be true if the objects were rotating around Earth at the same angular velocity which is certainly not the case here. In other words - ops, I was wrong.

They have a very good point. What I wrote would be true if the objects were rotating around Earth at the same angular velocity which is certainly not the case here. In other words - ops, I was wrong.

Hmm... so if it were to state that the velocities were the same, the centripetal force would now be proportional to r^-1 rather than r^-2?

I'm just confused because they don't offer different velocities as one of their reasons to use the gravitational force equation rather than centripetal force equation.

FGrav = Fac
GMm/rsq = Fac
mass is the same since they're identical
GMm/rsq = Fac

What douchebags. Now it makes sense.

GMm/rsq = Fac of object 1
GMm/rsq = Fac of object 2

They're saying the gravitational causes the centrip acceleration, which is true, and not asking you to solve any further.
I would have also done Fac = mv^2/r to get 1/2. ****.

Hmm... so if it were to state that the velocities were the same, the centripetal force would now be proportional to r^-1 rather than r^-2?

I'm just confused because they don't offer different velocities as one of their reasons to use the gravitational force equation rather than centripetal force equation.

what i don't understand is how to come to the conclusion that angular velocities differ in each. my thinking was hold everything else constant - distance changes. therefore, it is half.

what prompts one to look at the gravitational force equation?

what i don't understand is how to come to the conclusion that angular velocities differ in each. my thinking was hold everything else constant - distance changes. therefore, it is half.

what prompts one to look at the gravitational force equation?

TPR says you should be asking "what causes centripedal acceleration", so in this case, it's FGrav... I would have never thought of this on my exam. thumbdown

Yes, but now you have 2 conflict equations, one that says it's proportional to 1/r and one that says it's proportional to 1/r^2. The best reasoning for using the gravitational equation was brought up by saying that, since the velocities were not stated to be equal, you can't use the centripetal force equation, whereas everything is constant except r in the gravitational force equation.

Using that equation assumes that their tangential velocities are equal, which is not the case. The tangential velocity is also dependent on the radius from earth. The easiest way to solve this is set centripetal force and then using the gravitational force equation, exactly how TBR explains.

TPR says you should be asking "what causes centripedal acceleration", so in this case, it's FGrav... I would have never thought of this on my exam. thumbdown

Using that equation assumes that their tangential velocities are equal, which is not the case. The tangential velocity is also dependent on the radius from earth. The easiest way to solve this is set centripetal force and then using the gravitational force equation, exactly how TBR explains.

Using that equation assumes that their tangential velocities are equal, which is not the case. The tangential velocity is also dependent on the radius from earth. The easiest way to solve this is set centripetal force and then using the gravitational force equation, exactly how TBR explains.

There's nothing conflicting about the two equations. F=mv^2/r is correct but both v and r change, so you cannot say anything directly from here unless you calculate what the magnitude of the velocity will be. It's much easier to consider that the only force acting is gravity and use that it is proportional to 1/r^2, like Tatertots said.

For a given tangential velocity there will be one acceleration (and one force) which keeps the body in uniform circular motion. If you vary the force, you can vary the velocity at which the body rotates around earth at a fixed distance. But since there are no additional forces described in the problem, the only force is due to gravity. That means that for a certain distance there will only one velocity at which UCM continues. That velocity will be different for different r.

For a given tangential velocity there will be one acceleration (and one force) which keeps the body in uniform circular motion. If you vary the force, you can vary the velocity at which the body rotates around earth at a fixed distance. But since there are no additional forces described in the problem, the only force is due to gravity. That means that for a certain distance there will only one velocity at which UCM continues. That velocity will be different for different r.

There's nothing conflicting about the two equations. F=mv^2/r is correct but both v and r change, so you cannot say anything directly from here unless you calculate what the magnitude of the velocity will be. It's much easier to consider that the only force acting is gravity and use that it is proportional to 1/r^2, like Tatertots said.

b. we have to ask ourselves some questions. first of all, what is changing in this question? we see that as radius increases, velocity changes too due to a changing force.

looking at F=mv^2/r, does it make sense to use this equation when there are three variables changing? no. what is an alternative so we can compare only two?

gravitational force works, since masses of the objects are constant and we can compare radius and force directly.

the important thing to learn, having read this thread, is that just because the question does not explicitly say velocity is changing doesn't mean you count out the possibility.

the important thing to learn, having read this thread, is that just because the question does not explicitly say velocity is changing doesn't mean you count out the possibility.

That's exactly what I didn't know/remember, that as radius increases the velocity decreases, so two variables no good - have to focus on one that works for both.

That's exactly what I didn't know/remember, that as radius increases the velocity decreases, so two variables no good - have to focus on one that works for both.

As the radius increases velocity decreases when something is in orbit(because angular velocity is not the same) with gravity but don't let this confuse your general circular motion questions. If two objects traveling in circular motion have the same w then the one with the largest radius is going to have the highest tangential velocity because v=rw.

A) It's a good question, I would use it if I was writing the test.
B) There is no distinction to be made - UCM is UCM and the formulas hold. What went wrong for me and OP is that we assumed the velocities are the same. There is nothing in the problem indicating that. You can start with that equation, derive what the velocities will be, plug them in and get the same result.

As the radius increases velocity decreases when something is in orbit(because angular velocity is not the same) with gravity but don't let this confuse your general circular motion questions. If two objects traveling in circular motion have the same w then the one with the largest radius is going to have the highest tangential velocity because v=rw.

This is the general equation of motion of a planet or comet (m) with the sun as origin of coordinates. m subscript j is the action of disturbing planets. This same equation can be used for the motion of a satellite around its primary.

Newton only describes the forces acting between two point masses that are inertial, not rotating or subject to acceleration. If the distance between m subscript a and m subscript b is r, then thf force acting between them is

F=k^2mamb/r^2

K depends on units of mass, time and length. If the sun, for example is taken as unity and mean solar day and astronomical unit as length then k= Gaussian constant (0.01720209895) this is exact.

This is the general equation of motion of a planet or comet (m) with the sun as origin of coordinates. m subscript j is the action of disturbing planets. This same equation can be used for the motion of a satellite around its primary.

all i meant was that the equation you posted wouldn't really help here because the vast majority of premeds are not well versed with such physics equations.

all i meant was that the equation you posted wouldn't really help here because the vast majority of premeds are not well versed with such physics equations.