# Centripetal Force / circular motion question

• Latinized
In summary, the first question is asking for the period of rotation of a space station so that an astronaut inside will feel a normal force equal to 60% of their weight on Earth. This force is caused by the centripetal force of the station's circular motion and is unrelated to the force of gravity. In contrast, the second question is asking for the orbital radius of a satellite around Mars, where the force of gravity is a significant factor in determining the satellite's motion.
Latinized

## Homework Statement

I'm not asking for a full on solution to my question, but instead wanted to know what was the difference in these two questions. So, here are the two questions
1) A space station of radius 90 m is rotating to simulate a gravitational field.

What is the period of the space station’s rotation so that a 70 kg astronaut will experience a normal force by the outer wall equal to 60% of his weight on the surface of the earth?
Now the solution to the equation is fairly simple for me, however I don't get why the force of gravity does not matter for the centripetal force in this question.
Fnet = mac
Fn = m4(pi)^2 (r)/ T^2
0.60 mg = m4(pi)^2 (r)/ T^2
T = 25s
While in this question:
2) A 720 kg communication satellite is in synchronous orbit around the planet Mars. This synchronous orbit matches the period of rotation so that the satellite appears to be stationary over a position on the equator of Mars. What is the orbital radius of this satellite?
Here, in this question, the force of gravity does matter for the centripetal force. Why is that when #1 it didn't matter.
Solution btw:
Fg = mac
GmM/R^2 = m4π^2/ T^2
r = 2.0 x 10^7 m

Thank you very much! Sorry for the long post.

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Hello Latinized,
Latinized said:
0.60 mg = m4(pi)^2 (r)/ T^2
There is a factor ##g## in your expression, so the magnitude of ##g## does matter for the outome ... and, like in the other question, ##g## depends on ##G##.

BvU said:
Hello Latinized,
There is a factor ##g## in your expression, so the magnitude of ##g## does matter for the outome ... and, like in the other question, ##g## depends on ##G##.
That g is for the astronaut's normal force on earth. The question says that what period must be for the Fn on the astronaut to be 60% of his weight on earth. Thus 0.6 mg is the Fn.

Latinized said:
however I don't get why the force of gravity does not matter for the centripetal force in this question.
and my response was that the force of gravity does matter: the normal gravitational force on the surface of the earth, mg, is proportional to the gravitational constant: ##\ g={GM_{\rm earth}\over R_{\rm earth}^2}## , just like you used in the second exercise.

BvU said:
and my response was that the force of gravity does matter: the normal gravitational force on the surface of the earth, mg, is proportional to the gravitational constant: ##\ g={GM_{\rm earth}\over R_{\rm earth}^2}## , just like you used in the second exercise.

I should have been more clear earlier. I meant why is the force of gravity on the astronaut in the space station not included in the centripetal force for that question.

Ah, misunderstanding.

For this exercise 1 the space station is supposed to be either far away from all planetary or stellar gravitational influences, or in orbit around a planet (which means in a state of free fall) .

So the only force is from having to follow the circular trajectory

Wouldn't the space station still experience a force of gravity when it's in orbit? That is exactly what the satelitte experiences and it is in orbit in question 2. Plus if something is in free fall, there has to be a force of gravity.

Latinized said:
Wouldn't the space station still experience a force of gravity when it's in orbit?
The effect of gravity on the space station is to keep it in orbit around the planet it is circling. If a space capsule (rotating or not) is affected by gravity and an astronaut inside is affected by gravity, what will the astronaut "experience"?

Latinized said:
Plus if something is in free fall, there has to be a force of gravity.
The term "free fall" means that there are no external forces other than gravity. It does not imply that there is any force from gravity. Often, as in this case, it means that any external force from gravity can be ignored.

BvU

## 1. What is centripetal force?

Centripetal force is the force that acts on an object moving in a circular motion, directed towards the center of the circle. It is responsible for keeping the object in its circular path and preventing it from flying off in a straight line.

## 2. How is centripetal force different from centrifugal force?

Centripetal force is the actual force acting on the object, while centrifugal force is a perceived force that appears to push the object outwards due to its inertia. In reality, there is no centrifugal force, it is just the object's tendency to continue moving in a straight line.

## 3. What are some real-life examples of centripetal force?

Some common examples of centripetal force include the Earth's gravitational force keeping the Moon in its orbit, a car turning a corner, or a person swinging a bucket of water in a circle without spilling it.

## 4. What is the relationship between centripetal force and circular motion?

Centripetal force is necessary for an object to move in a circular path. Without this force, the object would continue moving in a straight line due to its inertia. The magnitude of the centripetal force is directly proportional to the object's mass, velocity, and the radius of the circular path.

## 5. How is centripetal force calculated?

The formula for calculating centripetal force is Fc = mv²/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 circular path. This formula can be derived from Newton's second law of motion, F=ma, by substituting a with v²/r.

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