Rotating objects in non-inertial frames

In summary, a non-inertial frame is a reference frame in which Newton's first law does not hold true, causing objects to experience fictitious forces. Rotating objects in non-inertial frames will appear to deviate from their expected motion, due to the presence of fictitious forces such as the Coriolis effect. These effects can be mathematically described using the laws of rotational motion and equations for non-inertial frames. It is important to consider rotating objects in non-inertial frames for scientific and engineering applications, as well as for making accurate predictions and calculations.
  • #1
frenchyc
4
0
So the homework question is this. In a donut shaped space station that is rotating, what is the force on an astronaut inside the space station (he is on the outside) in both an inertial frame, and the frame of the space station.

Intuitively in the frame of the space station the two forces are a)The centripital force and b) the normal force of the space station.

However when i try to think of the forces on the astronaut in a inertial frame my mind goes blank. Any ideas?
 
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  • #2
Newton's 2nd law.
 
  • #3


In an inertial frame, the astronaut is experiencing two forces: the force of gravity pulling them towards the center of the donut-shaped space station, and the force of inertia pushing them outwards due to the rotation of the station. These forces are equal in magnitude but opposite in direction, resulting in the astronaut feeling weightless.

In the frame of the rotating space station, the astronaut is experiencing the centrifugal force pushing them away from the center of rotation, and the normal force of the space station pushing them towards the center. These forces are also equal in magnitude but opposite in direction, resulting in the astronaut feeling a sense of gravity towards the outer walls of the station.

It is important to note that the concept of force in a non-inertial frame is different from that in an inertial frame. In a non-inertial frame, fictitious forces, such as the centrifugal force, are introduced to account for the observed motion of objects. These forces do not exist in an inertial frame and are a result of the chosen reference frame. In an inertial frame, only real forces, such as gravity and inertia, are considered.

In summary, the force on an astronaut in a donut-shaped space station depends on the chosen frame of reference. In an inertial frame, the astronaut experiences weightlessness due to the balance of gravity and inertia. In the frame of the rotating space station, the astronaut experiences a sense of gravity towards the outer walls due to the centrifugal force and normal force of the station.
 

1. What is a non-inertial frame?

A non-inertial frame is a reference frame in which Newton's first law of motion (the law of inertia) does not hold true. This means that objects in a non-inertial frame will experience fictitious forces, such as centrifugal and Coriolis forces.

2. How do rotating objects behave in non-inertial frames?

In a non-inertial frame, rotating objects will appear to experience fictitious forces that cause them to deviate from their expected motion. For example, a pendulum swinging in a rotating frame will appear to be deflected in a direction opposite to the rotation.

3. What is the Coriolis effect?

The Coriolis effect is a fictitious force that appears to act on objects in a rotating reference frame. It is responsible for the curved paths of objects moving in a rotating frame.

4. How do we mathematically describe the motion of rotating objects in non-inertial frames?

The motion of rotating objects in non-inertial frames can be described using the laws of rotational motion and the equations of motion in non-inertial frames, which take into account the fictitious forces acting on the objects.

5. Why is it important to consider rotating objects in non-inertial frames?

Understanding the behavior of rotating objects in non-inertial frames is important in many scientific and engineering applications, such as navigation systems, spacecraft dynamics, and the motion of objects on Earth's surface. It also allows us to make accurate predictions and calculations in these situations.

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