Rotational Intertia of a rotating Space Station

In summary, the conversation discusses the calculation of the rotational inertia of a space station with four rockets attached to it, which exert a force of 65.5N and cause the station's angular velocity to increase at a constant acceleration of 3.63 x 10^-3 rads^-2. The solution involves using the equation τ=Iα and solving for I using the given values. The correct method is to multiply the force (N) by the distance (m), resulting in a torque unit of N-m, and then dividing by the acceleration (rads^-2) to get the correct units of kg-m^2 for the moment of inertia. The final answer for the moment of inertia is 808374.7 kg
  • #1
slingshotnz
2
0

Homework Statement


Four rockets attached to a (wheel) space station exert a force of 65.5N to rotate it . The space station's angular velocity is increased at a constant acceleration of 3.63 x 10-3 rads-2. Each rocket is 11.2m away from the centre. Calculate the rotational inertia of the system.

Homework Equations



τ=Iα , others unknown.

The Attempt at a Solution


Torque of all 4 rockets. (65.5N * 11.2) * 4 = 2934.4N
since τ=Iα, I=τ/α hence I= 2934.4/3.63x10-3 = 808374.7Kgm2

Can anyone confirm if this is the correct method.

Thanks.
 
Last edited:
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  • #2
The units for inertia are wrong. What are the derived units for the Newton? (Hint: F = ma)
 
  • #3
Sorry Kg metres squared?. Other than that does the working look fine? I appreciate the advice.
 
Last edited:
  • #4
Not sure, but I think SteamKing may be referring to this item:
slingshotnz said:
Torque of all 4 rockets. (65.5N * 11.2) * 4 = 2934.4N
force in N * distance in m gives what units?
(Your method and answer look ok.)
 
  • #5
I missed the torque units. But the units for moment of inertia should be kg-m^2. OP originally had kg-m^-2.
 

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is the measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of the object's mass relative to its axis of rotation.

2. How does rotational inertia affect a rotating space station?

A rotating space station experiences rotational inertia as it rotates, which causes it to resist changes in its rotational motion. This allows the station to maintain a stable and predictable rotation, even when external forces act on it.

3. How is rotational inertia calculated for a rotating space station?

The rotational inertia of a rotating space station can be calculated using the formula I = MR^2, where I is the rotational inertia, M is the total mass of the station, and R is the distance from the axis of rotation to the mass element being considered.

4. Can the rotational inertia of a rotating space station be changed?

Yes, the rotational inertia of a rotating space station can be changed by altering its mass or its distribution of mass. For example, adding or removing objects or shifting their position can change the rotational inertia of the station.

5. What are the practical implications of understanding rotational inertia for a rotating space station?

Understanding rotational inertia is important for designing and operating a rotating space station, as it allows for the prediction and control of its rotational motion. It also affects the energy required to change the rotation speed or direction of the station, as well as the stability and comfort of the environment for occupants.

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