Torque and inertia of a space object

In summary: It's like the problem of the astronaut pushing off from the space station. The space station has to move away by the same amount as the astronaut but it has a much greater mass.In summary, the alien artifact that Vasily encounters while spacewalking has a mass of 524 kg and a radius of 6 meters. It is spinning slowly at an angular velocity of 0.16 radians per second. The object's moment of inertia is 18.86E3kg*m^2 and its rotational kinetic energy is 241.5 J. When Vasily presses his glove against the surface with a normal force of 57 N and a coefficient of kinetic friction of 0.25, the torque applied to the object is
  • #1
ac7597
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Homework Statement
Vasily Kosmonaut takes a spacewalk near an alien artifact which is floating in space, somewhere between Mars and Jupiter. The object appears to be a large hoop of some shiny substance, with radius R=6 meters and mass M=524 kg. The object is spinning slowly at an angular velocity of ω=0.16 radians per second.

What is the object's moment of inertia?
What is the object's rotational kinetic energy?

Vasily approaches the object and sticks out his hand to touch it. He presses his glove against the outer rim of the spinning hoop with a normal force of F=57 N. The coefficient of kinetic friction between his glove and the shiny surface is μk=0.25.

What is the magnitude of the torque applied to the object by Vasily?

The object begins to rotate more slowly. What is the magnitude of the angular acceleration of the hoop?

If Vasily maintains this force on the surface, how long will it take for the artifact to stop spinning?
Relevant Equations
I= mass * radius^2
KE=(1/2) (I) (angular velocity)^2
torque= F* (distance)
I= 524kg * 6m^2 = 18.86E3kg*m^2
KE=(1/2) (18.86E3kg*m^2) (0.16 rad/s )^2= 241.5 J

torque= 0.25* 57N* (6m)=85.5 N*m
 
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  • #2
ac7597 said:
Homework Statement: Vasily Kosmonaut takes a spacewalk near an alien artifact which is floating in space, somewhere between Mars and Jupiter. The object appears to be a large hoop of some shiny substance, with radius R=6 meters and mass M=524 kg. The object is spinning slowly at an angular velocity of ω=0.16 radians per second.

What is the object's moment of inertia?
What is the object's rotational kinetic energy?

Vasily approaches the object and sticks out his hand to touch it. He presses his glove against the outer rim of the spinning hoop with a normal force of F=57 N. The coefficient of kinetic friction between his glove and the shiny surface is μk=0.25.

What is the magnitude of the torque applied to the object by Vasily?

The object begins to rotate more slowly. What is the magnitude of the angular acceleration of the hoop?

If Vasily maintains this force on the surface, how long will it take for the artifact to stop spinning?
Homework Equations: I= mass * radius^2
KE=(1/2) (I) (angular velocity)^2
torque= F* (distance)

I= 524kg * 6m^2 = 18.86E3kg*m^2
KE=(1/2) (18.86E3kg*m^2) (0.16 rad/s )^2= 241.5 J

torque= 0.25* 57N* (6m)=85.5 N*m
Looks okay as far as you got.

I wonder how you would know the mass of something floating in space? How did Vasily know the mass was ##524kg##?

One way would be to apply a known torque and measure the angular acceleration. In a way, therefore, this question is the wrong way round. The purpose should be to find the mass of the object.

Why do people setting physics problems not think like this?
 
  • #3
Since torque=85.5N*m
85.5N*m= (18.86E3kg*m^2) (angular acceleration)
angular acceleration= 4.5E-3rad/s^2

0= 0.16rad/s + (-4.5E-3rad/s^2)(time)
time=35.5 seconds
 
  • #4
PeroK said:
Why do people setting physics problems not think like this?
Why indeed. I think the last 3 questions of this problem are not well thought out. Isn't Vasily's mass needed? Will Vasily not be accelerated by the friction the artifact exerts on him? This problem is analogous to the spinning turntable on which a mass is dropped at its rim. There are no external torques acting on the artifact + Vasily system so the angular momentum of that system must be conserved. $$I_{art.}\omega_i=(I_{art.}+m_{Vas.}R^2)\omega_f.$$ Also, the artifact will not stop spinning unless Vasily has infinite mass, no?
 
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  • #5
kuruman said:
Why indeed. I think the last 3 questions of this problem are not well thought out. Isn't Vasily's mass needed? Will Vasily not be accelerated by the friction the artifact exerts on him? This problem is analogous to the spinning turntable on which a mass is dropped at its rim. There are no external torques acting on the artifact + Vasily system so the angular momentum of that system must be conserved. $$I_{art.}\omega_i=(I_{art.}+m_{Vas.}R^2)\omega_f.$$ Also, the artifact will not stop spinning unless Vasily has infinite mass, no?

Yes, that's a particularly good point given its mass is about four-five time that of Vasily plus his spacesuit.
 

Related to Torque and inertia of a space object

1. What is torque and inertia?

Torque is a measure of the rotational force applied to an object, while inertia is an object's resistance to changes in its state of motion.

2. How do torque and inertia affect a space object?

Torque and inertia play a crucial role in the movement and stability of a space object. They determine how the object will respond to external forces and how it will maintain its orientation and trajectory in space.

3. How are torque and inertia measured?

Torque is typically measured in units of newton-meters (Nm), while inertia is measured in units of kilogram-meters squared (kg•m²).

4. Can torque and inertia be altered?

Yes, torque and inertia can be altered by changing the mass, shape, or distribution of mass of a space object. For example, adding thrusters or adjusting the position of weight can alter the torque and inertia of a spacecraft.

5. What are some real-world applications of torque and inertia in space exploration?

Torque and inertia are essential for maneuvers such as docking, orbit changes, and attitude control of spacecraft. They are also critical for maintaining the stability and orientation of satellites and other space objects in orbit.

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