Torque and inertia of a space object

[ac7597]

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

 

[PeroK]

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?

 

[ac7597]

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

 

[kuruman]

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?

 

[PeroK]

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.