Spinning object losing mass implies torque?

[mishima]

Does a spinning uniform object which is losing mass experience a change in angular velocity?

It seems to me the angular momentum changes due to a change in the moment of inertia of the object, which depends on mass. The angular momentum of the object would decrease, if we just look at the object alone (L=Iw). So there is some torque since change in L implies a torque. But then that also means an angular acceleration so that w is not constant.

The answer given is that angular velocity for the object is constant. Why?

 

[rcgldr]

Assuming no external forces, the angular (and linear) momentum of the closed system consisting of the spinning object and any "lost" mass remains constant, so it depends on how the object is losing mass.

 

[tiny-tim]

treat it as two bodies, a big mass and a little mass …

the question is, does the angular velocity of the big mass change?

(and the only force on the big mass is the "kick" from the little mass, if any)

 

[mishima]

There is no force on the big mass during release, the released weight follows a tangent to the path of the extremity of the object. This should imply no torque and no change in angular velocity. Like if a spinning ice skater had weights attached to her outstretched arms and then the weights were released by some mechanism. I guess its just counter intuitive to me that the skater would not change angular speed in that case.

 

[asteriatic]

The statement that the angular velocity is constant may not be entirely accurate. While the angular velocity may remain relatively constant, there will likely be a decrease in angular velocity as the mass of the object decreases. This is because the moment of inertia, which is a factor in calculating angular velocity, is dependent on mass. As the mass decreases, the moment of inertia decreases as well, leading to a decrease in angular velocity. However, it is possible that the decrease in mass is small enough that the change in angular velocity is negligible and can be considered constant. Additionally, other factors such as external forces or friction may also play a role in the change of angular velocity. In general, the concept of torque and angular velocity is complex and requires a more detailed analysis to fully understand the effects of a spinning object losing mass.