When an object is rotating on an axis, it has stored rotational energy in it. Since energy and mass are related, does this stored rotation increase the mass of the object? And if so, will it be harder to move the rotating object in a linear direction than when it is not rotating? Does the rotating object have more inertia? Is there more force required when you push in a linear direction to make it go to the same speed as with a non-rotating object? With pushing and linear direction I mean causing a translational motion. And furthermore, does the rotating object have a stronger gravitational pull?
[Physics] Does a rotating object have more inertia, mass and gravitational pull
energyforcesinertiakinematicsmass
Related Solutions
Imagine two masses connected by a spring, like this:
If the entire thing spins at a constant angular velocity, the masses are moving in circles. Then $m_1$ and $m_2$ must have forces on them, since circular motion is a form of accelerated motion.
These forces are supplied by the spring. The spring will stretch somewhat, exerting forces pulling the masses back towards their equilibrium position. The magnitude of these forces is the usual centripetal force $m \omega^2 r$.
Now suppose you have a disk rotating like this:
The situation is very similar. If you take a point on this disk (besides the center), it's going in a circle. Therefore, this point has a centripetal acceleration, and must feel a force. Where is this force coming from?
The answer is that the force is coming from the disk itself. Imagine the disk as being a mesh of many points, all connected by springs. When you start the disk spinning, all the springs will stretch a little bit, exerting forces on the masses they're connected to. The net force of the springs on any given mass will be the centripetal force.
The way we usually express this is to say the entire disk is under tension (negative pressure). The tension decreases from a maximum at the center to zero at the edge. The gradient of the tension gives the force per unit volume, and that force is $\omega^2 r \rho \mathrm{d}V$ on a volume element $\mathrm{d}V$.
The moment of inertia is merely a generalisation/application of the ‘usual’ inertia to rotations. Since translations and rotations are different kinds of motion, it appears sensible (to me) to have different kinds of inertia associated with them.
Regarding your second question: Imagine a particle at position $(x,0,0)$ which you would like to rotate with angular velocity $\omega$ about the $(0,0,z)$ axis. To do so, you have to initially accelerate the particle along the $(0,y,0)$ axis to velocity $v_y = \omega x, v_{x,z} = 0$, as this is the velocity the particle would have at this point if it were already rotating.
As you can clearly see, the momentum $p$ associated with this velocity is proportional to $r$ ($p_y = m v_y = m \omega x$), hence it takes more energy to accelerate a particle to angular velocity $\omega$ if it is further away from the centre of rotation. As this is exactly the quantity described by the ‘moment of inertia’, the moment of inertia depends on the radial distance of the mass.
Best Answer
If the object is spinning close to the speed of light then it has significantly more energy than if it were at rest. This does contribute to an increase in gravitational pull and is significant in astrophysical phenomena like neutron stars!
https://arxiv.org/abs/1003.5015
The Earth is also more massive because its spinning but we have no hope of detecting the slight difference due to this effect.