# Does a rotating object have more inertia, mass and gravitational pull?

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?

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.

• Thanks, but without reading that paper, will the object that's spinning have more inertia too? And therefore be harder to push? Sep 15 '15 at 18:54
• Yes it will be harder to push. Sep 15 '15 at 19:33

As per mass-energy relation, mass of object (ignoring relativity effects) is : $$m = \frac E {c^2}$$

Energy of object can be split into initial (rest, etc) and translational + rotational kinetic energies : $$m = \frac {E_{_0} + 0.5~mv^2 ~+ 0.5~I\omega^2} {c^2}$$

Gravity and inertia are directly proportional to the object mass, so answer is YES to your all three questions.

In addition to that, it's worth to mention that ALL energy types which object accumulates affects it's mass. Including, but not limited to heat stored as internal energy distributed as molecules average kinetic speed. In hot object molecules moves more faster, so has bigger kinetic energies, thus making hot body more heavier than cold.

Also interesting fact that 3 quark masses in a nucleon (proton/neutron) accounts only for $$1\%$$ of nucleon mass, the rest $$99\%$$ of mass - binding energy between quarks. Given that most atom mass is concentrated in a nucleus, composed from nucleons,- all ordinary matter (thus mass) IS actually a pure quantum mechanical binding energy.