# Is there any relation between inertia and momentum?

Inertia is the that property of an object because of which that object resists a change in its state of rest or motion.

Momentum of an object is the product of mass and velocity, or its the quantity of motion an object with mass have.

Both of these terms are related to rest mass, or rest energy of an object.

So is there any relation between inertia and momentum, or is their any better definition of anyone which more closely relates both of them ? Pls explain

An intuitive way to imagine momentum is how hard it is to stop a moving object.

For example it's easy to stop a tennis ball going at 10m/s, but not easy to stop a car going at the same speed. Which would you rather stand in front of and try to stop?

momentum is mass times velocity.

It's easy to stop a car going at 0.1m/s, but hard to stop a tennis ball going at 2000m/s.

According to special relativity, we could imagine these objects as stopped initially (by moving with them in a moving reference frame at their own velocity) and in each case we have to accelerate them to the same speed that they had in the original frame - then they would be stopped in the original frame.

The same impulse would be needed.

But this time, as we are accelerating an object from zero speed, it feels like the inertia of the object is providing the resistance to the motion, instead of us experiencing the momentum of the object.

• Ohh I see, that's actually a really nice explanation. Thank you very much. But a small question, when a body is moving, and when we stop it, did momentum provided the difficulty or inertia of motion or both? Aug 6, 2021 at 14:31
• @ Shriesh Kumar it's probably just a matter of what people mean by the different expressions: 'inertia' sounds like resistance to motion when something is accelerated from rest, but 'momentum' and 'inertia of motion' sound like the same thing, so either could be said to provide the difficulty Aug 7, 2021 at 21:20
• Ok, thank you again for helping me. Aug 9, 2021 at 2:41

One difference is that mass is a property of an object, while momentum is not.

To get momentum, you need velocity. Velocity is always relative to another object. Or to say it another way, to a coordinate system, a frame of reference. (You can imagine an object sitting at the origin of the coordinate system.)

Suppose you are floating in space, and two spaceships drift by at different velocities. Each will say you have a different speed and therefore a different momentum. You will say your speed and momentum are $$0$$. But all of you will agree on your mass.

Suppose an asteroid drifts by and hits you. You bounce off. Both you and the asteroid change velocity. All three observers have different numbers for the momenta of you and the asteroid before and after. But all will agree on the change in your momentum and the asteroid's momentum. All will agree that momentum was conserved.

• Since I know these basics of Special Relativity, your explanation helped understand momentum really well. Thank you so much. Aug 6, 2021 at 14:34

yes there is relation between inertia and angular momentum (L) and angular velocity in rotational dynamics which is given by $$L=I\omega$$

Inertia is a phenomenon. We measure it using the measure "mass".

Motion (your words) is a phenomenon. We measure it using the measure "momentum". It happens to contain "mass" in its formula.