Physics Answers - Part 2

Two objects have the same kinetic energy. Which one has the bigger magnitude of momentum?

The more massive object will have a greater linear momentum.

Lets look at an example here: Take two objects. One of mass 3 kg and the other of mass 1 kg. Assume they have the same Ek = 9 J.

Since Ek = 1/2m(v^2) we can rearrange and solve for v therefore v = (2*Ek/m)^0.5.

For the more massive object v = 2.45 m/s

For the less massive object v = 4.24 m/s.

Now lets go to linear momentum

p for more massive object = mv = (3)(2.45) = 7.35 kgm/s

p for the less massive object = mv = (1) (4.25) = 4.25 kgm/s.

So why is it the case? The reason is that in order for Ek to be equal a high mass must be offset with a lower v squared. Sounds good. However linear momentum is the product of mass and velocity. Velocity on its own cannot offset mass to the extent that velocity squared can in the Ek equation therefore the linear momentum of the larger object dominates. Think of this as the power of squares.

Does direction matter in momentum?

Very much so. Linear momentum is a vector quantity and therefore has a directional aspect to it. Here is an example to think about. Two carts with the same mass moving toward each other with the same speed have equal magnitudes of linear momentum. However their velocity vectors are 180 degrees reversed which implies that the linear momentum of each have opposite directions.

Remember that the linear momentum of an object is the product of its mass and its velocity. This means that the total momentum for the system - where the system is defined as both cars only - is equal to 0 kgm/s. Momentum vectors cancel each other out for the system as a whole. Not so for each cart specifically.

Could the universe exist without gravity? If so how would it look?

Yes you could have such a universe hypothetically however it will look extremely different to anything we could conceive of. You will for one have no large clumping of matter. So don’t expect to find any planets, stars, stellar clusters, galaxies, galactic clusters etc.

You would still likely have atoms as the nuclei of these are hold together by the nuclear forces (strong and weak) with the electromagnetic force ensuring that the electrons are attracted to the nuclei. Other than that…Who knows? A giant particle soup makes sense. Also without gravity one could expect this universe to have no resistance to expansion so that it will likely proceed to an eventual big rip at a faster rate.

What is the difference between momentum and Inertia?

Inertia is the property of matter that resists a change in motion or acceleration. It is directly related to the mass (sometimes called Inertial Mass) of the object and is measured in kilograms. Mass of course, in the classical world, refers to the amount of matter an object contains and is a scalar quantity.

Linear Momentum is a vector quantity and can be viewed as essentially ‘intertia-in-motion’. It is the product of the object’s mass and its velocity. It has units of kg.m/s or N.s.

In the world of modern physics - the linear momentum of a massless particle (eg. a photon) can be determined by dividing Planck’s constant (h) with the wavelength of the photon. This expression comes from a rework of the linear momentum equation based using the notion of mass-energy equivalency.