Answer to Question #111745 in Mechanics | Relativity for evonn

Question

If kinetic energy of an object is been constant at all times, how does momentum of that object works?.....i think kinetic energy can change to another type of energy such as potential energy(ex:projected ball).that is the way energy is conserved.but here is asking about a motion which kinetic energy is always constant.then how momentum works of that object??i think there is no doubt about linearly motions,because if kinetic energy is constant ,momentum also constant. (mv*v) /2=k ,m is constant .v is also constant. if there`s a direction change in linear motions v should get zero for a moment. it`s mean in there kinetic energy is not constant,that`s why i`m saying there is no doubt about linear motions. because if k is constant then p is also constant.but in angular motions(circle) if kinetic energy is constant ,then linear momentum is not constant. because of the change of direction.but angular momentum can be constant.because we get it using the right hand law.am i right or not?

Answer 1

1.Your conclusion is correct but they don't take into account case when $m$ is a change.

If $E=mv^2/2$ and $\vec{p}=m\vec{v}$ then $|\vec{p}|=\sqrt{2mE}=\sqrt{2k}\sqrt{m}=const\sqrt{m}$ or

$m|\vec{v}|=const\sqrt{m}$ then $|\vec{v}|=\frac{const}{\sqrt{m}}$ . With an increase in $m$ ,$v$ decreases and vice versa.

2.In angular motion (circle) with $|\vec{v}|=const$ angular momentum must be constant.