Conservation of Momentum & Energy

Conservation of Momentum & Energy

Equation

L = mvr

2.11

Angular Momentum

Things that move in circles have angular or rotational momentum. This is the counterpart of linear momentum which applies to straight line motion. Angular momentum, L, is:

angular momentum = mass x velocity x radial distance
L = mvr

Notice that mv is the same as in linear momentum; the term r is the distance or radius from the center of the object that is spinning.

Like linear momentum, L is also conserved. The most common example of the conservation of angular momentum is the spinning ice skater. When the skater starts, she (and it always seems to be a female) extends her arms out, and then they are brought in toward her body, and she spins much more rapidly. Equation 2.10 shows why that happens. If mvr when starting to spin equals mvr when going fastest, the skater’s mass doesn’t change, so when r decreases (as arms are brought in) v must increase. Its all because of physics – the conservation of angular momentum. Here is a video of a skater setting the Guinness world record for spinning at 308 rpm – revolutions per minute.

Is this important in space? Yes! If you haven’t before, its time to consider neutron stars. The first was discovered by a graduate student in 1967 using a radio telescope that recorded pulses of energy every 1.3 seconds. At first it was thought that this might be the fabled LGM – Little Green Men, or an alien civilization – but further analysis showed that the rapid pulses were due to a tiny star that was rotating unbelievably fast - once every 1.3 seconds!

Neutron stars are thought to have begun as normal stars 10 to 20 times more massive than our Sun. When their radiation and gravity become unbalanced they collapse and explode as supernovae. In the collapse, atoms are squeezed together so tightly that they become more dense and hotter than any other known material. The neutron star which originally was huge and rotating in 10-30 days now is about the size of a city, and because of conservation of angular momentum, rotates in a second or less. Energy that is expelled from the poles of the star flashes pass Earth as the star rotates.

(A combined optical and x-ray image of the Crab Nebula, a star that exploded in 1054 AD and is now a powerful neutron star. NASA – Chandra image.)