Some Things Never Change!
i) Momentum
ii) Angular Momentum
iii) Energy
iv) Charge, etc
Conservation of Momentum p mv
In the absence of an external force, the total linear momentum of a system remains constant.
Before Collision
After Collision
v1i v2i
v1fv2f
m1 m2
Impulse = change in momentum
F t m v m vf i1 1 1 1 1
F t m v m vf i2 2 2 2 2
F1 2F F
Newton’s 3rd: F t F t1 2
m v m v m v m vf i f i1 1 1 1 2 2 2 2 ( )
2F
m v m v m v m vf f i i1 1 2 2 1 1 2 2
final momentum = initial momentum Conserved!
Is momentum conserved if you jump up from the earth?
What about a Mexican jumping bean?
Problem: A canon of mass 100 kg is initially at rest and fires a 1 kg canonball with speed 75 m/s horizontally. What is the recoil velocity of the canon?
Mm
Demo of carts on track
Gun aimed downward
Total momentum zero
mV
Mv
0ip 0f rocket exhaustp Mv mV
Molecular bullets
rocketMv
exhaustmv
Conservation of Angular Momentum
For point mass around circle,
L mvrIf there are no external torques, angular momentum is conserved.
mvR mVr Rr
Conservation of Energy
The total energy of an isolated system is always conserved.
Conservative forces: work done by conservative force is independent of path taken.
A BAllow you to define potential energy.
If you have only conservative forces, then the sum of potential and kinetic energy is conserved.
i i f fKE PE KE PE
For gravity near earth’s surface,
2 21 1
2 2i i f fmv mgy mv mgy
Roller coaster
10 m
5 m 8 m
A B C D
If initially at rest at A, what is speed at B, C, D?
Other conservation laws:
Conservation of Baryon number (nucleon number):
Alpha decay: nucleus emits helium nucleus (alpha particle).
138 n
88 p
8 82 2 6Ra
136 n
86 p
8 62 2 2 Rn
+
24 He
parent daughter
ZA
ZAX Y H e
24
24
Baryons interact via strong nuclear force, e.g. protons and neutrons.
Conservation of electric charge
Possible particle reaction:
p n p n p p B = +1 +1 = +1 +1 -1 +1
Conservation of Lepton number
Leptons interact via weak nuclear force, e.g., electrons and neutrinos.
en p e Neutron decay
L = 0 = 0 + 1 - 1
