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