Everything Science Grade 12

6.3 CHAPTER 6. MOTIONIN TWO DIMENSIONS

6.3 Conservation of Momentum in Two Dimensions

ESCDB

We have seen in Grade11 that the momentum of a system is conserved when there are

no external forces actingon the system. Conversely, an external force causes a change

in momentum Δp, with the impulse delivered by the force, F acting for a time Δt

given by:

Δp = F· Δt

The same principles that were studied in applying the conservation ofmomentum to

problems in one dimension, can be applied to solving problems in two dimensions.

The calculation of momentum is the same in twodimensions as in one dimension. The

calculation of momentum in two dimensions isbroken down into determining the x

and y components of momentum and applying the conservation of momentumto each

set of components.

Consider two objects moving towards each other as shown in Figure 6.4. We analyse

this situation by calculating the x and y components of the momentum of each object.

vi 1 y

vi 1 x

vi 1

m θ^1

1

vi 2 y

vi 2 x

vi 2

θ (^2) m
2
�

P

(a) Before the collision

vf 1 y

vf 1 x

vf 1

φ 1

m 1

vf 2 y

vf 2 x

vf 2

φ 2

m 2

P�

(b) After the collision

Figure 6.4: Two balls collide at point P.

Before the collision

Total momentum:

pi 1 = m 1 vi 1

pi 2 = m 2 vi 2