Everything Science Grade 11

CHAPTER 12. FORCE,MOMENTUM AND IMPULSE 12.5

The magnitude of the average velocity is the same as the speed. Therefore:

s =

d

Δt

We are given the time the Moon takes for one orbit but not how far it travels

in that time. However, we can work this out fromthe distance to the Moon and

the fact that the Moon has a circular orbit. Using the equation for the circumfer-

ence, C, of a circle in terms of its radius, we can determine the distance travelled

by the Moon in one orbit:

C = 2πr

= 2π(3, 844 × 108 m)

= 2, 42 × 109 m

Combining the distancetravelled by the Moonin an orbit and the time

taken by the Moon to complete one orbit, wecan determine the magnitude of

the Moon’s velocity or speed,

s =

d

Δt

=

C

T

=

2 , 42 × 109 m

2 , 36 × 106 s

= 1, 02 × 103 m· s−^1.

Step 3 : Finally calculate the momentum and quote theanswer

The magnitude of the Moon’s momentum is:

p = m· v

= (7, 35 × 1022 kg)(1, 02 × 103 m· s−^1 )

= 7, 50 × 1025 kg· m· s−^1

Vector Nature of Momentum ESBFG

As we have said, momentum is a vector quantity.Since momentum is a vector, the techniques of vector
addition discussed in Chapter 11 must be used tocalculate the total momentum of a system.