A Classical Approach of Newtonian Mechanics

10 STATICS 10.6 Jointed rods

!

l 1

l 2

coordinate system correspond to the pivot point. The centre of mass of the first

rod is situated at its mid-point, whose coordinates are

(x 1 , y 1 ) = (0, l 1 /2).

Likewise, the centre of mass of the second rod is situated at its mid-point, whose

coordinates are

(x 2 , y 2 ) = (l 2 /2, l 1 ).

It follows that the coordinates of the centre of mass of the whole system are given

by

and

xcm = m^1 x^1 +^ m^2 x^2

m 1 + m 2

=

1 m 2 l 2

2 m 1 + m 2

=

3.4 × 0.7

2 × 8.6

= 0.138 m,

ycm =^

m 1 y 1 + m 2 y 2

m 1 + m 2

=

m 1 l 1 /2 + m 2 l 1

m 1 + m 2

=

5.2 × 1.3/2 + 3.4 × 1.3

8.6

= 0.907 m.

The angle θ subtended between the line joining the pivot point and the overall
centre of mass, and the first rod is simply

θ = tan−^1

xcm

= tan−^1 0.152 = 8.65◦.

ycm

When the system reaches a stable equilibrium state then its centre of mass is
aligned directly below the pivot point. This implies that the first rod subtends an

angle θ = 8.65◦ with the downward vertical.

pivot

x

y