From Mechanics

Theory

Exercises

Key Points

The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.

\displaystyle \text{Moment }=Fd \displaystyle \ \ \ \ \ \ \ \ \ \text{Moment }=Fd\sin \theta

Clockwise moments are negative. Anti-clockwise moments are positive.

Example 11.1 Find the moment of each force shown below about the point O.

(a) (b)

Solution (a) (b)

\displaystyle 20\times 0.8=16

\displaystyle 12\times 1.2=14.4

Moment is -16 Nm Moment is 14.4 Nm

Example 13.2 Find the moment of each force shown below about the point O. (a) (b)

Solution (a) (b)

\displaystyle 40\times 3\sin 60{}^\circ =104

\displaystyle 100\times 2\sin 20{}^\circ =68.4

Moment is 104 Nm (to 3 sf) Moment is 68.4 Nm (to 3 sf)

Example 13.3 For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.

Solution

Force Moment 5N at O \displaystyle 5\times 0=0

8 N \displaystyle -8\times 1.2=-9.6

7 N \displaystyle 7\times 0=0

6 N \displaystyle -6\times 0.5=-3

5 N \displaystyle 5\times 1.2=6

4 N \displaystyle 4\times 0.5=2

Total Moment \displaystyle 0-9.6+0-3+6+2=-4.6\text{ Nm}