Engineering MechanicsLecture 3

5/10, Friday

4-5am

Tendency of Force to Rotate a Body

Two effects of force: 1) Move a body in the direction of its application2) Rotate a body around an axis.

Moment Arm

M Fd

Tendency of the force to rotate a bodyIs proportional to

F and d

d: perpendicular distance from the axis to the line of force action

Right-Hand Rule

Moment in the direction of thumb

Fingers curl in the direction of the tendency to rotate

Sign of Moment (2D Convention)

Plus sign (+): counter clockwiseMinus sign (-): clockwise

Many-Particle Interactions

1

2f21

f13

3

f12

f31

f23

f32

F3

F1

ii

F 0

For an N particles system, in equilibrium

Many-Particle Interactions

i ijj i

F f 0 1,2,i

i i i iji i j i

r F r f 0

i i i ijj i

r F r f 0

For an N particles system, in equilibrium

Can you prove: i iji j i

r f 0 ?

i ii

r F 0Therefore:

Need Newton’s 3rd law

Newton’s 1st law:

Many-Particle System

For a N-particle system, in equilibrium

i ii

r F 0

ii

F 0 resultant force 0

resultant moment (torque) 0