Mechanics 1 - Scalars, Vectors and moments

• The two conditions required for an object to be in equilibrium are: the resultant force must be zero and the resultant moment around any point should be zero.
• The vector quantities are: Velocity, Acceleration, Force, Displacement, Weight, Momentum
• The scalar quantities are: Speed, Distance, Mass, Energy, Power, Temperature
• Force vectors can be arranged to show that an object has constant velocity. Vectors make a closed shape when rearranged (by scale drawing) or you can resolve into components where total up forces = total down forces and total left forces = total right forces
• The centre of mass is the point in a body where the weight of the object appears to act. Also, the resultant moment about this point = 0
• The moment of a force is the product of the force and the perpendicular distance from the line of action of the force to the point.
• The principle of moments is the sum of the clockwise moments about a point is equal to the sum of the anti-clockwise moments for a system in equillibrium.
• A couple is a pair of equal and opposite coplanar forces which do not act along the same line of action
• An object is uniform if it has a constant density so its centre of mass acts from the physical centre point of the object.
• Moments should be used in any situation that has two unknown forces acting on an object.