Physics: Mechanics 1

Physics

Vectors and scalars

• Scalars have a magnitude only
• Vectors have both magnitude and direction
• we can resolve a vector into horizontal and vertical components
• components of vectors are added to give the resultant force
• missing vectors can be calculated using trigonometry

Balancing forces

Coplanar:

• an object is in equilibrium if the forces acting on it are balanced
• an object with zero acceleration is moving at a constant velocity or remaining at rest
• the resultant force of an object in equilibrium is zero
• the resultant force is the vector sum of all forces acting on a body
• coplanar forces act in one plane

On a slope

• For an object in equilibrium on a slope we resolve perpendicular and parallel to the slope, which must balance
• for an object in equilibrium, when three forces act upon a body, the sum of any two forces = magnitude of the third

Principle of moments

• the moment of a force about a point is defined as:

    force x perpendicular distance between line of action and the point

• the principle of moments states that for a body in equilibrium

    sum of clockwise moments = sum of anticlockwise moments

• the centre of mass of a body is the point through which a single force has no turning effect
• when there is one normal reaction force, moments are taken around it to render its moment zero
• in set ups with two normal reaction forces, moments are taken around one
• a torque is a pair of equal and opposite forces acting on the same body with differing lines of action

        torque = one of the forces x perpendicular distance between the lines of actions                                .                       of the forces