This mind map includes a lot of concepts such as moments, CG, Center of mass, stability, Hooke's Law, objects in equilibrium and pressure (Atmospheric & Hydrostatic Pressure).
1.1 Defined as the product of the force and the perpendicular distance
from the pivot to the line of action of the force.
1.1.1 Moment of a force about the pivot = F x d ,
where F= force and d=perpendicular
distance from the pivot
1.1.1.1 Moments have a unit of Nm
1.1.1.2 The equation of moments can also be t = r x F , where t = torque
(another term for moments), r = radius (picture the distance from the
pivot as a radius) and F = force.
1.1.2 is a vector quantity, since force is
also a vector quantity.
2 2. Centre of Mass and Centre of Gravity
2.1 Centre of Mass
2.1.1 The Centre of Mass of a body is a single point at which the
entire mass of the body is considered to act.
2.2 Centre of Gravity
2.2.1 The Centre of Gravity of a body is a single point at which the
entire weight of the body is considered to act.
2.3 At places with uniform gravitational fields, (where gravitational force is constant),
the Centre of Mass coincides with the Centre of Gravity.
2.3.1 Objects close to the ground are under uniform gravitational fields,
so their Centre of Mass and Gravity coincides.
2.3.2 Gravitational force decreases with increasing distance from the ground.
2.3.2.1 A tall building has a Centre of Gravity that is lower than its Centre of Mass.
3 3. Stability
3.1 An object is said to be in stable equilibrium if it returns to
its original position after being displaced slightly.
3.1.1 Toppling occurs when the centre of gravity of an object falls outside of its base.
3.1.1.1 Increasing Stability
3.1.1.1.1 Increasing the base area of an object.
3.1.1.1.1.1 Because a larger base area means that an object would
have to be displaced greatly in order for the centre of
gravity to fall outside of its base.
3.1.1.1.2 Lowering the Centre of Gravity of an object.
3.1.1.1.2.1 A lower Centre of Gravity does not fall outside of the
object's base easily
4 4. Equilibrium
4.1 For an object acted upon by two or more coplanar forces (forces acting in the
same plane) to be in static equilibrium (at rest or uniform motion)...
4.1.1 The resultant force on the system is zero.
4.1.1.1 This is translational equilibrium = no linear
acceleration, i.e. no acceleration in a straight line in
one direction.
4.1.1.1.1 When doing vector additions, the vector sum of the forces would be 0.
4.1.1.1.2 Graphical methods (drawing the vectors in a
triangular/polygonal shape) will yield a closed
triangle/polygon.
4.1.2 The resultant moment of the system about every axis is zero.
4.1.2.1 This is rotational equilibrium
4.1.2.1.1 Principle of moments: sum of anticlockwise moments = sum of clockwise moments
5 5. Hooke's Law
5.1 When the top of a spring is attached to a fixed point
and a force (weight) is applied at the bottom of the
spring, the spring will extend.
5.1.1 Hooke's Law states that within the limit of proportionality, the
extension produced in a material is directly proportional to the load attached to the spring.
5.1.1.1 F = kx , where F=force/load (i.e. weight), x = the
extension of the spring, k= spring constant
5.1.1.2 The weight attached to the bottom of the spring is the load.
6 6. Pressure
6.1 Pressure is defined as the force per unit area acting in the
direction perpendicular to the surface of the object.
6.1.1 P = F/A
6.1.1.1 With the SI unit Nm^-2 or Pa (Pascal)
6.1.1.2 where P=pressure, F=force, A=area
6.2 Atmospheric Pressure
6.2.1 Is the force per unit area exerted against a surface by the weight of air
above the surface at any given point in Earth's Atmosphere.
6.2.1.1 Earth's atmospheric pressure is 101kPa (101kN/m^2)
6.2.1.1.1 but this value varies at different altitudes
6.2.1.1.1.1 it decreases at higher altitudes
6.2.1.1.1.2 it increases at lower altitudes
6.3 Hydrostatic Pressure
6.3.1 Is the pressure at any given point in a non-moving, static liquid. (Such as water)
6.3.1.1 It is calculated by the formula: P = hpg,
where P=pressure, h=height of the
liquid above the point. p (rho)=density,
g=gravitational acceleration
6.3.1.1.1 However, the actual pressure at a given point in the liquid is:
hpg+atmospheric pressure on the surface of the liquid.
6.3.2 The hydrostatic pressure of a static liquid is equal at the same level/height.
6.3.2.1 If a liquid had different hydrostatic pressures at the same height, it would mean that the liquid is moving.