Week 10 Moments Flashcards
Moment of force
Moment of force is a physical quantity which gives a measure of the effect that a force has on an object in terms of rotation about a certain point/axis
Magnitude of a moment depends on the magnitude of the force which generates it and the distance between the point at which the force acts and the point about which the moment is calculated. The unit for the moment is consequently Newton-metre (Nm)
In a general three-dimensional case the moment is a vector whose direction is aligned with the axis about which the object rotates
In two-dimensional problems occurring in a single plane it is sufficient to define the magnitude of the moment and the direction of the rotation caused. Counter-clockwise rotation is usually considered to be positive and clockwise rotation is considered to be negative
Moment of force: mathematical definition
The “line of action” of a force is a line aligned with the direction of the force vector
The “ moment arm” of a force vector about a certain point is the shortest distance between that point and the line of action of the force. It is obtained by drawing a line perpendicular to the line of action of the force and passing through the point about which the moment is calculated
The (magnitude of the) moment of a force about a certain point is equal to the product of the magnitude of the force and the moment arm
M= f x d
Moment of force: symbol and notation
Moment is denoted by capital M
To specify that a moment is calculated for a specific point (say A) we add a superscript with the letter denoting that point, i.e., MA
We use the symbol indicating rotation to represent a moment
Torques and Moments
Torque or moment of force is the turning effect produced by a force.
The torque is equal to the product of the magnitude of the force and the distance between the line of action of the force and the axis of rotation.
Note, the distance is always the distance perpendicular to the line of action.
M is torque (moment of force) F is force is the moment arm length Anti clockwise = positive Clockwise negative
Anatomical Levers
Every bone in the skeleton can be looked upon as a lever.
Levers form the basis of human movement.
Bones = levers
Muscles = effort
Joints = fulcrum/ pivot
Objects or segment weights provide the load/resistant
1st class lever
EFL
Mechanical advantage is balance
Can be used to magnify the effect of efforts
e.g. increase speed or range of motion
2nd class lever
Can be used to magnify the effects of effort so that it takes less force to move the load.
Range of motion is sacrificed
3rd class
Small amount of motion at effort point produces large range of motion at load.
Takes greater effort to overcome load.
Centre of gravity: definition
Weight of an object is a “body force” that is distributed throughout the volume of the object
However, it is convenient to represent the body weight as a concentrated force acting at a single point. The question is at which point to place the concentrated body weight so that its mechanical effect is the same as that of the (real) distributed weight
Weight is a force N
Mass is a measure of inertia kg
The solution is to place the concentrated body weight at such a location that its moment about any arbitrary point is the same as the moment created by the (real) distributed weight
That point is called “centre of gravity”
Since the weight can be concentrated in the centre of gravity, it follows that the net moment of weight about the centre of gravity is zero
Centre of mass and centre of gravity coordinates
The formulas for the coordinates of the centre of gravity are identical to the formulas for the coordinates of the centre of mass
Consequently, the position of the centre of gravity can be determined using the anthropometric tables and following the same procedure as the one used for finding the centre of mass
However, the physical meaning of the centre of gravity and the centre of mass is different
Conditions of static equilibrium for an object
For a particle (point mass) the sufficient condition for equilibrium is that the (vector) sum of all forces that act on the particle is zero
The equilibrium of a material object requires an additional condition which has to do with the rotation (change of orientation) of the object
That additional condition is that the sum of moment from all forces acting on the object about any arbitrary point is zero
Mathematically, the necessary conditions for the equilibrium are expressed as follows:
F= 0
M=0
Conditions of static equilibrium in 2D: Component form
is customary to present the equilibrium conditions in scalar form by resolving all the forces in their components
For a two-dimensional problem there are then three conditions of equilibrium:
The sum of all force components in the horizontal (x) direction is zero
The sum of all force components in the vertical (z) direction is zero
The sum of moments of all forces (about any arbitrary point) is zero
Mathematically, the necessary conditions for the equilibrium are expressed as follows:
Key points
Moment of force is a physical quantity that gives a measure of the effect that a force has in terms of rotating an object about a certain point
The magnitude of moment depends on the magnitude of the force that creates it, and the distance between the point at which the force acts and the point about which the moment is calculated
The centre of mass of an object is the point at which the moment from its distributed weight equals zero
Within the scope of problems relevant for biomechanics, the centre of mass and the centre of gravity of an object are coincident
Static equilibrium of a material object is achieved if the net sum of all forces acting on it is zero, and the net moment about any arbitrary point is also zero
The position of the centre of gravity can be determined experimentally
