Biomechanics

Biomechanics is the science concerned with the internal and external forces acting on the human body and the effects produced by these forces.

Kinetics is a study of the cause of motion, namely forces and torques e.g. forces between the feet and the ground when jumping and Kinematics is the study of movement with reference to the amount of time taken to carry out the activity.

Distance and displacement

Distance (length of the path a body follows) and displacement (length of a straight line joining the start and finish points) are quantities used to describe a body's motion. e.g. in a 400m race on a 400m track the distance is 400 metres but their displacement will be zero metres (start and finish at the same point).

Speed and velocity

Speed and velocity describe the rate at which a body moves from one location to another. Average speed of a body is obtained by dividing the distance by the time taken and average velocity is obtained by dividing the displacement by the time taken e.g. a swimmer in a 50m race in a 25m length pool who completes the race in 71 seconds - distance is 50m and displacement is 0m (swimmer is back where they started) so speed is 50/71= 0.70m/s and velocity is 0/71=0 m/s.

• Speed and Velocity = distance travelled ÷ time taken

Acceleration

Acceleration is defined as the rate at which velocity changes with respect to time.

• average acceleration = (final velocity - initial velocity) ÷ elapsed time

From Newton's 2nd law:

• Force = Mass x Acceleration
• Acceleration = Force ÷ Mass

If the mass of a sprinter is 60kg and the force exerted on the starting blocks is 600N then acceleration = 600 ÷ 60 = 10 msec²

Acceleration due to gravity

Whilst a body is in the air it is subject to a downward acceleration, due to gravity, of approximately 9.81m/s²

Vectors and scalars

Distance and speed can be described in terms of magnitude (amount) and are known as scalars. Displacement, velocity and acceleration require magnitude and direction and are known as vectors.

Components of a vector

Let us consider the horizontal and vertical components of velocity of the shot put.

indicates the angle of release of the put ball is 35° and the velocity at release as 12 metres/second.

• Vertical component Vv = 12 x sin 35° = 6.88 m/sec
• Horizontal component Vh = 12 x cos 35° = 9.82 m/sec

Let us now consider the distance the put ball will travel horizontally (its displacement).

Distance (D) = ((v² × sinØ × cosØ) + (v × cosØ × sqrt((v × sinØ)² + 2gh))) ÷ g

Where v = 12, Ø = 35, h = 2m (height of the shot above the ground at release) and g = 9.81

• D = ((12² × sin35 × cos35) + (12 × cos35 × sqrt((12 × sin35)² + 2 x 9.81 x 2))) ÷ 9.81
• D = 16.22m

The time of flight of the shot can be determined from the equation:

• Time of flight = Distance (D) ÷ velocity (Vh)
• Time of flight = 16.22 ÷ 9.82 = 1.65 seconds

Uniformly accelerated motion

When a body experiences the same acceleration throughout an interval of time, its acceleration is said to be constant or uniform and the following equations apply:

• Final velocity = initial velocity + (acceleration x time)
• Distance = (initial velocity x time) + (½ x acceleration x time²)

Moment of force (torque)

The moment of force or torque (τ) is defined as the application of a force at a perpendicular distance to a joint or point of rotation.

Torque (τ = rFsin θ ) depends on three quantities:

• the length of the lever arm connecting the axis to the point of force application (r)
• the force applied (F)
• the angle between the force vector and the lever arm (sin θ)

Angular Kinematics

(i) Angular distance and displacement 

When a rotating body moves from one position to another, the angular distance through which it moves is equal to the length of the angular path. The angular displacement that a rotating body experiences is equal to the angle between the initial and final position of the body. 

Angular movement is usually expressed in radians where 1 radian = 57.3°

(ii) Angular speed, velocity and acceleration

• Angular speed = angular displacement ÷ time
• Angular velocity = angular displacement ÷ time
• Angular acceleration = (final angular velocity - initial angular velocity) ÷ time

(iii) Angular Momentum

Angular momentum is defined as: angular velocity x moment of inertia.

The angular momentum of a system remains constant throughout a movement provided nothing outside of the system acts with a turning moment on it. This is known as the Law Conservation of Angular Momentum. (e.g. if a skater, when already spinning, moves their arms out to the side, then the rate of spin will change but the angular momentum will stay the same).

Linear Kinetics

Kinetics is concerned with what causes a body to move.

Momentum, inertia, mass, weight and force

• Momentum: mass x velocity
• Inertia: the reluctance of a body to change whatever it is doing
• Mass: the quantity of matter of which a body is composed of - not affected by gravity - measured in kilograms (kg)
• Weight: force due to gravity -9.81m/s²
• Force: a pushing or pulling action that causes a change of state (rest/motion) of a body is proportional to mass x acceleration. It is measured in Newtons (N) where 1N is the force that will produce an acceleration of 1 m/s² in a body of 1kg mass

The classification of external or internal forces depends on the definition of the 'system'. In biomechanics, the body is seen as the 'system' so any force exerted by one part of the system on another part of the 'system' is known as an internal force all other forces are external.

Newton's Laws of Motion

• First Law: Every body continues in its state of rest or motion in a straight line unless compelled to change that state by external forces exerted upon it.
• Second Law: The rate of change of momentum of a body is proportional to the force causing it and the change takes place in the direction in which the force acts
• Third Law: To every action there is an equal and opposite reaction OR for every force that is exerted by one body on another there is an equal and opposite force exerted by the second body on the first

Newton's law of gravitation

• Any two particles of matter attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 

Kinetic Energy and Power

Kinetic energy is the mechanical energy possessed by a moving object.

Kinetic Energy = ½ x mass x velocity² (joules)

Power is defined as the rate at which energy is used or created from other forms

• Power = energy used ÷ time taken
• Power = (force x distance) ÷ time taken
• Power = force x velocity 

Angular Kinetics

Translation and couple

A force that acts through the centre of a body result in movement (translation). A force whose line of action which does not pass through the body's centre of gravity is called an eccentric force and results in movement and rotation.

Example - if you push through the centre of an object it will move forward in the direction of the force. if you push to one side of the object (eccentric force) it will move forward and rotate.

A couple is an arrangement of two equal and opposite forces that cause a body to rotate.

Levers

A lever is a rigid structure, hinged at one point and to which forces are applied at two other points. The hinge is known as the fulcrum. The two forces forces that act on the lever are the weight that opposes movement and a force that causes movement. For more details see the page on Levers.

Bernoulli Effect

If an object has a curved top and flat bottom (e.g. the wing of an aircraft), the air will have further to travel over the top of the wing than the bottom. For the two airflows to reach the rear of the wing at the same time the air flowing over the top of the wing will have to flow faster resulting in less pressure above the wing (air is thinner) than below it and the aircraft will lift. This is known as the Bernoulli effect.