Sports, Exercise and Health Science | Forces, motion and movement

👋 Welcome to Biomechanics: Forces, Motion and Movement (B.2)

Hello future SEHS expert! This chapter is where we unlock the physics behind peak athletic performance. Biomechanics might sound intimidating, but it’s simply the study of how forces affect the human body and its movement. Think of this chapter as understanding the hidden engine and steering wheel of every athlete.
Don't worry if this seems tricky at first; we’ll break down these concepts using real-world sports examples!

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1. Describing Motion: The Language of Kinematics

When we describe movement, we need specific, precise terms. Kinematics is the study of motion without reference to the forces causing it.

Scalars vs. Vectors: Direction Matters!

The first crucial distinction is between quantities that include direction and those that don't.

• Scalar Quantities: Defined only by their magnitude (size).
  Examples: Distance, Speed, Mass, Time.
• Vector Quantities: Defined by both magnitude and direction.
  Examples: Displacement, Velocity, Acceleration, Force, Momentum.

Analogy: Think of a treasure map. A scalar tells you "walk 5 kilometers" (magnitude). A vector tells you "walk 5 kilometers north" (magnitude + direction).

Distance vs. Displacement

• Distance (Scalar): The total path covered by an object.
  Example: Running 400m around a track.
• Displacement (Vector): The straight-line distance from the starting point to the finishing point (and includes direction).
  Example: If you run one lap on a 400m track, your total distance is 400m, but your displacement is zero because you finished exactly where you started!

Speed vs. Velocity

These terms are often used interchangeably in daily life, but they are very different in physics:

• Speed (Scalar): The rate of change of distance. \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Units: \(\text{m s}^{-1}\)
• Velocity (Vector): The rate of change of displacement. \[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \] Units: \(\text{m s}^{-1}\)

Quick Review: An aeroplane travelling at 800 km/h has a certain speed. If we say it is travelling at 800 km/h due east, we are describing its velocity.

Acceleration

Acceleration (Vector) is the rate of change of velocity. Since velocity is a vector, acceleration happens in three ways:

1. Speeding up (positive acceleration)
2. Slowing down (negative acceleration, often called deceleration)
3. Changing direction (even if speed remains constant, like a cyclist rounding a bend).

The formula for average acceleration (\(a\)) is:

\[ a = \frac{\text{Final Velocity } (v_f) - \text{Initial Velocity } (v_i)}{\text{Time } (t)} \]

Units: \(\text{m s}^{-2}\)

2. The Drivers of Motion: Newton’s Laws

Kinetics is the study of the forces that cause motion. The cornerstone of kinetics is Sir Isaac Newton’s three laws of motion. A Force (F) is a push or pull that changes, or tends to change, the state of motion of an object. Forces are measured in Newtons (N).

Newton’s First Law: The Law of Inertia

Statement: A body continues in a state of rest or uniform motion unless acted upon by an external force.

This law explains Inertia—the resistance of an object to changes in its state of motion. The more mass an object has, the greater its inertia.

Real-World Example: A basketball being dribbled keeps moving horizontally until the player's hand applies a downward force and gravity pulls it down. If you kick a football in space, it would travel forever in a straight line because there is no air resistance or friction to stop it.

Newton’s Second Law: The Law of Acceleration

Statement: The acceleration of an object is directly proportional to the force causing it, is in the same direction as the force, and is inversely proportional to the mass of the object.

This is the most famous equation in biomechanics:

\[ F = ma \]

Where: \(F\) = Net Force (N), \(m\) = Mass (kg), \(a\) = Acceleration (\(\text{m s}^{-2}\))

• Force and Acceleration: If a weightlifter applies a greater force to the bar (F increases), the bar accelerates faster (a increases). (Directly proportional)
• Mass and Acceleration: If you apply the same force to a heavy shot put versus a light baseball, the baseball will accelerate much faster. (Inversely proportional)

Newton’s Third Law: The Law of Action and Reaction

Statement: For every action force, there is an equal and opposite reaction force.

This law explains how we move on Earth. When an athlete exerts a force on the ground (Action), the ground exerts an equal and opposite Ground Reaction Force (GRF) back onto the athlete (Reaction).

Real-World Example:

• A sprinter pushes backward and downward against the starting blocks (Action). The blocks push forward and upward on the sprinter (Reaction), launching them forward.
• When swimming, your hands push backward on the water (Action). The water pushes forward on your hands (Reaction), propelling you across the pool.

Did you know? These forces act on different objects. The sprinter's action is on the block; the reaction is on the sprinter. They don't cancel each other out!

3. Momentum, Impulse, Friction, and Drag

Momentum (p)

Momentum (Vector) is a measure of the quantity of motion contained in a body. It’s what makes a moving object hard to stop.

\[ p = mv \]

Where: \(p\) = Momentum, \(m\) = Mass (kg), \(v\) = Velocity (\(\text{m s}^{-1}\))

Example: A heavy rugby player running slowly can have the same momentum as a light football player running very fast.

Impulse (I)

Impulse (Vector) is the change in momentum of an object. Impulse is generated by applying a force over a period of time.

\[ \text{Impulse } (I) = F \times \Delta t \]

Where: \(F\) = Average force, \(\Delta t\) = Time the force is applied.

Crucially, Impulse is equal to the change in momentum (\(\Delta p\)).

\( F \Delta t = \Delta p \)

This relationship is incredibly important for coaching:

• Increasing Momentum: To launch a javelin faster (greater momentum), the athlete must maximize the force (F) and the time (Δt) over which they push the javelin (e.g., maximizing the throwing arc).
• Reducing Impact Force: When catching a fast baseball, a catcher pulls their glove backward. This increases the time (\(\Delta t\)) over which the momentum changes, thereby decreasing the average force (F) felt by the hand. (This is why soft landings matter!)

Friction and Drag: Forces Opposing Motion

In the real world, movement is always opposed by resistive forces, primarily friction and drag.

1. Friction (Solid Surfaces)

Friction is a force that opposes motion when two surfaces are in contact. It is essential for most sports, particularly those involving changing direction.

• Static Friction: Friction preventing movement (starting a sprint).
• Dynamic (Kinetic) Friction: Friction opposing movement once it has started (sliding across the pitch).

Sport Application: Studs on rugby boots increase friction, allowing players to push off the ground without slipping.

2. Drag (Fluid Resistance)

Drag is the force opposing the movement of a body through a fluid (either air or water). Drag includes:

• Surface Drag (Skin Friction): Caused by the fluid sticking to the surface of the object (e.g., using specialized low-friction swimsuits).
• Form Drag (Shape/Pressure Drag): Caused by the pressure difference between the front and back of the object (e.g., the wide body of a cyclist causes a lot of drag).

To reduce drag, athletes and engineers focus on streamlining (making the body or equipment more teardrop-shaped) and reducing the object's surface area facing the fluid (e.g., tucking in a cycling time trial).