Welcome to Linear Motion!

In this chapter, we are looking at how athletes and objects move in a straight or curved line where all parts move the same distance, in the same direction, and at the same speed. Whether you are a 100m sprinter exploding out of the blocks or a long-jumper soaring through the air, linear motion is the foundation of your performance. We will break down the forces that act on you and the mathematical ways we measure how you move.

Note: This chapter focuses on movement in a line. For information on rotations and turning, see the "Angular Motion" chapter. For the basic laws of physics governing these movements, check "Biomechanical Principles."

1. Forces Acting on a Performer

In A-level PE, you need to identify the specific forces that influence an athlete's movement. A force is simply a push or a pull that alters the state of motion of a body.

There are five key forces you need to know:

  • Gravity: The force that pulls us toward the centre of the Earth. It keeps your feet on the ground and brings a high-jumper back to the mat.
  • Weight: This is the force exerted on a body by gravity. It acts downwards from the centre of mass.
  • Frictional Force: The force that occurs when two surfaces move across each other. Think of the grip between a sprinter’s spikes and the track.
  • Air Resistance: A type of friction caused by the air hitting a moving object. Cyclists wear aerodynamic helmets to reduce this.
  • Internal-Muscular Force: The force generated by the contraction of your skeletal muscles. This is what allows you to apply force to the ground or an object.
Key Takeaway:

Movement only happens when the internal-muscular force is strong enough to overcome external forces like gravity and friction.

2. Scalars vs. Vectors

Don't let the names scare you! This is just a way of categorising the "measurements" we use in sport. To keep it simple: Scalars only care about "how much," while Vectors care about "how much" AND "which direction."

Scalars (Magnitude only)

  • Mass: The amount of "matter" in a body. Measured in kilograms \( (kg) \).
  • Distance: The total length of the path covered. Example: A player runs 10km during a football match. Measured in metres \( (m) \).
  • Speed: How fast a body is moving. Measured in metres per second \( (m/s) \).
    Equation: \( Speed = \frac{Distance}{Time} \)

Vectors (Magnitude AND Direction)

  • Weight: The force of gravity acting on a mass. Measured in Newtons \( (N) \).
  • Displacement: The shortest straight-line distance from start to finish. Example: If a swimmer does one 50m lap of a 25m pool, their distance is 50m, but their displacement is 0m because they are back where they started! Measured in metres \( (m) \).
  • Velocity: Speed in a given direction. Measured in metres per second \( (m/s) \).
    Equation: \( Velocity = \frac{Displacement}{Time} \)
  • Acceleration: The rate at which velocity changes. Measured in metres per second squared \( (m/s^2) \).
    Equation: \( Acceleration = \frac{Change in Velocity}{Time} \)
  • Momentum: The "quantity of motion" a body possesses. Measured in \( kg \cdot m/s \).
    Equation: \( Momentum = Mass \times Velocity \)

Quick Tip: If the question asks for a vector, always mention the direction if possible!

3. Momentum and Impulse

Momentum is a measure of how hard it is to stop a moving object. A rugby prop has high momentum because they have a large mass; a sprinter has high momentum because they have a high velocity.

Impulse

Impulse is the change in momentum. It describes how long a force is applied to an object. In sport, we are usually trying to either increase impulse (to speed up) or decrease it (to slow down/absorb impact).

Equation: \( Impulse = Force \times Time \)

Measured in Newton-seconds \( (Ns) \).

Increasing Momentum (Sprinting Start)

To get a massive boost of speed out of the blocks, a sprinter needs a large impulse. They do this by applying a large force into the blocks and staying in contact with the blocks for as long as possible (increasing time).

Decreasing Momentum (Landing)

When a gymnast lands a vault, they "give" with their knees. This increases the time it takes to stop, which reduces the amount of force felt by their joints. The impulse (change in momentum) remains the same, but the landing is safer.

4. Force-Time Graphs

In your exam, you might be asked to interpret a Force-Time graph for a sprinter. The area under the curve on these graphs represents Impulse.

  • Net Positive Impulse: This occurs when the force applied to accelerate (drive phase) is greater than the resistance forces. The athlete speeds up.
  • Net Negative Impulse: This occurs during the braking phase of a stride. The athlete slows down.

Key Fact: For a sprinter to increase their velocity, their positive impulse (pushing off) must be greater than their negative impulse (the foot hitting the ground in front of the body).

5. Summary and Common Mistakes

Quick Review Box:

1. Scalars: Mass, Speed, Distance (No direction).
2. Vectors: Weight, Velocity, Displacement, Acceleration, Momentum (Include direction).
3. Force: \( Mass \times Acceleration \).
4. Impulse: \( Force \times Time \) (The change in momentum).

Common Mistakes to Avoid:
  • Confusing Mass and Weight: Mass is constant (measured in \( kg \)), but Weight is a force that changes depending on gravity (measured in \( N \)).
  • Mixing up Distance and Displacement: Remember the swimmer example! Displacement is the "as the crow flies" straight line from start to finish.
  • Units: Always include your units! If you calculate velocity, it must be \( m/s \). If you calculate force, it must be \( N \).

Don't worry if the math seems a bit heavy at first. Just remember that in PE, we use these formulas to explain why athletes perform the way they do—like why a sprinter stays low in the blocks to increase the time they can apply force!