Friction, drag and projectile motion in sport

Friction is a force that resists motion between two surfaces in contact. In sport, it can be both a friend and a foe. High friction is essential for grip, such as between a rock climber's shoes and the rock face, or a sprinter's spikes and the track. Conversely, low friction is desirable in sports like skiing, curling, and ice skating to allow for smooth, fast gliding. We distinguish between static friction (which prevents initial movement) and dynamic friction (which resists ongoing movement).

Force of friction ($F_f$) = Coefficient of friction ($\mu$) $\times$ Normal reaction force ($R$)

$F_f = \mu R$

Drag is a resistive force experienced by any object moving through a fluid (a liquid or a gas). It always acts in the opposite direction to the object's motion. The two primary components are surface drag, related to the fluid's friction against the object's surface, and form drag, related to the object's shape and the pressure differential it creates. Athletes in sports like cycling, swimming, and speed skating go to great lengths to minimise drag through specialised equipment, clothing, and body positions (streamlining).

Drag Force ($F_D$) = $\frac{1}{2} \times$ fluid density ($\rho$) $\times$ velocity² ($v^2$) $\times$ drag coefficient ($C_D$) $\times$ cross-sectional area ($A$)

$F_D = \frac{1}{2} \rho v^2 C_D A$

A projectile is any object launched into the air, from a basketball to a javelin. Its path, or trajectory, is determined by three initial factors: the speed of release, the angle of release, and the height of release. In a theoretical vacuum, the trajectory is a perfect parabola, as gravity is the only force acting on it. However, in reality, air resistance (drag) significantly alters this path, reducing the projectile's range and maximum height.