🏃Sports Biomechanics Unit 4 – Kinetic Concepts

Key Concepts and Definitions

• Kinetics studies the forces that cause motion and how they affect the motion of objects or bodies
• Force is a push or pull that can change the motion, shape, or state of an object and is measured in Newtons (N)
• Mass is the amount of matter in an object and is measured in kilograms (kg)
  • Differs from weight, which is the force exerted on an object due to gravity
• Acceleration is the rate of change of velocity over time and is measured in meters per second squared (m/s²)
• Momentum is the product of an object's mass and velocity and is measured in kilogram-meters per second (kg·m/s)
  • Calculated using the formula: $p = mv$, where $p$ is momentum, $m$ is mass, and $v$ is velocity
• Impulse is the product of force and time, representing the change in momentum, and is measured in Newton-seconds (N·s)
  • Calculated using the formula: $J = F \Delta t$, where $J$ is impulse, $F$ is force, and $\Delta t$ is the change in time
• Work is the product of force and displacement in the direction of the force and is measured in Joules (J)
  • Calculated using the formula: $W = Fd \cos \theta$, where $W$ is work, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and displacement vectors

Fundamental Principles of Kinetics

• Newton's First Law of Motion states that an object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an unbalanced force
• Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass ($F = ma$)
• Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction
• The Law of Conservation of Momentum states that the total momentum of a closed system remains constant, provided no external forces act on the system
• The Law of Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another
  • Kinetic energy is the energy of motion, calculated using the formula: $KE = \frac{1}{2}mv^2$
  • Potential energy is the stored energy due to an object's position or configuration, such as gravitational potential energy: $PE = mgh$
• The Impulse-Momentum Theorem states that the change in momentum of an object is equal to the impulse applied to it ($J = \Delta p$)

Forces and Motion in Sports

• Gravity is a fundamental force that attracts objects with mass towards each other, causing downward acceleration (9.81 m/s² on Earth)
• Friction is a force that opposes the relative motion between two surfaces in contact, classified as static, kinetic, or rolling friction
  • Friction can be beneficial (providing traction) or detrimental (causing resistance) in sports
• Air resistance or drag is a force that opposes the motion of an object through a fluid (such as air) and depends on factors like velocity, surface area, and shape
• Centripetal force is a force that causes an object to follow a curved path, directed towards the center of the curve (e.g., a runner on a curved track)
• Muscular forces are generated by the contraction of muscles and are responsible for initiating and controlling movement in sports
  • Concentric contractions occur when the muscle shortens while generating force (e.g., bicep curl)
  • Eccentric contractions occur when the muscle lengthens while generating force (e.g., lowering a weight)
• Ground reaction forces are the forces exerted by the ground on an object or person in contact with it, equal and opposite to the force applied (e.g., during running or jumping)

Linear Kinetics

• Linear motion is motion along a straight line, characterized by displacement, velocity, and acceleration
• Displacement is the shortest distance between the initial and final positions of an object, measured in meters (m)
• Velocity is the rate of change of displacement over time, measured in meters per second (m/s)
  • Average velocity is calculated using the formula: $v_{avg} = \frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position and $\Delta t$ is the change in time
  • Instantaneous velocity is the velocity at a specific instant in time, represented by the slope of the tangent line on a position-time graph
• Acceleration is the rate of change of velocity over time, measured in meters per second squared (m/s²)
  • Average acceleration is calculated using the formula: $a_{avg} = \frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time
  • Instantaneous acceleration is the acceleration at a specific instant in time, represented by the slope of the tangent line on a velocity-time graph
• The equations of motion describe the relationships between displacement, velocity, acceleration, and time for an object undergoing constant acceleration
  • $v = v_0 + at$, where $v$ is the final velocity, $v_0$ is the initial velocity, $a$ is the acceleration, and $t$ is the time
  • $x = x_0 + v_0t + \frac{1}{2}at^2$, where $x$ is the final position, $x_0$ is the initial position, $v_0$ is the initial velocity, $a$ is the acceleration, and $t$ is the time
  • $v^2 = v_0^2 + 2a(x - x_0)$, where $v$ is the final velocity, $v_0$ is the initial velocity, $a$ is the acceleration, $x$ is the final position, and $x_0$ is the initial position

Angular Kinetics

• Angular motion is motion around a fixed point or axis, characterized by angular displacement, angular velocity, and angular acceleration
• Angular displacement is the angle through which an object rotates, measured in radians (rad) or degrees (°)
• Angular velocity is the rate of change of angular displacement over time, measured in radians per second (rad/s) or degrees per second (°/s)
  • Average angular velocity is calculated using the formula: $\omega_{avg} = \frac{\Delta \theta}{\Delta t}$, where $\Delta \theta$ is the change in angular displacement and $\Delta t$ is the change in time
  • Instantaneous angular velocity is the angular velocity at a specific instant in time, represented by the slope of the tangent line on an angular displacement-time graph
• Angular acceleration is the rate of change of angular velocity over time, measured in radians per second squared (rad/s²) or degrees per second squared (°/s²)
  • Average angular acceleration is calculated using the formula: $\alpha_{avg} = \frac{\Delta \omega}{\Delta t}$, where $\Delta \omega$ is the change in angular velocity and $\Delta t$ is the change in time
  • Instantaneous angular acceleration is the angular acceleration at a specific instant in time, represented by the slope of the tangent line on an angular velocity-time graph
• Torque is the rotational equivalent of force, causing an object to rotate about an axis, measured in Newton-meters (N·m)
  • Calculated using the formula: $\tau = rF \sin \theta$, where $\tau$ is torque, $r$ is the perpendicular distance from the axis of rotation to the line of action of the force, $F$ is the force, and $\theta$ is the angle between the force and the moment arm
• Moment of inertia is the rotational equivalent of mass, representing an object's resistance to angular acceleration, measured in kilogram-meters squared (kg·m²)
  • Depends on the object's mass and its distribution relative to the axis of rotation
• Angular momentum is the product of an object's moment of inertia and angular velocity, measured in kilogram-meters squared per second (kg·m²/s)
  • Calculated using the formula: $L = I\omega$, where $L$ is angular momentum, $I$ is the moment of inertia, and $\omega$ is the angular velocity

Kinetic Analysis Methods

• Free body diagrams are visual representations of the forces acting on an object, used to analyze the kinetics of a system
  • Include the object of interest, all forces acting on the object (represented by arrows), and a coordinate system
  • Forces should be labeled and drawn to scale, with the length of the arrow proportional to the magnitude of the force
• Force plates are devices that measure the ground reaction forces and moments generated by an object or person in contact with the plate
  • Commonly used in sports biomechanics to analyze running, jumping, and other activities
  • Provide data on the magnitude, direction, and timing of forces applied to the plate
• Motion capture systems use cameras and reflective markers placed on the body to record the three-dimensional positions of the markers over time
  • Enable the calculation of kinematic variables (e.g., joint angles, velocities, and accelerations) and kinetic variables (e.g., joint moments and powers) through inverse dynamics
  • Examples include optical systems (e.g., Vicon, Optitrack) and inertial measurement units (IMUs)
• Electromyography (EMG) is a technique that measures the electrical activity of muscles during contraction
  • Surface EMG involves placing electrodes on the skin over the muscle of interest to record the collective activity of the underlying motor units
  • Provides information on the timing, intensity, and duration of muscle activation, which can be related to the kinetics of the movement
• Inverse dynamics is a method used to calculate the joint forces and moments responsible for a given motion, based on kinematic and anthropometric data
  • Involves solving the equations of motion for each body segment, starting from the most distal segment and working proximally
  • Requires data on the segment masses, moments of inertia, and accelerations, as well as the external forces acting on the system (e.g., ground reaction forces)

Applications in Sports Performance

• Sprinting mechanics can be analyzed using kinetic methods to identify factors contributing to performance, such as ground reaction forces, leg stiffness, and power output
  • Faster sprinters typically exhibit higher peak ground reaction forces, shorter ground contact times, and greater leg stiffness during the stance phase
  • Kinetic analysis can help guide training interventions to improve sprint performance, such as plyometric exercises to enhance power output and reactive strength
• Jumping performance is often assessed using measures of kinetic variables, such as peak force, rate of force development, and impulse
  • Vertical jump height is determined by the vertical impulse generated during the propulsive phase, which depends on the magnitude and duration of the ground reaction force
  • Kinetic analysis can inform training strategies to improve jumping ability, such as weightlifting exercises to increase maximal strength and explosive power
• Throwing and striking motions, such as baseball pitching, tennis serves, and golf swings, involve complex kinetic chains that transfer energy from the lower body to the upper body and ultimately to the object being thrown or struck
  • Kinetic analysis can identify key variables that contribute to performance, such as ground reaction forces, joint torques, and segmental angular velocities
  • Coaches and athletes can use this information to optimize technique, prevent injuries, and design sport-specific training programs
• Running economy, or the energy cost of running at a given velocity, is influenced by various kinetic factors, such as ground reaction forces, leg stiffness, and joint moments
  • More economical runners tend to exhibit lower vertical oscillation of the center of mass, higher leg stiffness, and more efficient storage and return of elastic energy in the tendons and muscles
  • Kinetic analysis can help identify biomechanical factors that contribute to running economy and guide interventions to improve performance, such as gait retraining or strength training
• Injury prevention strategies can be informed by kinetic analysis, which can identify biomechanical risk factors for common sports injuries, such as stress fractures, anterior cruciate ligament (ACL) tears, and overuse injuries
  • For example, high peak ground reaction forces and rapid loading rates during running have been associated with an increased risk of tibial stress fractures
  • Kinetic analysis can guide the development of injury prevention programs that target specific risk factors, such as neuromuscular training to improve landing mechanics and reduce ACL injury risk

Common Misconceptions and FAQs

• Misconception: Mass and weight are the same things.
  • Fact: Mass is the amount of matter in an object and is independent of gravity, while weight is the force exerted on an object due to gravity and varies with location.
• Misconception: An object with a larger mass always has a larger momentum.
  • Fact: Momentum depends on both mass and velocity. A lighter object moving at a higher velocity can have a larger momentum than a heavier object moving at a lower velocity.
• Misconception: A net force is required to maintain motion at a constant velocity.
  • Fact: According to Newton's First Law, an object in motion will continue to move at a constant velocity unless acted upon by an unbalanced force. No net force is required to maintain motion at a constant velocity.
• Misconception: Impulse and momentum are the same things.
  • Fact: Impulse is the product of force and time, representing the change in momentum. Momentum is the product of mass and velocity, representing the quantity of motion possessed by an object.
• Misconception: Torque and force are the same things.
  • Fact: Torque is the rotational equivalent of force, causing an object to rotate about an axis. Force, on the other hand, causes an object to change its linear motion (i.e., accelerate).
• FAQ: What is the difference between linear and angular kinetics?
  • Answer: Linear kinetics deals with motion along a straight line and involves variables such as force, mass, acceleration, and momentum. Angular kinetics deals with rotational motion around a fixed point or axis and involves variables such as torque, moment of inertia, angular velocity, and angular momentum.
• FAQ: How do ground reaction forces influence sports performance?
  • Answer: Ground reaction forces play a crucial role in many sports activities, such as running, jumping, and changing direction. The magnitude, direction, and timing of these forces can affect variables such as velocity, acceleration, and power output. Athletes who can generate higher ground reaction forces in a shorter time tend to exhibit better performance in activities that require explosive movements.
• FAQ: What is the relationship between impulse and change in momentum?
  • Answer: According to the Impulse-Momentum Theorem, the change in momentum of an object is equal to the impulse applied to it. Mathematically, this is expressed as $J = \Delta p$, where $J$ is impulse and $\Delta p$ is the change in momentum. This relationship highlights the fact that a larger impulse (i.e., a larger force applied over a longer time) will result in a greater change in momentum.