Newton's Laws of Motion and Kinematics

B.2.1 Newton's Laws of Motion

Overview of Newton's Laws

• Linear and angular motion can be analyzed using Newton's laws of motion.

• The motion of an object can be described using:

  • Speed

  • Velocity

  • Acceleration

• Resultant motion is determined by the sum of the forces acting on it.

Principles Relating to Applications of Newton’s Laws

• Stability:

  • Factors affecting stability include:

  • Height of the center of mass relative to the supporting surface.

  • Size of the support base.

  • Position of the line of gravity relative to the support base.

  • Mass.

• Summing Joint Forces:

  • The importance of understanding joint forces in movement.

• Linear Motion:

  • The greater the impulse applied, the greater the change in momentum.

• Impulse Direction:

  • The application of impulse affects the direction of motion.

• Angular Motion:

  • Produced by applying a force acting at a distance from the center of mass (eccentric force).

  • Angular momentum is conserved when an athlete or object experiences no additional eccentric forces.

Relevant Equations

• The equations for:

  • Speed

  • Linear velocity

  • Angular velocity

  • Acceleration

  • Linear momentum

  • Force and weight

• Found in the SEHS data booklet.

• Trigonometry is not assessed; calculations are limited to:

  • Three terms for SL (Standard Level)

  • Four terms for HL (Higher Level).

AHL Overview

Collision and Momentum (12 hours)

• Collisions:

  • A collision results in a change in momentum in the colliding bodies.

  • The change in momentum equals the impulse applied to the object.

  • Coefficient of restitution affects collisions involving a ball.

  • Coefficient of restitution equation is in the SEHS data booklet.

  • Assessment calculations are limited to one dimension.

Friction (12 hours)

• The force of friction is determined by the coefficient of friction.

• Coefficients of static and dynamic friction depend on the materials in contact.

• Frictional force can be modified to enhance sports performance.

• Equations for coefficients of static and dynamic friction are available in the data booklet.

Work and Power (12 hours)

• Work results from applying a force over a distance;

  • Energy is transformed from one form to others when work is done.

• Power measures the rate at which work is done, impacting work intensity in sports through:

  • Correct technique

  • Effective sports equipment design.

• Relevant equations are in the SEHS data booklet.

Learning Intentions and Success Criteria (LI’s & SC’s)

• Students should be able to:

  • Outline Newton’s three laws of motion.

  • Apply laws to analyze linear and angular motion.

  • Understand conservation of momentum in collisions.

  • Interpret coefficient of restitution values.

  • Distinguish between static and dynamic friction.

  • Explain friction's influence on sports performance.

  • Understand relationships between force, work, and energy.

• Students can:

  • Describe and explain Newton’s first, second, and third laws.

  • Use laws to analyze linear and rotational movements in sports.

  • Explain conservation of momentum principles in sporting collisions.

  • Interpret variable coefficients of restitution regarding collision elasticity.

  • Distinguish between static and dynamic friction and their applications.

  • Explain how friction affects movement, control, safety, and performance.

  • Relate force, work, and power, detailing how changes affect one another.

Introduction to Movement & Forces

• Body movements and sporting equipment motions are governed by Newton’s laws.

• Understanding these laws aids in:

  • Performance analysis

  • Injury reduction

  • Technique development.

Key Mechanical Terms

• Scientific terms like:

  • Force

  • Power

  • Velocity

  • Energy

• Definitions are crucial for precise analyses of human movement.

Importance of Mechanics

• Mechanics elaborates on how moving bodies perform actions, forming the foundation for understanding movement.

• A crucial concept is that analyzing sports or physical activity necessitates knowledge of Newton’s laws.

Kinematics

• Kinematics is the study of motion including:

  • Whole body movement

  • Movement of body parts.

Types of Motion

• Linear Motion:

  • Movement in a straight line (e.g., ice hockey puck).

• Curvilinear Motion:

  • Movement along a curved path (e.g., shot-put).

• Angular (Rotational) Motion:

  • Movement around an axis (e.g., gymnasts on apparatus).

• General Motion:

  • Combination of linear and angular motions.

Key Idea in Sports & Exercise

• General motion is prevalent; even linear movement requires limb rotation at synovial joints.

Measurements and Position

Vector and Scalar Measurements

• Vector:

  • Has size and direction; direction must match for combinations.

• Scalar:

  • Has size only; can be added or multiplied easily.

Position Description

• Position:

  • Described using coordinates:

  • 2D coordinates (x - horizontal, y - vertical)

  • 3D coordinates (x, y, z for horizontal, vertical, lateral).

• Angular Position:

  • Described using angles around axes.

Linear Kinematics

Linear Displacement vs Distance

• Linear Displacement (s):

  • Change in position from start to end.

  • Vector quantity.

  • SI unit: $ext{metres (m)}$.

• Linear Distance (d):

  • Total path length; scalar quantity without direction.

Key Distinction

• Displacement = where you end up; Distance = how far you travel overall.

Linear Velocity

Linear Velocity (v or u)

• Defined as the rate of change in displacement over time.

• Includes both speed and direction, indicated as:

  • Vector quantity with formula: $v = rac{Δs}{Δt}$.

Speed

• The magnitude of velocity, scalar quantity with SI unit: $ext{m/s}$.

Example

• Running a 100m race in 20 seconds results in:

  • Average velocity = $rac{100m}{20s} = 5 m/s$.

Linear Speed vs Velocity

• Speed: Simply how fast you are traveling; e.g., traveling at 10 m/s.

• Velocity: Speed with direction; e.g., 10 m/s east.

Linear Acceleration

Definition

• Change in velocity over time, can be linear or angular.

• Formula: $a = rac{Δv}{Δt} = rac{(v-u)}{t}$.

Units

• SI unit: $ext{m/s}^2$.

Example

• Running 100m reaching max speed of 6 m/s in 3 seconds yields:

  • Acceleration of $2 m/s/s$.

Angular Kinematics

Definition

• Study of rotational motion about an axis, with applications in sports.

Sport Applications

• Includes:

  • Figure skating

  • Soccer

  • Swimming

  • Baseball

  • Cricket.

Importance

• Understanding angular kinematics improves performance and decreases injury risk.

Angular Displacement and Velocity

Angular Displacement

• Defined as the angle an object rotates around a fixed point or axis.

• Measured in radians or degrees; vector quantity.

Angular Velocity

• Rate of angular displacement over time, expressed in rad/s.

• Formula: $rac{Δ heta}{Δt}$ or $ext{angular velocity} = ω$.

Angular Acceleration

Definition

• Change in angular velocity per unit time, also a vector quantity.

Examples

• Calculating angular acceleration during exercises or sports activities, based on starting and final velocities over time.

Instantaneous vs Average Kinematics

Importance of Time Measurement

• Velocity and acceleration vary based on measurement duration.

• Instantaneous measures involve calculus or graphing.

Formulas

• Average Velocity: $ext{average velocity} = rac{change in displacement}{time}$.

• Average Acceleration: $ext{average acceleration} = rac{change in velocity}{time}$.

Graphical Analysis

Distance-Time Graphs

• The gradient indicates velocity; flat lines indicate stationary motion.

Velocity-Time Graphs

• Gradient represents acceleration; area under the curve indicates displacement.

Calculations

• Methods of determining total displacement, speed, average velocity, and instantaneous velocity through graphical analysis.

Kinetics

Definition

• Study of forces affecting motion, categorized as linear or angular.

Newton’s Laws Overview

• First Law (Law of Inertia): Objects remain at rest or in uniform motion unless acted upon.

• Second Law (Law of Acceleration): Acceleration is proportional to unbalanced force (F=ma).

• Third Law (Law of Reaction): For every action, there is an equal and opposite reaction.

Applications in Sports

Stability

• Defined by center of mass, base of support, and mass.

Joint Forces

• Summation of muscle forces at joints affects movements.

Linear Momentum

• Property due to movement, calculated as $p = mv$.

Impulse and Direction

Impulse Definition

• Impulse relates to changes in momentum, directional influences in sports.

Application in Sports

• Importance of applying forces correctly in ball sports for desired outcomes.

Angular Momentum and Torque

Angular Momentum Definition

• Related to rotational movement, generated through torque.

• Important in various sports contexts such as gymnastics and throwing activities.

Torque Definition

• Created through applied force not directly through the axis of rotation.

Moment of Inertia

• Measure of difficulty for an object to rotate, affected by mass distribution.

Conservation of Angular Momentum

• In the absence of external torque, angular momentum remains constant over time.

Summary of Concepts

• Key concepts reviewed include:

  • Linear and angular kinematics

  • Newton’s laws and implications in motion

  • Friction's role in performance

  • Work and power relationships in sports

• Optimization of performance is achieved through understanding and applying these principles effectively in various sports contexts.