Newton's Laws of Motion

Define impulse and explain the impulse-momentum relationship with its formula.

Impulse is the product of a force and the time interval over which it is applied.

Formula: J=FΔt

Impulse equals the change in momentum: Change in momentum=Δp=J=FΔt

Where J is impulse (N·s), F is force (N), and Δt is the time over which the force acts (s).

Explain why increasing the time of force application can reduce impact force in sports, even if the impulse (change in momentum) is the same.

From the impulse-momentum relationship J=FΔt=Δp, if the change in momentum Δp is fixed, increasing the time interval Δt means the average force F must decrease. In sport, for example, bending the knees when landing from a jump increases the time over which the body is brought to rest, reducing the impact force on joints while producing the same impulse (same change in momentum).

What is kinematics in the context of sport and exercise science?

Kinematics is the branch of mechanics that studies motion without considering the forces that cause it. It describes motion using position, displacement, speed, velocity, and acceleration.

What is motion?

Motion is the change in position of an object or body over time. It can involve movement from one location to another or changes in the position of body parts, and is described using displacement, velocity, and acceleration.

List the four main types of motion in sport and give a simple example of each.

1. Linear motion - movement in a straight line (for example, a sprinter running down a track).

2. Curvilinear motion - movement along a curved path (for example, a football following an arced trajectory when kicked).

3. Angular or rotational motion - movement around an axis (for example, a figure skater spinning on one foot).

4. General motion - combination of linear and angular motion (for example, a cyclist pedaling while moving forward).

What is linear motion?

Linear motion is movement along a straight path, where all parts of the object move the same distance in the same direction over a given time.

Linear motion is movement along a straight path, where all parts of the object move the same distance in the same direction over a given time.

• Position: The location of an object or body, usually described relative to an origin.

• Coordinates: Numerical values that measure distance from an origin (in meters), given in 2D as (x,y)(x,y) or in 3D as (x,y,z)(x,y,z), representing horizontal, vertical, and lateral directions depending on the coordinate system.

What is the difference between distance and displacement?

• Distance: The total length of the path traveled, regardless of direction - it is a scalar quantity.

• Displacement: The shortest straight-line distance between the starting and ending positions, including direction - it is a vector quantity.

Define speed and give its formula and units.

Speed is the rate of change of distance over time. It is a scalar quantity.

Formula: Speed=Distance/Time

Units: meters per second (m/s).

Define velocity and give its formula and units.

Velocity is the rate of change of displacement over time and includes direction. It is a vector quantity.

Formula: Velocity=Displacement/Time​

Units: meters per second (m/s), with a specified direction (for example, 10 m/s east).

Define acceleration and give its formula and units.

Acceleration is the rate of change of velocity over time.

Formula: Acceleration=Change in velocity/Time taken = v−ut​

Units: meters per second squared (m/s²).

It can be positive (speeding up) or negative (slowing down).

What is inertia and how is it related to mass?

Inertia is the property of matter that causes an object to resist changes in its state of motion (resist starting, stopping, or changing direction). The greater the mass of an object, the greater its inertia.

State Newton's First Law of Motion (law of inertia).

Newton's First Law states that an object will remain at rest or continue moving at a constant velocity in a straight line unless acted upon by an external force.

State Newton's Second Law of Motion and give its equation.

Newton's Second Law states that the acceleration of an object is proportional to the net force applied and inversely proportional to its mass.

Equation: F=ma

Where F is force (N), m is mass (kg), and a is acceleration (m/s²).

Rearrange Newton's Second Law using change in velocity and time, and explain the terms.

Newton's Second Law can be written as: F=m(v−u)/t

Where:

• F is force (N)

• m is mass (kg)

• u is initial velocity (m/s)

• v is final velocity (m/s)

• t is time taken for the change (s).

State Newton's Third Law of Motion (law of action-reaction).

Newton's Third Law states that when two objects interact, they exert forces on each other that are equal in magnitude and opposite in direction. These action and reaction forces act on different objects.

Why do action and reaction forces in Newton's Third Law not cancel each other out?

Action and reaction forces do not cancel because they act on different objects. For example, when an athlete pushes down on the ground, the ground exerts an equal and opposite force on the athlete, propelling them upward or forward.

What is stability in sport, and what are the four key factors that influence it?

Stability is the ability to maintain equilibrium and resist changes in position.

Four key factors:

1. Height of center of mass - lower height increases stability.

2. Size of base of support - wider base increases stability.

3. Position of line of gravity - should fall within the base of support.

4. Total mass - greater mass generally increases stability.

Distinguish between stability and balance with a sporting example.

• Stability: Resistance to movement or change in position. For example, a sumo wrestler has high stability due to low center of mass, wide base of support, and large mass.

• Balance: Ability to maintain a controlled body position. A gymnast may have excellent balance but less overall stability when performing on a narrow beam.

Define momentum and give its formula and units.

Momentum is the quantity of motion of a moving body, equal to the product of its mass and velocity.

Formula: p=mv

Where p is momentum (kg·m/s), m is mass (kg), and v is velocity (m/s).

Around what can angular motion occur in sport movements?

Angular motion can occur around a real axis (such as a bicycle wheel axle) or an imaginary axis (such as a gymnast rotating around their center of mass in mid-air).

What is angular displacement (θ)?

Angular displacement is the change in the angular position of a rotating body. It is a vector quantity with both magnitude and direction.

How is the direction of angular displacement or angular velocity defined?

Direction is defined using the right-hand rule: counterclockwise rotation is taken as positive, and clockwise rotation as negative.

What is angular velocity (ω) and its basic formula?

Angular velocity is the rate at which an object rotates around an axis. It is given by: ω=θ/t where:

• ω - angular velocity (rad/s)

• θ - angular displacement (rad)

• t - time (s)

What is angular acceleration (α) and its formula?

Angular acceleration is the rate at which angular velocity changes over time. It is given by: α=Δω/Δt​ where:

• α - angular acceleration (rad/s²)

• Δω - change in angular velocity (rad/s)

• Δt - time interval (s)

How are linear velocity and angular velocity related?

Linear velocity v and angular velocity ωω are related by: v=r⋅ω where:

• v - linear velocity (m/s)

• r - radius (m)

• ω - angular velocity (rad/s).

In angular motion, how do linear speeds of different points on a rotating body compare?

All points share the same angular displacement, angular velocity, and angular acceleration, but points farther from the axis have a greater linear speed because v=r⋅ω.

What is a force in the context of sports biomechanics?

A force is a mechanical interaction between two objects or bodies that can change the motion (linear or angular) of an object.

What is the difference between mass and weight?

• Mass is the amount of material in a body.

• Weight is the gravitational force acting on a body due to a gravitational field.

What is angular momentum (L) and its formula?

Angular momentum measures the amount of rotational motion an object has or can achieve. It is a vector quantity and is given by: L=I⋅ωL=I⋅ω where:

• L - angular momentum (kg·m²/s)

• I - moment of inertia (kg·m²)

• ω - angular velocity (rad/s).

What is the conservation of angular momentum?

The conservation of angular momentum states that the angular momentum of a spinning system remains constant unless acted upon by an external torque.

When can a gymnast or diver change their total angular momentum during a skill?

They can only change total angular momentum during contact phases (for example, when in contact with the ground or equipment). While airborne with no external torque, total angular momentum remains constant.

What is moment of inertia (I)?

Moment of inertia is a measure of how difficult it is for an object or body to rotate about an axis. It depends on the mass and how that mass is distributed relative to the axis.

How does changing body position affect moment of inertia and angular velocity in athletes?

Bringing mass closer to the axis (tucking) decreases moment of inertia and increases angular velocity. Moving mass farther from the axis (extending) increases moment of inertia and decreases angular velocity, if angular momentum is conserved.

What is torque in rotational motion?

Torque is the turning effect of an eccentric force (a force not acting through the axis of rotation) on an object that can rotate. It depends on:

• Size of the force

• Direction of the force

• Distance from the axis of rotation (moment arm).

Explain why a diver can spin faster when tucking compared to when fully extended, assuming no external torque.

With constant angular momentum, L=I⋅ω

• Tucking decreases moment of inertia (I).

• To keep L constant, angular velocity (ω) must increase.

So the diver spins faster when tucking and slower when extending.

What is meant by transfer of angular momentum between body segments?

In the absence of external torque, total angular momentum of the body stays constant, but different body segments can speed up or slow down relative to each other. When one part increases its angular velocity, another part must decrease its angular velocity to maintain total angular momentum.

How can an athlete use trading angular momentum to create twisting during a somersault?

Because angular momentum is a vector, an athlete rotating about one axis (somersault) can tilt their body so that some of that angular momentum is redirected into rotation about another axis (twist). The combination of vectors results in a new axis of rotation, producing twisting motion during the somersault.

List the four main factors that affect stability in sport and how each one influences stability.

Stability depends on:

1. Height of the center of mass - Lowering the center of mass increases stability.

2. Size of the base of support - A wider base increases stability.

3. Position of the line of gravity - Stability is greatest when the line of gravity falls within the base of support.

4. Mass - Greater mass generally increases stability by making the body harder to move.

What is angular motion in biomechanics?

Angular motion is the motion of a body about a fixed point or fixed axis, where the body rotates rather than moving in a straight line.

What is the formula for momentum? (HL)

p=mv

What are the two factors that momentum depends on? (HL)

1. Mass (m: kg)

2. Velocity (v: ms^-1).

Define impulse. (HL)

The change in momentum, calculated as the product of force and time: F×Δt.

How is impulse related to momentum change? (HL)

The change in momentum equals the impulse.

What does it mean for momentum to be conserved in a closed system? (HL)

Total momentum before a collision equals total momentum after a collision.

What is the difference between momentum and force? (HL)

Momentum is mass×velocity (mv), while force is mass×acceleration (ma).

What are the three types of collisions? (HL)

1. Elastic collisions

2. Inelastic collisions

3. Perfectly inelastic collisions.

What happens in a perfectly inelastic collision? (HL)

The objects stick together, resulting in maximum energy loss.

What is the coefficient of restitution (CR)? (HL)

A measure of how much kinetic energy remains after a collision, determining the elasticity of the impact.

What is the formula for calculating CR? (HL)

CR= v2 - v1 / u1 - u2

What factors affect the coefficient of restitution? (HL)

1. Material properties

2. Surface conditions

3. Temperature

4. Impact velocity.

How does temperature affect COR? (HL)

Warmer objects have a higher COR due to increased elasticity, while cold temperatures reduce elasticity, decreasing COR.

What is the difference between CR and the amount of energy conserved? (HL)

CR measures the ratio of velocities, not energy. High CR doesn't mean all energy is conserved.

Give an example of CR application in sports. (HL)

Tennis balls lose COR over time, affecting their rebound on different court surfaces.

How can impulse be maximized in high jump? (HL)

By applying force over a longer time during take-off.

What is one way safety engineering uses the principles of momentum? (HL)

Car crumple zones increase impact time to reduce force.

What role do tennis racquet strings play in collisions? (HL)

They affect the 'bounce' and coefficient of restitution (CR) after impact.

What is the relationship between momentum change and energy transfer in a collision? (HL)

Every collision involves a change in momentum and a transfer of energy between objects.

What does a high coefficient of restitution indicate? (HL)

Maximum energy retention and a greater ability for objects to bounce back after a collision.

Why are boxing gloves designed to increase impact time? (HL)

To reduce the force felt by the opponent by increasing the time of the impact.

What is friction? (HL)

Friction is a force that opposes the motion between two surfaces in contact, acting parallel to the surfaces and in the opposite direction of motion.

Give an example of friction in action. (HL)

When you push a box across the floor, friction acts against the direction of your push, making it harder to move the box.

What is static friction? (HL)

Static friction is the force that prevents two surfaces from sliding past each other when at rest.

What is dynamic friction? (HL)

Dynamic friction is the force that opposes the motion of two surfaces sliding against each other.

What is the difference between static and dynamic friction? (HL)

Static friction prevents movement, while dynamic friction opposes movement that is already occurring.

Which is greater: static friction or dynamic friction? (HL)

Static friction is always greater than dynamic friction.

Why is it harder to start moving a stationary object than to keep it moving? (HL)

Because static friction is greater than dynamic friction.

What is the coefficient of friction? (HL)

The coefficient of friction is a number that measures how much friction exists between two surfaces.

What does the coefficient of friction depend on? (HL)

It depends on the materials in contact and their surface characteristics.

What is the formula for static friction? (HL)

Fs​=μs​×N

Where Fs is the static friction force, μs is the coefficient of static friction, and N is the normal force.

What is the formula for dynamic friction? (HL)

Fk​=μk​×N

Where Fk is the dynamic friction force, μk​ is the coefficient of dynamic friction, and N is the normal force.

Are heavier objects associated with higher coefficients of friction? (HL)

No, the coefficient of friction is independent of weight and only depends on the surfaces in contact.

What factors affect the coefficient of friction? (HL)

1. Surface characteristics (roughness, material, temperature, cleanliness)

2. Environmental conditions (moisture, temperature, debris, air pressure)

3. Applied forces (normal force, direction of motion, speed)

How can friction be increased for better performance in sports? (HL)

1. Gymnasts use chalk

2. Basketball players choose high-traction shoes

3. Rock climbers use specialized rubber footwear

4. Rugby players wear studded boots

How can friction be decreased for speed in sports? (HL)

1. Skiers wax their skis

2. Swimmers wear streamlined suits

3. Bobsled runners are highly polished

4. Speed skaters minimize ice contact

What is the difference between the coefficient of friction and frictional force? (HL)

The coefficient of friction is a ratio and has no units, while the frictional force is measured in newtons (N).

What is the key to optimal performance regarding friction in sports? (HL)

Managing friction - not just maximizing or minimizing it.

Why is understanding friction important in sports? (HL)

It challenges the notion that 'natural' athletic ability is all that matters and shows how technology and science can transform sports equipment and techniques.

What is the definition of work? (HL)

Work is the application of force over distance, transforming energy from one form to another.

When is work considered to be done? (HL)

Work is done if displacement occurs.

What happens to work when force and displacement are in the same direction? (HL)

Work is positive.

What happens to work when force and displacement are in opposite directions? (HL)

Work is negative.

Is work done if the force is perpendicular to movement? (HL)

No, no work is done.

What is the formula for calculating work? (HL)

W=F×D

What does each variable in the work formula represent? (HL)

W = Work (J), F = Force (N), D = Displacement (m)

Give an example of positive, negative, and no work in weightlifting. (HL)

Positive: Lifting a weight, Negative: Lowering a weight, No work: Holding a weight overhead.

What is the definition of power? (HL)

Power is the amount of energy transferred or converted per unit time.

What is the formula for power? (HL)

P=ΔW/Δt

What does ΔW and Δt represent in the power formula? (HL)

ΔW = change in work done, Δt = change in time.

What are the key factors affecting power? (HL)

1. Force applied 2. Speed of movement.

How is power relevant in sports? (HL)

Power is crucial for explosive movements and sustained power in various activities.

What is the difference between explosive power and sustained power? (HL)

Explosive power is high output for short bursts (e.g., sprinting), sustained power is lower output over time (e.g., distance running).

What are some ways to optimize power output? (HL)

Through technique (biomechanics, efficient patterns) and equipment (sizing, material selection).

What is energy? (HL)

The ability to do work, which is the ability to exert a force causing displacement.

What is kinetic energy? (HL)

Energy of motion, which depends on mass and speed.

What is potential energy? (HL)

Stored energy due to an object's position or condition.

What is elastic potential energy? (HL)

Energy stored in objects that can stretch or compress, like springs or muscle tendons.

How does work relate to energy? (HL)

Work is needed to change an object's energy.

What is the relationship between power and work? (HL)

Power determines how quickly an athlete can use energy to perform work.

Give an example of power and energy in sports. (HL)

A cyclist generates power by continuously applying force to the pedals.