Unit 2: Dynamics

# Dynamics

In AP Physics 1, dynamics is a crucial topic that deals with the study of the causes of motion and changes in motion. It is a fundamental concept that helps us understand the behavior of objects and systems in the physical world. Dynamics involves the application of Newton's laws of motion, which are the backbone of classical mechanics. These laws explain how forces affect the motion of an object and how the motion of an object affects the forces acting upon it.

# Newton's Laws of Motion

## First Law: Law of Inertia

This law is also referred as **The Law of Inertia** because it explains the tendency of objects to resist changes in their state of motion. For example, an object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant speed, unless acted upon by an external force. This law is particularly important in understanding the behavior of moving objects, such as planets, satellites, and even cars.

An object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity, unless acted upon by a net external force.

Inertia is the tendency of an object to resist changes in its motion.

# Gravitational vs Inertial Mass

## Gravitational Mass

Gravitational Mass is determined by the strength of the gravitational force experienced by the body. Gravitational Mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass hence the equation:

`F= G*m1m2/r^2`

Gravitational mass is the measure of the strength of the gravitational force experienced by an object when it is placed in a gravitational field.

It is the mass that determines the strength of the gravitational attraction between two objects.

Gravitational mass is measured by comparing the weight of an object to a known standard mass under the influence of gravity.

## Inertial Mass

Inertial mass is found my applying a known force to an unknown mass, and applying a = F/M hence the formula:

`a = F/m`

Inertial mass is the measure of an object's resistance to a change in its state of motion.

It is the mass that determines the force required to accelerate an object.

Inertial mass is measured by applying a known force to an object and measuring its resulting acceleration.

## Second Law: Law of Acceleration

Newton’s second law predicts what will happen if an unbalanced force does not act on an object which is that the object will accelerate. Precisely, his law states that the objects acceleration a, will be directly proportional to the strength of the total force Fnet and inversely proportional to the object’s mass, m.

`a = F/M`

Fnet = ma or ΣF = ma

The acceleration of an object is directly proportional to the net external force acting on the object, and inversely proportional to its mass.

F = ma, where F is the net external force, m is the mass of the object, and a is its acceleration.

## Third Law: Law of Action-Reaction

Newton’s Third Law states, “For every action, there is an equal and opposite reaction.” This means that in every interaction between forces, there is ALWAYS a pair or forces action on the same object. The magnitude of each force is the same keeping the object balanced and in equilibrium. Forces always come in pair - equal and opposite action - reaction force pairs.

For every action, there is an equal and opposite reaction.

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

When two bodies interact, they exert forces on each other. These forces are equal in magnitude and opposite in direction.

Force pairs always act in opposite directions, but they do not always cancel each other out.

## Limitations and Applications of Newton's Laws

Projectile motion: the motion of an object that is launched into the air and then moves under the influence of gravity.

Circular motion: the motion of an object that moves in a circular path.

Friction: the force that opposes motion between two surfaces that are in contact.

Tension: the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.

Newton's laws are only valid in inertial reference frames.

Newton's laws do not apply to objects that are moving at speeds close to the speed of light.

Newton's laws do not take into account the effects of quantum mechanics.

# Key Information for Gravity and Forces

**Gravity**: Two bodies with mass attract each other and exert gravitational forces.**Normal Force:**A surface exerts an upward force on a body to balance the downward force of gravity.**Tension**: A rope or string pulled tight exerts a force on connected objects.**Compression:**A rope or string pushed together exerts a force on connect objects.**Friction**: Two surfaces rubbing against each other exert a force that resists relative motion.**Applied Force:**A force applied to a body causes the body to exert a force in the opposite direction.

Understanding the different types of forces and how they interact with each other is crucial in many fields, including physics, engineering, and even everyday life. By analyzing the forces at play in a given situation, we can predict how objects will move and interact with each other, and design systems and structures that are safe and efficient. These are some important forces to know for the AP Physics 1 exam, and it can help you with many MCQs and FRQs.

# Unit 2: Dynamics

# Dynamics

In AP Physics 1, dynamics is a crucial topic that deals with the study of the causes of motion and changes in motion. It is a fundamental concept that helps us understand the behavior of objects and systems in the physical world. Dynamics involves the application of Newton's laws of motion, which are the backbone of classical mechanics. These laws explain how forces affect the motion of an object and how the motion of an object affects the forces acting upon it.

# Newton's Laws of Motion

## First Law: Law of Inertia

This law is also referred as **The Law of Inertia** because it explains the tendency of objects to resist changes in their state of motion. For example, an object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant speed, unless acted upon by an external force. This law is particularly important in understanding the behavior of moving objects, such as planets, satellites, and even cars.

An object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity, unless acted upon by a net external force.

Inertia is the tendency of an object to resist changes in its motion.

# Gravitational vs Inertial Mass

## Gravitational Mass

Gravitational Mass is determined by the strength of the gravitational force experienced by the body. Gravitational Mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass hence the equation:

`F= G*m1m2/r^2`

Gravitational mass is the measure of the strength of the gravitational force experienced by an object when it is placed in a gravitational field.

It is the mass that determines the strength of the gravitational attraction between two objects.

Gravitational mass is measured by comparing the weight of an object to a known standard mass under the influence of gravity.

## Inertial Mass

Inertial mass is found my applying a known force to an unknown mass, and applying a = F/M hence the formula:

`a = F/m`

Inertial mass is the measure of an object's resistance to a change in its state of motion.

It is the mass that determines the force required to accelerate an object.

Inertial mass is measured by applying a known force to an object and measuring its resulting acceleration.

## Second Law: Law of Acceleration

Newton’s second law predicts what will happen if an unbalanced force does not act on an object which is that the object will accelerate. Precisely, his law states that the objects acceleration a, will be directly proportional to the strength of the total force Fnet and inversely proportional to the object’s mass, m.

`a = F/M`

Fnet = ma or ΣF = ma

The acceleration of an object is directly proportional to the net external force acting on the object, and inversely proportional to its mass.

F = ma, where F is the net external force, m is the mass of the object, and a is its acceleration.

## Third Law: Law of Action-Reaction

Newton’s Third Law states, “For every action, there is an equal and opposite reaction.” This means that in every interaction between forces, there is ALWAYS a pair or forces action on the same object. The magnitude of each force is the same keeping the object balanced and in equilibrium. Forces always come in pair - equal and opposite action - reaction force pairs.

For every action, there is an equal and opposite reaction.

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

When two bodies interact, they exert forces on each other. These forces are equal in magnitude and opposite in direction.

Force pairs always act in opposite directions, but they do not always cancel each other out.

## Limitations and Applications of Newton's Laws

Projectile motion: the motion of an object that is launched into the air and then moves under the influence of gravity.

Circular motion: the motion of an object that moves in a circular path.

Friction: the force that opposes motion between two surfaces that are in contact.

Tension: the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.

Newton's laws are only valid in inertial reference frames.

Newton's laws do not apply to objects that are moving at speeds close to the speed of light.

Newton's laws do not take into account the effects of quantum mechanics.

# Key Information for Gravity and Forces

**Gravity**: Two bodies with mass attract each other and exert gravitational forces.**Normal Force:**A surface exerts an upward force on a body to balance the downward force of gravity.**Tension**: A rope or string pulled tight exerts a force on connected objects.**Compression:**A rope or string pushed together exerts a force on connect objects.**Friction**: Two surfaces rubbing against each other exert a force that resists relative motion.**Applied Force:**A force applied to a body causes the body to exert a force in the opposite direction.

Understanding the different types of forces and how they interact with each other is crucial in many fields, including physics, engineering, and even everyday life. By analyzing the forces at play in a given situation, we can predict how objects will move and interact with each other, and design systems and structures that are safe and efficient. These are some important forces to know for the AP Physics 1 exam, and it can help you with many MCQs and FRQs.