AS Level Physics (9702) Study Notes: Chapter 3 – Dynamics

Hello future physicist! Welcome to the chapter on Dynamics. If Kinematics (Chapter 2) taught you how things move (speed, acceleration), Dynamics explains why they move—it’s the study of forces and how they create motion.


This chapter is the foundation for almost all future mechanics topics, so mastering Newton’s Laws and the concept of momentum here will make the rest of your AS journey much smoother! Let’s dive in.

3.1 Mass, Inertia, and Newton’s Laws of Motion

Mass and Inertia

Before we talk about forces, we need to understand the concept of mass.

  • Mass (\(m\)): This is a measure of the amount of matter in an object. It is a scalar quantity (only magnitude).
  • Inertia: Mass is fundamentally the property of an object that resists change in motion. The more massive an object is, the harder it is to start moving, stop moving, or change direction.

Analogy: Imagine pushing a shopping cart full of feathers versus a shopping cart full of bricks. The bricks cart has more mass and therefore more inertia, making it harder to change its speed.

Newton’s First Law: The Law of Inertia

Newton’s First Law states that an object will remain in its state of rest or uniform velocity unless acted upon by a resultant (net) external force.

  • If the resultant force \(F_{resultant} = 0\), the object maintains a constant velocity (which includes being at rest, \(v=0\)).
Newton’s Second Law: Force and Acceleration

Newton’s Second Law is the core mathematical relationship in Dynamics. It links force, mass, and acceleration.

Definition 1: \(F = ma\)

The resultant force acting on an object is directly proportional to the acceleration it produces, and the acceleration is in the same direction as the resultant force.

$$F = ma$$

  • \(F\) must be the Resultant Force (the vector sum of all forces acting on the object).
  • \(F\) is measured in Newtons (N). \(1 \text{ N} = 1 \text{ kg m s}^{-2}\).

Definition 2: Force as Rate of Change of Momentum

The more fundamental definition of force, which applies universally (even when mass changes), is:

Force is equal to the rate of change of momentum.

$$F = \frac{\Delta p}{\Delta t}$$

We will explore momentum (\(p\)) more in Section 3.3.

Weight (\(W\))

Weight is defined as the effect of a gravitational field on a mass. It is a force, always acting downwards (towards the center of the gravitational field).

$$W = mg$$

  • \(W\) is Weight (Force, N).
  • \(m\) is Mass (kg).
  • \(g\) is the acceleration of free fall (gravitational field strength, m s\(^{-2}\) or N kg\(^{-1}\)).

Key distinction: Mass is constant everywhere; Weight depends on the local gravitational field strength (\(g\)).

Newton’s Third Law: Action and Reaction

Newton’s Third Law states that if body A exerts a force on body B (the action force), then body B exerts an equal and opposite force on body A (the reaction force).

  • The forces must be of the same type (e.g., both gravitational or both contact forces).
  • The forces act on different bodies.

Example: A rocket pushes hot gas downwards (action). The hot gas pushes the rocket upwards with an equal and opposite force (reaction). This upward force is what propels the rocket.

Quick Review: Newton's Laws Mnemonic (I-A-R)
  • Inertia (N1L): If \(F_{net}=0\), velocity is constant.
  • Acceleration (N2L): \(F_{net} = ma\).
  • Reaction (N3L): Forces come in equal and opposite pairs acting on different objects.

3.2 Non-Uniform Motion and Resistive Forces

Understanding Resistive Forces

In the real world, objects rarely move freely. They usually encounter resistive forces like friction and drag (viscous forces, air resistance).

  • Friction: A force opposing motion between two surfaces in contact.
  • Viscous/Drag Forces (Air Resistance): Forces opposing motion through a fluid (liquid or gas).

Qualitative Understanding: We don't need complex equations for these forces in AS Level, but you must know that:

  1. Resistive forces generally oppose motion.
  2. Viscous/drag forces increase as the speed increases. (Think about cycling slowly vs. cycling very fast—air resistance is much greater when you're fast.)
The Concept of Terminal Velocity

When an object falls in a uniform gravitational field and encounters air resistance (or viscous drag), its motion is non-uniform until it reaches a constant maximum speed called terminal velocity.

Step-by-Step Motion of a Falling Object (e.g., a Skydiver):

  1. Start (\(t=0\)): The object accelerates rapidly. The only forces acting are Weight (W, downwards) and zero Drag (D=0). Resultant force \(F_{net} = W\).
  2. Acceleration Phase: Speed increases. As speed increases, the Drag (D) force also increases. \(F_{net} = W - D\). Since \(F_{net} > 0\), the object is still accelerating, but the acceleration is decreasing.
  3. Terminal Velocity (\(v_T\)): The object reaches a speed where the Drag force (D) becomes exactly equal to the Weight (W).
    At this point, \(D = W\). Therefore, the Resultant Force \(F_{net} = 0\).
  4. Since \(F_{net} = 0\), Newton's First Law applies: the object stops accelerating and continues falling at a maximum, constant speed, which is the terminal velocity.

Did you know? Parachutes work by dramatically increasing the surface area, which in turn dramatically increases the drag force (D) at a lower speed, allowing the parachutist to reach a much lower, safer terminal velocity.

3.3 Linear Momentum and its Conservation

Linear Momentum (\(p\))

Linear Momentum is a measure of the "quantity of motion" an object has.

It is defined as the product of an object's mass and its velocity.

$$p = mv$$

  • Momentum (\(p\)) is a vector quantity (it has direction, the same direction as velocity).
  • Units: kg m s\(^{-1}\) (kilogram meters per second).
Force and Momentum (Revisiting N2L)

We saw earlier that force is the rate of change of momentum: \(F = \Delta p / \Delta t\).

This equation is particularly useful in collision scenarios:

If a force \(F\) acts for a time interval \(\Delta t\), the total change in momentum is:

$$\text{Change in Momentum } (\Delta p) = F \times \Delta t$$

The quantity \(F \Delta t\) is often called Impulse, representing the sudden push or pull needed to change an object's motion.

The Principle of Conservation of Momentum (PCM)

The PCM is one of the most important laws in Physics.

Statement: For a system of interacting objects, the total momentum remains constant, provided no external resultant force acts on the system.

In simpler terms:

$$\text{Total Momentum Before Interaction} = \text{Total Momentum After Interaction}$$

$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$

(Remember: Since momentum is a vector, you must assign directions—e.g., motion to the right is positive, motion to the left is negative.)

Applying the Conservation of Momentum

PCM is used to solve problems involving collisions (objects hitting each other) and explosions (objects separating from rest).

Example (Recoil): When a gun fires a bullet, the total momentum of the gun-bullet system is zero before firing. After firing, the bullet gains momentum in one direction, and the gun gains an equal and opposite momentum (recoil) in the other direction, ensuring the total momentum remains zero.

$$0 = (m_{bullet} v_{bullet}) + (m_{gun} v_{gun})$$

3.4 Collisions: Elastic and Inelastic

While momentum is always conserved in any interaction (as long as there are no external forces), the total energy of the system may or may not be conserved. This leads to the distinction between two types of interactions:

1. Elastic Collisions

In an elastic collision, both total momentum and total kinetic energy (KE) are conserved.

  • Momentum: Conserved (\(m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2\)).
  • Kinetic Energy: Conserved (\(\Sigma KE_{before} = \Sigma KE_{after}\)).
  • Relative Speeds: The relative speed of approach before the collision is equal to the relative speed of separation after the collision.

Example: Collisions between atomic particles or billiard balls (nearly elastic).

2. Inelastic Collisions

In an inelastic collision, total momentum is conserved, but total kinetic energy is NOT conserved. Some kinetic energy is converted into other forms, such as heat, sound, or permanent deformation (damage).

  • Momentum: Always conserved.
  • Kinetic Energy: Not conserved (\(\Sigma KE_{before} > \Sigma KE_{after}\)). Some KE is lost/changed.

Example: A car crash, or when two sticky pieces of clay collide and stick together (a perfectly inelastic collision).

Momentum in Two Dimensions

The Principle of Conservation of Momentum applies to vectors. If an interaction happens in two dimensions (like two hockey pucks colliding at an angle), you must apply the PCM separately to the components:

  • Total momentum in the x-direction is conserved.
  • Total momentum in the y-direction is conserved.
🛑 Common Mistake to Avoid

Students often confuse the conservation laws:

  • NEVER assume Kinetic Energy is conserved unless the problem explicitly states the collision is elastic.
  • ALWAYS assume Momentum is conserved in collisions/explosions, regardless of whether they are elastic or inelastic (assuming zero net external force).


Key Takeaway from Dynamics (Chapter 3)

Dynamics explains motion through forces. Newton’s Second Law (\(F=ma\) or \(F=\Delta p / \Delta t\)) is the key tool for finding acceleration when a resultant force is present. If there is no resultant force, momentum is conserved. When analyzing motion with resistance, remember that terminal velocity is reached when the resistive force balances the weight, resulting in zero net force.