Ch 3 · 3 Dynamics · A Level Physics 9702
Topic 3 of 3 in Physical Quantities, Kinematics and Dynamics — A Level Physics 9702 — 64 lessons.
Introduction
Kinematics describes motion; dynamics explains it. Newton's three laws and the idea of momentum let you predict how forces change motion, from a falling skydiver to colliding snooker balls. (Syllabus topic 3: sections 3.1–3.3.)
Key ideas — 3.1 (a) Mass, force and acceleration
Mass is the property of an object that resists change in its motion (its inertia). The greater the mass, the harder it is to speed up, slow down or change direction.
🧑🏫 Teacher's explanation
Imagine you are pushing a shopping trolley. If the trolley is empty, it is easy to speed up or stop; if it is filled with heavy bags of rice, it becomes much harder to change its speed. This 'stubbornness' or resistance to changing motion is what we call mass. It is not just 'how much stuff' is there, but a measure of how much an object resists being moved.
📖 Definitions
🔍 Worked example — Easy
A constant force of 15 N is applied to a mass of 3.0 kg. Calculate the acceleration of the mass.
🔍 Worked example — Standard
A 0.50 kg object is moving through a fluid. A drag force of 2.5 N acts against its motion. If the object is being pushed forward by a driving force of 6.5 N, calculate the acceleration.
🔍 Worked example — Exam-style
A skydiver of mass 85 kg is falling at terminal velocity. Calculate the magnitude of the air resistance acting on the skydiver.
⚠️ Common errors
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🎯 Exam question
Key ideas — 3.1 (b) Linear momentum and force
Linear momentum p is the product of mass and velocity:
🧑🏫 Teacher's explanation
Think of momentum as 'how hard it is to stop something.' A heavy truck moving slowly and a small bullet moving very fast both have a lot of momentum. Because momentum is a vector, direction matters—if two objects are moving towards each other, their momenta are in opposite directions.
📖 Definitions
🔍 Worked example — Easy
A car of mass 1200 kg is traveling at 20 m s^-1. Calculate its momentum.
🔍 Worked example — Standard
A 0.5 kg ball moving at 10 m s^-1 hits a wall and rebounds at 8 m s^-1 in the opposite direction. Calculate the change in momentum.
🔍 Worked example — Exam-style
A 2.0 kg trolley moving at 3.0 m s^-1 collides with a stationary 1.0 kg trolley. After the collision, they move together as a single unit. Calculate their common velocity.
⚠️ Common errors
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🎯 Exam question
Key ideas — 3.1 (c) Newton's laws of motion
Example of a third-law pair: the Earth pulls you down with your weight; you pull the Earth up with an equal gravitational force. (Your weight and the floor's normal contact force are not a third-law pair: they act on the same body and are different types of force.)
🧑🏫 Teacher's explanation
Imagine you are pushing a heavy shopping trolley. If the trolley is moving at a constant speed in a straight line, you aren't actually changing its motion; you are just balancing out the friction from the floor. This is Newton's First Law: motion only changes when there is an unbalanced (resultant) force.
📖 Definitions
🔍 Worked example — Easy
A car of mass m = 1200 kg is traveling at a constant velocity of 20 m s^-1. Calculate the resultant force acting on the car.
🔍 Worked example — Standard
A force of 50 N is applied to a 2.5 kg mass for 3.0 s. Calculate the change in momentum Δ p.
🔍 Worked example — Exam-style
A 0.50 kg ball moving at 4.0 m s^-1 hits a wall and rebounds at 3.0 m s^-1 in the opposite direction. Calculate the average force exerted by the wall if the collision lasts 0.050 s.
⚠️ Common errors
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🎯 Exam question
Key ideas — 3.1 (d) Weight
Weight is the effect of a gravitational field on a mass: the gravitational force on it.
🧑🏫 Teacher's explanation
Imagine you are holding a heavy backpack. The backpack itself has a certain amount of 'stuff' inside it—this is its mass. Now, imagine you are standing on Earth. Earth is pulling on that 'stuff' with a gravitational force. That pull you feel tugging your shoulders down is what we call weight.
📖 Definitions
🔍 Worked example — Easy
A textbook has a mass of 1.5 kg. Calculate its weight on Earth, where g = 9.81 m s^-2.
🔍 Worked example — Standard
An astronaut weighs 785 N on Earth. Calculate the mass of the astronaut.
🔍 Worked example — Exam-style
A probe is sent to Mars, where the gravitational field strength is 3.71 m s^-2. If the probe has a mass of 450 kg, calculate its weight on Mars.
⚠️ Common errors
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🎯 Exam question
Key ideas — 3.2 Friction, drag and terminal velocity
(No coefficients of friction or viscosity are needed.)
🧑🏫 Teacher's explanation
Imagine you are running through a swimming pool. At first, you accelerate easily, but as you move faster, the water pushes back against you harder and harder. This resistance is called drag. In physics, when an object moves through a fluid (like air or water), it experiences a resistive force that increases as the object's speed increases.
📖 Definitions
🔍 Worked example — Easy
A skydiver has a mass of 80.0 kg. Calculate the weight of the skydiver. Use g = 9.81 m/s^2.
🔍 Worked example — Standard
A small sphere falls through a viscous liquid. At a certain moment, the drag force acting upwards is 0.45 N and the weight of the sphere is 1.20 N. Calculate the resultant force acting on the sphere.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — 3.3 Conservation of momentum
Principle of conservation of momentum: for a system of interacting objects, the total momentum remains constant, provided no resultant external force acts on the system.
🧑🏫 Teacher's explanation
Imagine you are on ice skates and you throw a heavy medicine ball forward. Even though you haven't pushed off a wall, you will slide backward. Why? Because the total 'quantity of motion' (momentum) of the system—you plus the ball—must stay the same if no outside force pushes you. If the ball gains momentum in one direction, you must gain an equal amount in the opposite direction to keep the total at zero.
📖 Definitions
🔍 Worked example — Easy
A 2.0 kg trolley moving at 3.0 m s^-1 collides with a stationary 1.0 kg trolley. After the collision, they move together as a single unit. Calculate their common velocity.
🔍 Worked example — Standard
A 0.50 kg ball moving at 4.0 m s^-1 undergoes a perfectly elastic collision with a 0.50 kg ball moving at 2.0 m s^-1 in the opposite direction. Calculate the velocity of the first ball after the collision, assuming the second ball comes to rest.
🔍 Worked example — Exam-style
A 5.0 kg projectile is fired from a cannon. The explosion provides an initial momentum of 25 kg m s^-1 to the projectile. If the projectile has a mass of 0.050 kg, calculate its launch velocity. Then, determine the momentum of the cannon (mass 500 kg) after the shot.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Worked example
Example 1: force from momentum. A 0.15 kg ball hits a wall at 20 m s⁻¹ and rebounds at 15 m s⁻¹ along the same line. Contact lasts 0.050 s. Find the average force on the ball.
Common mistakes
Practice
Answers: (1) If A exerts a force on B, B exerts an equal and opposite force of the same type on A. (2) 1200/900 = 1.33 m s⁻². (3) 0 = 60v + 40(1.5) ⇒ v = -1.0 m s⁻¹ (1.0 m s⁻¹ in the opposite direction). (4) As speed increases, drag increases until it equals the weight; the resultant force and acceleration become zero, so the velocity is constant. (5) 3.0 × 4.0 = 3.0 × 2.0 + 1.0 v ⇒ v = 6.0 m s⁻¹. Approach 4.0, separation 6.0 - 2.0 = 4.0: elastic (KE 24 J before and 6 + 18 = 24 J after).