AQA A-Level Physics Paper 1, June 2025: Question 25

AQA A-Level Physics • Periodic Motion

SHM: Pendulum Dynamics & Energy Exchanges

What this question tests

Understanding the relationship between displacement, acceleration, velocity/momentum, and potential energy in simple harmonic motion (SHM). Specifically, locating the equilibrium position and identifying key physical quantities at that point.

Question 25 Analysis

Multiple Choice: Identifying Momentum and GPE at Zero Acceleration

✅ Correct Answer: B

Momentum: maximum
GPE: minimum

Award: 1 Mark (AO1) for option B selected.

💡 Key Knowledge

Defining SHM equation: a = −ω²x . Acceleration is directly proportional to displacement and directed towards the equilibrium position.
When acceleration a = 0 , displacement x = 0 . This is the equilibrium (centre) position.
Velocity & Momentum: Speed reaches its peak at the equilibrium position ( v max = ±ωA ), so momentum ( p = mv ) is maximum.
Energy changes: A pendulum bob is at its lowest vertical height at equilibrium, meaning gravitational potential energy ( E p = mgh ) is at a minimum (and kinetic energy is maximum).

🔧 Step-by-Step Deduction

Identify where a = 0 :
From a = −ω²x , if a = 0 , then x = 0 . The pendulum is swinging through its lowest central point (the equilibrium position).
Determine Momentum ( p ):
At x = 0 , speed is maximum ( v max ). Since p = mv , momentum must be maximum (eliminates options A and D).
Determine Gravitational Potential Energy ( GPE ):
At the centre of the swing, the bob is at its lowest height ( h min ). Since GPE = mgh , GPE is at a minimum (eliminates option C).
Conclusion: Row B is the only matching option.

🧠 Exam Technique

Translate words to positions: Whenever an SHM question specifies a condition (e.g. acceleration is zero or velocity is zero), instantly map it to either amplitude ( x = ±A ) or equilibrium ( x = 0 ).
Use Conservation of Energy: Total energy is constant ( E total = E k + E p ). Maximum kinetic energy (and maximum momentum) always coincides with minimum potential energy. This immediately rules out C and D!

❌ Common Traps & Misconceptions

Confusing the positions: Thinking acceleration is zero at the extremes/turning points. At the extremes, speed is zero, but acceleration and restoring force are at their maximum.
Confusing momentum with acceleration: Some students incorrectly assume that when acceleration is zero, the bob is "not moving" ( v = 0 , p = 0 ), leading them to select A. Remember: zero acceleration means constant instantaneous velocity (i.e. the turning point of velocity, where it reaches peak value), not zero velocity!
Choosing simultaneous maximums: Selecting C (maximum momentum AND maximum GPE) violates conservation of mechanical energy in a simple pendulum.

📊 Mental Diagram Check: The Pendulum Cycle

Extremes (Left / Right, x = ±A ): Height is greatest → GPE = max , KE = 0 , v = 0 , p = 0 , a = max .
Equilibrium (Centre, x = 0 ): Height is lowest → GPE = min , KE = max , v = max , p = max , a = 0 .