AQA A-Level Physics Paper 1, June 2024: Question 29

1 mark · Medium difficulty · Multiple Choice

Calculate the kinetic energy of a particle of mass m moving in a circle of radius r with frequency f.

Practise this question

Question

Multiple choice question numbered 29, worth 1 mark. It asks for the kinetic energy of a particle of mass m moving in a circle of radius r where the number of revolutions per second is f. Four options A, B, C, and D are given as algebraic expressions involving m, r, f, and pi.
Question text

29 A particle of mass m moves in a circle of radius r. The number of revolutions completed

per second is f.

What is the kinetic energy of the particle?

[1 mark]

22 2

A 4π mf r

22 2

B 2π mf r

mf r2 2

C 2

4π

mf r2 2

D

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is B, corresponding to the expression 2 pi squared m f squared r squared, assessed under AO1.

22 2

29 B 2π mf r AO1

How to answer it

Kinetic Energy in Circular Motion

📌 What this question tests

This question tests your ability to combine foundational equations of mechanics—specifically kinetic energy and circular motion—by linking linear speed to frequency and radius, and manipulating algebraic expressions correctly.

Question 29: Multiple Choice

Full Mark Breakdown: [1 mark] for option B

✅ Correct Answer: B

The correct option is B ( 2π²mf²r² ). Top-level responses quickly link the definition of kinetic energy with the circular velocity formula containing frequency.

💡 Key Knowledge

  • Kinetic Energy equation: Ek = ½mv²
  • Linear speed in terms of frequency and radius: v = ωr = 2πfr
  • Algebraic substitution and squaring rules for brackets.

🧠 Exam Technique

Instead of working blindly through all options, derive the correct expression on your rough paper first, then match it to the given choices. This saves valuable time in multiple-choice sections.

❌ Common Errors

Students frequently forget to square the entire term (2πfr) , leading to missing factors of 4 or forgotten squared values for π, frequency, or radius.

📐 Step-by-Step Derivation

  1. Start with the target quantity: Write down the formula for kinetic energy:
    Ek = ½mv²
  2. Relate linear speed to frequency ( f ): Recall that angular velocity ω = 2πf and linear speed v = ωr . Therefore:
    v = 2πfr
  3. Substitute speed into the kinetic energy formula:
    Ek = ½m(2πfr)²
  4. Expand the squared bracket carefully:
    (2πfr)² = 4π²f²r²
  5. Simplify the final expression:
    Ek = ½ × m × 4π²f²r² = 2π²mf²r²
Examiner Note (AO1): This is a standard Assessment Objective 1 (demonstrating knowledge and understanding of physics equations) multiple-choice item where successful recall and algebraic substitution secure the mark.

Topics

Physics · 3.6 Further mechanics and thermal physics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.