Ceist Eile

Ceist Eile is in development. Features, questions and prices may change while we refine it.

Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Horizontal circular motion

How often Horizontal circular motion comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

OL Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Horizontal circular motion, Higher Level(7 marks)

Quick ones on Horizontal circular motion.

(a)Speed of a particle moving in a circle of radius r with angular velocity ω?
  1. v = ω/r
  2. v = rω
  3. v = r²ω
(b)A particle moves in a circle at constant speed. Direction of its acceleration?
  1. Away from the centre
  2. Along the tangent
  3. Towards the centre
(c)A 0.5 kg mass moves in a circle of radius 2 m at 3 rad/s. Centripetal force?
  1. 9 N
  2. 4.5 N
  3. 3 N
Show the answers

(a) v = rω

(b) Towards the centre

(c) 9 N

Your turn: Higher Level questions on Horizontal circular motion.

Higher Level

Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q1
2024Q7
2023Q3

Links open the State Examinations Commission’s paper for that year.

More Horizontal circular motion questions

Horizontal circular motion, 3 marks

A 0.3 kg mass on a 0.5 m string moves in a circle on a smooth table at 2 m/s. Tension?

  1. 1.2 N
  2. 0.6 N
  3. 2.4 N
Show the answer

2.4 N

The tension is the only horizontal force, so it supplies mv²/r = 0.3 × 4 ÷ 0.5 = 2.4 N. Forgetting to square v gives 1.2 N.

Horizontal circular motion, 2 marks

Conical pendulum with string length l at angle θ to the vertical. Radius of the circle?

  1. r = l tan θ
  2. r = l sin θ
  3. r = l cos θ
Show the answer

r = l sin θ

The string is the hypotenuse and the radius is the side opposite θ (θ is measured from the vertical). So r = l sin θ; l cos θ is the depth below the pivot.

Horizontal circular motion, 3 marks

Conical pendulum: ω² = g/(l cos θ). What is l cos θ?

  1. The depth of the circle below the pivot
  2. The radius of the horizontal circle
  3. The length of the string to the bob
Show the answer

The depth of the circle below the pivot

The string of length l makes angle θ with the vertical, so its vertical drop is l cos θ. So ω depends only on how far below the pivot the circle is, not on the mass.

Ordinary Level

Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q7
2024Q3
2023Q2

Links open the State Examinations Commission’s paper for that year.

More Horizontal circular motion questions

Horizontal circular motion, 3 marks

A particle moves on a circle of radius 2 m with ω = 3 rad s⁻¹. Its speed?

  1. 1.5 m s⁻¹
  2. 18 m s⁻¹
  3. 6 m s⁻¹
Show the answer

6 m s⁻¹

v = rω = 2 × 3 = 6 m s⁻¹. 18 is rω², which is the acceleration in m s⁻², not the speed.

Horizontal circular motion, 3 marks

A wheel turns at 2π rad s⁻¹. How many revolutions per minute is this?

  1. 6.28
  2. 60
  3. 120
Show the answer

60

2π rad is one revolution, so 2π rad s⁻¹ is 1 revolution per second, which is 60 per minute.

Horizontal circular motion, 2 marks

The force needed to keep a mass m moving on a circle of radius r at speed v is…

  1. mv² ÷ r, towards the centre
  2. mv² ÷ r, away from the centre
  3. mv ÷ r, towards the centre
Show the answer

mv² ÷ r, towards the centre

Circular motion needs a centripetal force pointing to the centre, of size mv²/r, which is the same as mrω².

Other Applied Maths topics

All of Leaving Cert Applied Maths