Technique

Distance covered by a rolling wheel

Mensuration • Plane Figures • Circle

Statement

A wheel rolling without slipping advances by one circumference per revolution, so

distance = N \times 2 π r

and

N = \frac{distance}{2 π r}

; over a fixed distance the number of revolutions is inversely proportional to the radius.

How to use it

1Put the distance and the circumference in the same unit before dividing; a diameter in centimetres and a journey in kilometres is the usual trap.
2For two wheels covering the same distance, $N_{1} r_{1} = N_{2} r_{2}$ , so the smaller wheel turns more often.
3Where the count must be a whole number of complete revolutions, take the integer part of the quotient.

Worked example

A wheel of radius

35

cm rolls along a straight road. How far does it travel in

200

revolutions?

Step-by-step

1
$2 π r = 2 \times \frac{22}{7} \times 35 = 220$ cm
Why: One revolution advances the wheel by one circumference.
2
$200 \times 220 = 44000$ cm $= 440$ m

Answer

440

Watch out

It assumes rolling without slipping. The distance is one circumference per turn, not one diameter and not one radius, and a wheel's own rotation about its axle is irrelevant to how far its centre moves only if it slips.

Builds on

Area and circumference of a circle

Also known as

revolutions of a wheel, number of rounds, distance per revolution, rolling wheel

Distance covered by a rolling wheel

Statement

Worked example

Appears in past papers

2020 (II)

2016 (II)