IB Physics SL A.2.26 Angular and Linear Speed

Practise converting period, frequency, angular speed and tangential speed with ω = 2π/T and v = ωr, using radius rather than diameter and reporting angular units correctly.

Exam points

convert frequency or period to angular speed with ω = 2πf = 2π/T in rad s⁻¹
calculate tangential speed from v = ωr using the distance from the rotation axis
compare points on one rigid disc: equal angular speed but linear speed proportional to radius

[Maximum number: 3]

This question is in two parts. Part 1 is about two children on a merry-go-round. Part 2 is about electric circuits.

Part 1 Two children on a merry-go-round
Aibhe and Euan are sitting on opposite sides of a merry-go-round, which is rotating at constant speed around a fixed centre. The diagram below shows the view from above.

Figure for Question A.2.26—Angular and linear speed question 1 — IB Physics SL

Aibhe is moving at speed $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

Aibhe moves so that she is sitting at a distance of 0.75 m from the centre of the merry-go-round, as shown below.

Euan pushes the merry-go-round so that he is again moving at $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

Determine Aibhe's speed relative to the ground.

Aibhe's period of revolution is the same as before;
from $v=\frac{2 \pi r}{T}$ , since r is halved, v is halved;
$v=0.5\left(\mathrm{~ms}^{-1}\right) ;$

Marking guidance:

Award [3] for a bald correct answer.

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A.2.26—Angular and linear speed question 1