A rolling-distance indicator
8 written marks
A wheel of radius \(0.30\) m rolls without slipping at \(90\) revolutions per minute. A distance indicator calculates travel from the revolution count using this radius.
Part a · 3 marks
Find the angular speed in radians per second and the distance travelled per second.
Part b · 2 marks
How long does it take to travel \(63\pi\) m?
Part c · 3 marks
The wheel wears down to radius \(0.285\) m, but the indicator is not recalibrated. When it displays \(63\pi\) m, find the true distance and the percentage by which the displayed distance exceeds the true distance.
Complete-answer checking, worked solutions and indicative written criteria.
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