Physics A2 · Motion in a circle. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
For motion in a circle it is easier to measure the angle turned through than the distance travelled. Angles are measured in radians. One radian is the angle at the centre of a circle made by an arc whose length equals the radius, so a full circle is 2π rad.
Angular speed ω is the angle swept out by the radius per unit time. Every point on a rigid rotating body has the same ω, because every point turns through the same angle in the same time.
The linear speed v is the speed along the circular path. It depends on the radius: a point further from the axis travels a longer arc in the same time, so it moves faster.
Students put revolutions per minute straight into v = rω. First change to revolutions per second, then multiply by 2π to get ω in rad s−1. Also check whether the question gives the diameter instead of the radius.
Answer: About 7.9 m s−1.
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