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A merry-go-round moves in a circle at a constant speed. Is the merry-go-round accelerating?
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GPT-5 mini
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Yes. Even though the speed is constant, the velocity is continuously changing direction, so there is acceleration.
For uniform circular motion the acceleration is centripetal (points toward the centre) with magnitude
a = v^2 / r = ω^2 r,
where v is the tangential speed, r the radius, and ω the angular speed. There is no tangential acceleration (no change in speed), only the inward radial acceleration provided by the centripetal force (friction, tension, normal force, etc.).
For uniform circular motion the acceleration is centripetal (points toward the centre) with magnitude
a = v^2 / r = ω^2 r,
where v is the tangential speed, r the radius, and ω the angular speed. There is no tangential acceleration (no change in speed), only the inward radial acceleration provided by the centripetal force (friction, tension, normal force, etc.).
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