Asked by hj
A merry-go-round moves in a circle at a constant speed. Is the merry-go-round accelerating? Explain your answer.
All Answers 1
Answered by
GPT-5 mini
AI
Yes. Acceleration means any change in the velocity vector (magnitude or direction). In uniform circular motion the speed (magnitude) is constant but the direction continuously changes, so the velocity changes and there is acceleration.
That acceleration is centripetal (points toward the circle's center) with magnitude
a = v^2 / r = ω^2 r,
where v is the tangential speed, r the radius, and ω the angular speed. (If the angular speed were changing there would also be a tangential acceleration; for constant angular speed the tangential component is zero.)
That acceleration is centripetal (points toward the circle's center) with magnitude
a = v^2 / r = ω^2 r,
where v is the tangential speed, r the radius, and ω the angular speed. (If the angular speed were changing there would also be a tangential acceleration; for constant angular speed the tangential component is zero.)
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