The Problem. A person on a horizontal rotating platform at a
distance of 4.3 m from its center. This person experiences a
centripetal acceleration of 5.6 m/s. What centripetal acceleration
is experienced by another person who is at a distance of 2.5m from
the center of the platform?
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A quick pic of the scenario.
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The acceleration of an object moving in a circle (in this case,
riding a rotating platform) can be determined by this
equation:
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What is given..
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Solving for v..
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Now that we have the v..
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Centripetal Acceleration: The acceleration required to keep an
object moving in a circle, directed towards the center. The smaller
the radius (distance from the center), the smaller amount of
centripetal acceleration required to keep an object. The second
person had a smaller radius than the first person (2.5 m), so the
acceleration REQUIRED to keep him moving is smaller. However, both
people are experiencing the same constant velocity, so it actually
increases because of our formula.
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Ever been on a carousel?
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Conclusion: In a rotating circle.. Centripetal acceleration
increases as the radius decreases. Velocity increases as radius
increases.