Rotating Platform By Unknown.

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Presentation transcript:

Rotating Platform By Unknown

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?

A quick pic of the scenario…….

The acceleration of an object moving in a circle (in this case, riding a rotating platform) can be determined by this equation: 𝐶𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛= 𝑉 2 𝑅 (where v equals the velocity of the platform, and R equals the radius, or distance from the center)

What is given….. The first person: R=4.3 m, 𝐴 𝑐 =5.6 m/s The second person: R= 2.5 m

Solving for v….. Because both people are experiencing the same velocity, all one has to do is solve for v for the first person using the given information. 5.6= 𝑣 2 4.3 Solve for v……… V= 4.91 m/s

Now that we have the v….. Plug 4.91 m/s into the formula for the second person (with the different radius) with the given information and solve for acceleration!! 𝐴 𝑐 = 4.91 2 2.5 𝐴 𝑐 = 9.64 m/s

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.

Ever been on a carousel? Doesn’t it feel like you are going faster when you are further out from the center?? That’s because you are experiencing the same velocity, but you are covering a greater distance in the same time period!!! The greater circumference is caused by the increased radius. (Circumference= 2𝜋r) Thus, as the m portion of 𝑚 𝑠 increases, velocity for that individual increases.

Conclusion: In a rotating circle….. Centripetal acceleration increases as the radius decreases. Velocity increases as radius increases.

The End