What is the formula for finding centripital acceleration in a spinning disc?

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SUMMARY

The formula for calculating centripetal acceleration in a spinning disc is derived from the relationship between linear velocity and radius. For an object at distance R from the center, the velocity is given by VA = 2πR/T, while for an object at R/2, the velocity is VB = πR/T. The correct centripetal acceleration for object B is calculated as a = (2π²R)/T², confirming that the acceleration is dependent on the radius and the period of rotation. The key to resolving the discrepancy in the coefficient lies in correctly applying the radius in the formula.

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  • Understanding of centripetal acceleration formula: a = v²/R
  • Familiarity with angular velocity and linear velocity relationships
  • Knowledge of periodic motion and its mathematical representation
  • Basic algebra for manipulating equations
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  • Study the derivation of centripetal acceleration in circular motion
  • Learn about angular velocity and its impact on linear velocity
  • Explore the relationship between radius and acceleration in rotating systems
  • Practice solving problems involving centripetal acceleration with varying radii
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Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for clear explanations of centripetal acceleration concepts.

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Homework Statement


There is a spinning disc. Object A sits R distance from center and object B sits R/2 distance away. VB=piR/T and VA=2piR/T


Homework Equations


Find the magnitude of the acceleration of object B. Assume that the cylinder makes one complete turn in a period of time .



The Attempt at a Solution


The answer is a=(2pi2R)/T2 .


From using centripetal acceleration=v2/R , i got
ac=pi2R/T2

There is a coefficient of 2 that I am missing in my answer from the correct solution, but I have double checked. Am I using the wrong formula here? where did the 2 come from in the answer?
 
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NVM. spent an hour on it and finally got it. Supposed to divide by R/2 not R
 

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