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

In summary, Object A and B sit at different distances from a spinning disc, with VB and VA representing their respective velocities. The task is to find the magnitude of the acceleration of object B, given that the cylinder makes one complete turn in a period of time. The correct solution is a=(2pi2R)/T2, found using the formula for centripital acceleration. The error in the attempt at a solution was due to using the wrong formula and not accounting for the coefficient of 2.
  • #1
ttttrigg3r
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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 centripital 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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  • #2
NVM. spent an hour on it and finally got it. Supposed to divide by R/2 not R
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences when it moves in a circular path. It is always directed towards the center of the circle and is caused by the centripetal force acting on the object.

2. How is centripetal acceleration calculated?

Centripetal acceleration can be calculated using the formula: a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circle. Alternatively, it can also be calculated using the formula: a = ω^2r, where ω is the angular velocity of the object.

3. What are some real-life examples of centripetal acceleration?

Some common examples of centripetal acceleration include the motion of a satellite orbiting around the Earth, the motion of a car around a curve, and the motion of a rollercoaster around a loop.

4. How does centripetal acceleration differ from centrifugal force?

Centripetal acceleration is the actual acceleration that an object experiences when moving in a circular path, while centrifugal force is a fictitious force that appears to act on the object due to its inertia. Centrifugal force is directed away from the center of the circle and is equal in magnitude but opposite in direction to the centripetal force.

5. How does the centripetal acceleration of an object change with its speed and radius?

The centripetal acceleration of an object increases as its speed increases and as its radius decreases. This is because, for a given circular motion, a higher speed means a larger centripetal force is required to keep the object moving in the circle, and a smaller radius means the object has to make sharper turns, requiring a higher centripetal force.

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