Circular motion time/radius ratio question

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SUMMARY

The discussion centers on calculating the ratio of centripetal acceleration for a car completing circular motion at different radii and times. The car travels a radius of r in time T and then a radius of 2r in time T/2. The correct ratio of centripetal acceleration, ac2/ac1, is determined to be 8:1, confirming that the centripetal acceleration in the second circle is eight times that of the first circle. The calculations involve the formula for centripetal acceleration, which is dependent on radius and time.

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Homework Statement


16. A car completes a horizontal circle of radius r in time T. The same car then completes a larger horizontal circle of radius 2r in half the time. What is the ratio of the centripetal acceleration ac for the car in the second circle to that in the first circle a c2 a c1?

The Attempt at a Solution


iv never understood the whole ratio thing
i got (4pi^2*4R)/(T^2/4)
the answer is suppose 2 be 8:1 so i assume the second car is the 8

Ithink i got it actually (4pi^2*2R)/(T^2/4):(4pi^2*R)/T^2
that 8:1 did i do it right?
 
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