# Radius relation to centripetal force

## Homework Statement

The radius for the inside of a curve is half the radius for the outside. With 2 cars of equal mass, car A travels on the inside and car B travels on the outside at equal speed. Which statement is correct?
a. The force on A is half the force on B
b. The force on B is half the force on A
c. A 4 times of B
d. B 4 times of A

Fc = m*v2/R
v = 2piR/T

## The Attempt at a Solution

I substituted 2piR/T into v2 in the centripetal force equation, and then got
Fc = m*4pi2R/T2
So since the inside radius of half of the outside, the force on A should be half of that on B, which is answer a.
But the answer is apparently b.
But doesn't the equation show that it should be a?

TSny
Homework Helper
Gold Member
In the equation Fc = m*4pi2R/T2, what does the symbol T stand for? Does T have the same value for both cars?

Can you see how to answer the question based on Fc = m*v2/R?

T is the period, so I guess the period for B would be twice as long? So then if it is twice as long, then B would indeed be half of A.

Yes, I can see how to answer it with the general centripetal force equation, but I thought that you had to go further.