# Radius relation to centripetal force

• rasen58
In summary, the conversation discusses the relationship between the radius of a curve, the speed of two cars traveling on the inside and outside of the curve, and the corresponding centripetal force. The equation Fc = m*4pi2R/T2 is used to determine the force on each car, with T representing the period. The correct answer is option b, as the period for car B is twice as long as car A, making the force on car B half of the force on car A.

## 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?

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.

## 1. How does the radius affect the centripetal force?

The centripetal force is directly proportional to the radius. This means that as the radius increases, the centripetal force also increases. Conversely, as the radius decreases, the centripetal force decreases. This relationship can be expressed as Fc ∝ r, where Fc is the centripetal force and r is the radius.

## 2. Why does the radius affect the centripetal force?

This is because the radius is a key factor in determining the speed and acceleration of an object in circular motion. A larger radius means a longer distance for the object to travel, resulting in a higher speed and acceleration. This requires a larger force to maintain the circular motion, hence the direct relationship between radius and centripetal force.

## 3. Is there a limit to how large or small the radius can be for an object to experience centripetal force?

Yes, there is. If the radius becomes too large, the centripetal force required to maintain circular motion will also become extremely large, resulting in an unrealistic scenario. On the other hand, if the radius becomes too small, the speed and acceleration of the object will become too high, making it difficult for the object to maintain its circular path. Therefore, there is a limit to the size of the radius for an object to experience centripetal force.

## 4. Can the radius of an object in circular motion change?

Yes, the radius of an object in circular motion can change. This change can be caused by an external force, such as a change in the direction or magnitude of the centripetal force. It can also change due to internal forces, such as the object breaking into smaller pieces or colliding with another object.

## 5. How does the radius affect the period of an object in circular motion?

The period of an object in circular motion is the time taken for it to complete one full revolution. The radius has an inverse relationship with the period, meaning that as the radius increases, the period also increases. This is because a larger radius means a longer distance to travel, resulting in a longer time taken to complete one revolution. This relationship can be expressed as T ∝ 1/r, where T is the period and r is the radius.