# Length Contraction: Measuring Circumference of Moving Circle

• unchained1978
In summary, when observing a circle moving along a line without rotation, there is no length contraction in the direction perpendicular to the motion. This means that measuring the radius in the direction parallel to the motion would result in a contracted radius and a smaller circumference, while measuring the radius in the perpendicular direction would result in the inertial radius and circumference. This suggests that when calculating the circumference of a moving circle, it would need to be treated as an ellipse. Additionally, a spherical object will compress into an oblate spheroid shape along its axis of travel.
unchained1978
As I understand it, there is no length contraction in the direction perpendicular to the motion being described. So if I were to observe a circle moving along a line (not rostating) and I were to measure the radius in te direction parallel to the motion, I would observe a contracted radius, and therefore calculate a smaller circumference. But if I were to measure the radius in the direction perpendicular to motion, I would observe the inertial radius and therefore the inertial circumference. Does this mean that to calculate the circumference of a moving circle, I would need to treat it as an ellipse?

Yes, that is correct.

A spherical object will compress along its axis of travel into a disclike shape (an oblate spheroid).

## 1. What is length contraction?

Length contraction is a concept in physics that describes the phenomenon of an object appearing shorter in the direction of its motion due to the effects of relativity.

## 2. How does length contraction occur?

Length contraction occurs because of the time dilation effect of special relativity. As an object moves at high speeds, time appears to slow down for the object, causing its length to appear shorter in the direction of motion.

## 3. How is length contraction measured?

Length contraction can be measured by comparing the length of an object at rest to its length when it is moving at high speeds. This can be done using various techniques such as optical interferometry or time dilation measurements.

## 4. What is the equation for length contraction?

The equation for length contraction is L = L0√(1-(v2/c2)), where L is the contracted length, L0 is the rest length, v is the velocity of the object, and c is the speed of light.

## 5. How does length contraction affect the measurement of a moving circle's circumference?

Length contraction affects the measurement of a moving circle's circumference by making it appear shorter in the direction of motion. This means that the measured circumference will be smaller than the actual circumference of the circle at rest, according to the equation for length contraction.

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