# Explanation of this uniform circular motion statement?

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#### CaptainAmazon

##### Full Member
“In uniform circular motion, the displacement vector and force vector are always perpendicular."

What does this mean? I'm having trouble picturing it.

The force is the radius of the circle of motion, connected to the point of position. The displacement is the tangent to the circle at the point of position.

The radius and tangent will always be at a 90 degree angle.

Man, geometry and physics really are more fun than studying for my Internal Medicine shelf.

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“In uniform circular motion, the displacement vector and force vector are always perpendicular."

What does this mean? I'm having trouble picturing it.

The picture in the post above shows the two vectors quite well, but I believe there is an error in your original quoted statement. The acceleration vector (force) is perpendicular to the velocity vector (not displacement vector). If the object had no acceleration acting on it, then it would move in a straight line along the path of the tangential velocity. But because of the radial acceleration (perpendicular to velocity), it is forced to turn and traverse a circular pathway. The displacement of the object is the circle itself, as that is where it is moving.

The picture in the post above shows the two vectors quite well, but I believe there is an error in your original quoted statement. The acceleration vector (force) is perpendicular to the velocity vector (not displacement vector). If the object had no acceleration acting on it, then it would move in a straight line along the path of the tangential velocity. But because of the radial acceleration (perpendicular to velocity), it is forced to turn and traverse a circular pathway. The displacement of the object is the circle itself, as that is where it is moving.
The circle is actually the distance traveled... The displacement in circular motion is actually zero since the start and end points are the same. Everything else I think you're correct about. Acceleration(or force) and velocity are perpendicular, not acceleration and displacement.

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The picture in the post above shows the two vectors quite well, but I believe there is an error in your original quoted statement. The acceleration vector (force) is perpendicular to the velocity vector (not displacement vector). If the object had no acceleration acting on it, then it would move in a straight line along the path of the tangential velocity. But because of the radial acceleration (perpendicular to velocity), it is forced to turn and traverse a circular pathway. The displacement of the object is the circle itself, as that is where it is moving.
This is what I was thinking as well! But this is a statement I pulled directly from the Kaplan "Answers to Concept Checks". Its use of the word displacement instead of velocity confused me

The circle is actually the distance traveled... The displacement in circular motion is actually zero since the start and end points are the same. Everything else I think you're correct about. Acceleration(or force) and velocity are perpendicular, not acceleration and displacement.
This is what I was thinking as well! But this is a statement I pulled directly from the Kaplan "Answers to Concept Checks". Its use of the word displacement instead of velocity confused me

The circle is actually the distance traveled... The displacement in circular motion is actually zero since the start and end points are the same. Everything else I think you're correct about. Acceleration(or force) and velocity are perpendicular, not acceleration and displacement.

Circular motion is similar to periodically motion rather than translational motion, which means that the displacement changes over time. The displacement is 0 at only one point, and that is when it passes through its origin. At all other times, it has some net displacement. To represent the displacement, we need a cosine function based of the period of the motion. This is why we do not use the conventions of linear motion to describe circular motion.

But back to the crux of the OP's question. They probably meant to say velocity rather than displacement. Typos happen, and catching that typo is actually a useful training skill for the MCAT, given that eliminating wrong answers requires recognizing things that are incorrect.