# Constant quantities in circular motion

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A child runs in a circular path with constant speed. Which one of the following quantities is constant and non-zero?

A. Linear velocity

B. Angular velocity

C. Centripetal acceleration

D. Angular acceleration

E. Total acceleration

I thought none of them would be constant since the direction of the vectors would always be changing when you move in a circle. But since I had to pick an answer, I thought it might be between linear velocity and angular velocity and picked linear velocity since there is a constant speed.

But the answer is angular velocity. Why?

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A child runs in a circular path with constant speed. Which one of the following quantities is constant and non-zero?

A. Linear velocity

B. Angular velocity

C. Centripetal acceleration

D. Angular acceleration

E. Total acceleration

I thought none of them would be constant since the direction of the vectors would always be changing when you move in a circle. But since I had to pick an answer, I thought it might be between linear velocity and angular velocity and picked linear velocity since there is a constant speed.

But the answer is angular velocity. Why?

I might not think it is the only right answer but it is more right than angular acceleration for that is definitely wrong.

Angular velocity is the change of angle (in radians) over time. and that is constant by the description of the situation.

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You are correct to note that all are vectors and that the odd one out is to do with change of direction, not magnitude.

A,C, D & E are all vectors in the same plane as the circle, and their directions do indeed change as the child runs round the circle.

However B, the angular velocity is at right angles to the plane of the circle, poking out from the cente of the circle in right handed screw fashion.

This makes it (the only one) constant in both magnitude and direction.

This concept is important in Chemistry for magnetic and dipole moments.

Draw a diagram if you need to convince yourself.

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Yep, just learned that it is perpendicular so it makes sense now.

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