KE constant in circular motion?

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Discussion Overview

The discussion revolves around the concept of kinetic energy in the context of circular motion, specifically addressing whether kinetic energy remains constant when an object, such as a car, is undergoing circular motion. Participants explore the implications of constant speed and changing velocity on kinetic energy.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions how kinetic energy can remain constant if velocity is changing due to acceleration in circular motion.
  • Another participant asserts that kinetic energy is constant because it is a scalar quantity and the magnitude of velocity remains unchanged.
  • A participant challenges the notion of kinetic energy being a scalar by pointing out that it involves a vector quantity.
  • Further clarification is provided regarding the nature of acceleration in circular motion, noting that while its magnitude is constant, its direction changes.
  • Participants discuss the interpretation of the radius in circular motion, with some suggesting that the radius vector changes direction as the object moves around the circle.
  • There is a misunderstanding about whether the length of the radius itself is changing, which is clarified by another participant.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between kinetic energy and the changing velocity in circular motion. There is no consensus on the implications of these concepts, and the discussion remains unresolved.

Contextual Notes

Some participants' statements rely on specific interpretations of kinetic energy and acceleration, which may depend on definitions and context. The discussion includes nuances regarding the nature of vectors and scalars in physics.

LanguageNerd
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I was just wondering how the kinetic energy in, for example, a car undergoing circular motion is constant. We know that it's constantly acceleration due to the constant change in velocity, but surely that means that in the KE equation (1/2mv^2) the velocity is constantly changing as well. This would mean that the KE is also constantly changing, no?

Thanks for any help in advance!
 
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Kinetic energy is a scalar quantity. It does not have a direction. So nothing will change. Since the magnitude of the velocity is constant, kinetic energy will stay the same.
 
But how can it be a scalar quantity when it contains a vector quantity?
 
LanguageNerd said:
But how can it be a scalar quantity when it contains a vector quantity?
the inner product of two vector quantity is certainly a scalar quantity..
$\vec{v}\cdot\vec{v}$
 
Brilliant. Thanks all!
 
A nit-pick… For a body going in a circle at constant speed, the acceleration isn't constant. Its magnitude is constant, but its direction keeps changing, because it's radial, and the particular radius keeps changing!
 
Philip Wood said:
and the particular radius keeps changing!
What do you mean by this? The radius of circular rotation is changing?
 
adjacent said:
What do you mean by this? The radius of circular rotation is changing?
Think of the radius as a vector from the center to a particular point on the circle. It changes as you move around the circle.

At any point, the radial acceleration points toward the center of the circle (opposite to the radius vector at that point). That direction changes as you move around the circle.
 
Doc Al said:
Think of the radius as a vector from the center to a particular point on the circle. It changes as you move around the circle.

At any point, the radial acceleration points toward the center of the circle (opposite to the radius vector at that point). That direction changes as you move around the circle.
Oh. I thought he said that the radius(Length) is changing :shy:
 
  • #10
He ought to have been clearer!
 
  • #11
Philip Wood said:
He ought to have been clearer!
:smile:
 

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