Why is kinetic energy not a vector

Click For Summary

Discussion Overview

The discussion centers on the nature of kinetic energy and its classification as a scalar rather than a vector. Participants explore the implications of velocity in the kinetic energy formula, K = 1/2mv^2, and the distinctions between speed and velocity.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants argue that kinetic energy does not depend on direction, as illustrated by considering multiple particles moving at the same speed in different directions, suggesting that this lack of directional dependence indicates it is a scalar.
  • Others emphasize that kinetic energy is defined as the work required to move a stationary particle to a certain speed, clarifying that the equation involves speed (a scalar) rather than velocity (a vector).
  • One participant points out that kinetic energy is a magnitude, contrasting it with momentum, which is a vector quantity.
  • Another participant notes that the relationship between kinetic energy and work implies that both must share the same units and type, with work being defined as the dot product of force and displacement, leading to the conclusion that kinetic energy is also a scalar.
  • Some participants highlight the importance of distinguishing between speed and velocity in the context of kinetic energy, asserting that the equation for kinetic energy uses speed, which is the magnitude of the velocity vector.

Areas of Agreement / Disagreement

Participants express differing views on the classification of kinetic energy, with some asserting it is a scalar due to its dependence on speed rather than velocity, while others provide alternative definitions and explanations that challenge this perspective. The discussion remains unresolved, with multiple competing views present.

Contextual Notes

Some limitations in the discussion include potential misunderstandings regarding the definitions of kinetic energy and the roles of speed and velocity, as well as the implications of work and energy relationships. There are also unresolved aspects concerning the definitions and interpretations of scalar and vector quantities.

Fullperson
Messages
18
Reaction score
0
Why is kinetic energy not a vector, though it uses velocity in its definition of : K = 1/2mv^2
 
Physics news on Phys.org
Imagine 4 particles. One traveling 10m/s to the north, one 10 m/s to the south, one 10 m/s to the east, and one 10 m/s to the west. Is there any reason they should have different energies from each other? No of course not. There is no special preference given to any spatial direction. So kinetic energy does not depend on direction, hence it must be a scalar, not a vector. There is nothing that prohibits defining scalars in terms of vectors, although incidentally, the v in kinetic energy is speed (|v|, a scalar), not velocity.
 
KE is a magnitude. Momentum would be a vector. Why is the distance between two points not a vector? Same reason KE isn't.
 
Fullperson said:
Why is kinetic energy not a vector, though it uses velocity in its definition of : K = 1/2mv^2
Actually, it is defined as the work required to make a stationary particle of mass m to move at velocity v, where v is velocity. See http://scienceworld.wolfram.com/physics/KineticEnergy.html" for more information.
 
Last edited by a moderator:
Fullperson said:
Why is kinetic energy not a vector, though it uses velocity in its definition of : K = 1/2mv^2

Your confused with the difference between velocity and speed. Kinetic energy does not use velocity in the equation you stated. That equation uses speed, the magnitude of a velocity vector. Since the magnitude of a vector is a scalar, there is no vector term in the kinetic energy equation.

Also, as Hootenanny pointed out, that is not the definition of kinetic energy. See his post for more info.
 
Last edited:
Fullperson said:
Why is kinetic energy not a vector, though it uses velocity in its definition of : K = 1/2mv^2
The change in kinetic energy is equal to the work done by a conservative force. So KE and work must have the same units and type. Work is the dot product of force and displacement. Force and displacement are vectors, and the dot product of two vectors is a scalar. Therefore KE must also be a scalar. In fact, another way to write the expression for KE is 1/2 m v.v which makes it clear that it is a scalar.

The square of a vector quantity is almost always actually the dot product of the vector with itself, a scalar quantity.
 

Similar threads

Undergrad How can we prove the kinetic energy equation
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad The proportion of kinetic energy of a rotating rigid body?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How to calculate the kinetic energy of an object propelled by a magnet?
  • · Replies 15 ·
Replies
15
Views
1K
High School Can energy be decomposed?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Kinetic Energy derivation assumption?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Deriving formula for kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Why is momentum considered a vector and kinetic energy a scalar?
  • · Replies 15 ·
Replies
15
Views
4K
Undergrad Relationship between Concentration of a Force and Energy Density
  • · Replies 11 ·
Replies
11
Views
2K
High School About verification on Kinetic energy and work
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad I am confused about the meaning, and value, of kinetic energy
  • · Replies 7 ·
Replies
7
Views
2K