Kinetic Energy and Momentum Scalar

AI Thread Summary
Kinetic energy is defined as a scalar quantity, calculated using the formula (1/2)mv^2, where v represents velocity. Although velocity is a vector, the operation v^2 can be expressed as a dot product (v·v), which results in a scalar value. This means that even though kinetic energy involves a vector, its final representation is scalar due to the mathematical properties of the dot product. The discussion clarifies that the square of a vector indeed yields a scalar, reinforcing the scalar nature of kinetic energy. Understanding this relationship is crucial for grasping the concepts of kinetic energy and momentum in physics.
bravoghost
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This is a conceptual problem that I'm sure is pretty common. How can kinetic energy (1/2mv^2) be a scalar quantity when it includes a vector quantity like velocity?
 
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v^2 can be written as the dot product v*v, and a dot product is a scalar.
 
Because, as Svalbard stated, the square of a vector is a scalar.
 

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