vin300
- 602
- 4
This is a physics and math problem
The representation of a vector as a straight ray is problematic
Imagine an arc of a circle formed as a result of uniform circular motion.In time Δt, it traces out an arc of length vΔθ such that vΔθ/Δt =vω is the acceleration. v=rω comes from the fact that dx/dt=rdθ/dt and all higher derivatives are derived in exactly the same way with an ω in every next der.
The problem in depicting the velocity vector as a straight ray is clearly depicted in the faulty diagram of this wiki page
http://en.wikipedia.org/wiki/Areal_velocity"
The diagram is clearly wrong for the fact that it does not include the chord within the areal sector and the only solution to this is using the velocity, and in general, all vectors as path dependent (in space or space-time)
The representation of a vector as a straight ray is problematic
Imagine an arc of a circle formed as a result of uniform circular motion.In time Δt, it traces out an arc of length vΔθ such that vΔθ/Δt =vω is the acceleration. v=rω comes from the fact that dx/dt=rdθ/dt and all higher derivatives are derived in exactly the same way with an ω in every next der.
The problem in depicting the velocity vector as a straight ray is clearly depicted in the faulty diagram of this wiki page
http://en.wikipedia.org/wiki/Areal_velocity"
The diagram is clearly wrong for the fact that it does not include the chord within the areal sector and the only solution to this is using the velocity, and in general, all vectors as path dependent (in space or space-time)
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