Visual Proof: a= v^2/r

Visual proof that centripetal acceleration = v^2/r

Category:

Education

Tags:

• centripetal
• acceleration
• proof
• physics

[Altair9292]

omg we are learnin this in physics class...thx cause this has helped a lot

[richardbyronsmith]

great visual presentation, helps understand the idea of derivatives of position and speed.

[antiveta]

I thank you , really, because in my class I didn't get it clearly .

thanx thanx thanx

[CeaseFireTheAncient]

@Wid552 Velocity is a vector. It has a direction, and a magnitude. If it was a scalar it would have neither. [Speed is a scalar, velocity is a vector]

[Wid552]

(Continuing from my 1st comment) Is the velocity vector just directional?

[Wid552]

For the second circle, could you explain how the radius of the second circle represents the velocity? Or could it be represented in the same way by placing the velocity vectors on the circumference? Or is it just purely representative, regardless of positon?

[lolololort]

@Shadowolf64

QED

[lolololort]

@trollwarlord3

The radius of the circle drawn on the right isn't the circle with radius = r. It's a visual representation of how a relates to v ( v and a replotted). Rendering your comment WRONG

[trollwarlord3]

hey the radius of circle is not the magnitude of velocity!! rendering this proof WRONG

[Shadowolf64]

boobs.

[GoodDeedsLeadTo]

Could we go on one step further and relate 2 * pi * V /a to 2 * pi * a / (first derivative of acceleration)

And, What is first derivative of acceleration called?

[DuckyDipper0]

@shubhamrathi94

1. The magnitude of velocity is also known as speed; velocity is a vector which describes the direction of speed.

2. There are two different accelerations. You are confusing tangential acceleration with the acceleration that is inwards. The acceleration that is inwards is perpendicular to the velocity. Tangential acceleration is the acceleration tangent to the circle of motion. There is a tangential acceleration if there is a change in speed.