Vector Equation Help: Solve Radial Acceleration

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In summary, the conversation discusses two mathematical statements regarding vectors and radial acceleration. The first equation is successfully worked out and makes sense, while the second equation does not make sense when the first equation is used to work it out. The missing term in the second equation is questioned and it is later realized that the mistake was assuming r12 to be a constant instead of a differentiable value.
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Jonnyb42
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I am reading a book, and I see the following mathematical statements:

[PLAIN]http://mynqa.com/Cargo/Untitled2.bmp
and I have worked it out and it makes sense.
Then another statement comes up, regarding the radial acceleration this time:
[PLAIN]http://mynqa.com/Cargo/Untitled.bmp
This second equation does not make sense to me, when I work it out myself, using the first equation which I had successfully worked out, I arrive at the right side but missing the term:
[PLAIN]http://mynqa.com/Cargo/term.bmp
where does this middle term come from?

I know I am not providing much information as to what the equation is expressing, that is because what I am asking is primarily mathematical. These are vectors. OH one thing to know however, in the book they define vectors with the up-arrow/hat as soley direction, (magnitude 1) and the vectors with arrows pointing to the side as normal vectors, and corresponding letters without anything overhead is magnitude.

Thanks for any help.
 
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Well I found out why I wasn't getting that extra term, is it because I was foolishly considering r12 a constant, when it is differentiable.
 

FAQ: Vector Equation Help: Solve Radial Acceleration

What is a vector equation?

A vector equation is an equation that expresses the relationship between two or more vectors. It typically includes both the magnitude and direction of the vectors involved.

How is radial acceleration defined?

Radial acceleration is defined as the rate of change of the magnitude of a vector in a circular motion. It is always directed towards the center of the circle.

What is the formula for calculating radial acceleration?

The formula for radial acceleration is given by ar = v2/r, where ar is the radial acceleration, v is the velocity, and r is the radius of the circle.

How is radial acceleration different from tangential acceleration?

Radial acceleration and tangential acceleration are both components of the total acceleration of an object in circular motion. Radial acceleration is directed towards the center of the circle, while tangential acceleration is directed along the tangent to the circle.

Can you provide an example of solving a vector equation for radial acceleration?

Sure, let's say we have a car moving at a constant speed of 20 m/s along the edge of a circular track with a radius of 10 meters. The radial acceleration of the car can be calculated using the formula ar = v2/r, which gives us ar = (20 m/s)2 / 10 m = 400 m/s2. This means that the car is experiencing a radial acceleration of 400 m/s2 towards the center of the circle.

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