Question

a=v^2/r solve for v, solve for r

Answer 1

To rearrange these for v and r we must use BEDMAS.

First, times both sides by r, getting Ar = v²r/r
You can cancel out r/r to get Ar = v²

To get v, square root both sides. √Ar = √v²
Cancel out the square root and the squared v = √Ar

To get r, go back to Ar = v², then divide both sides by A. rA/A = v²/A
Then cancel out A/A to get r. r = v²/A

Answer 2

Solving for v and r we have: $V = \sqrt{ar}$ and $r = \frac{V^{2}}{a}$ respectively.

Centripetal acceleration can be defined as the acceleration experienced by an object (body) moving in uniform circular motion and due to an applied net external force.

Mathematically, centripetal acceleration is given by the formula:

$a = \frac{V^{2}}{r}$

Where;

• a is centripetal acceleration.

• V is the velocity of an object.

• r is the radius of the circular path.

In this exercise, you're required to make v and r the subject of formula;

For v:

In order to make v the subject of formula, we would cross-multiply the variables.

$a = \frac{V^{2}}{r}\\\\V^{2} = a \; * \; r$

Taking the square root of both sides, we have;

$V = \sqrt{ar}$

For a;

$a = \frac{V^{2}}{r}$

Cross-multiplying, we have;

$a \; * \; r = V^{2}$

Dividing both sides by "a", we have;

$r = \frac{V^{2}}{a}$

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