# Solve for v F=(jMv^2)/r F=jMv2r
Rewrite the equation as jMv2r=F.
jMv2r=F
Multiply both sides of the equation by r.
jMv2=F⋅(r)
Multiply F by r.
jMv2=Fr
Divide each term by jM and simplify.
Divide each term in jMv2=Fr by jM.
jMv2jM=FrjM
Simplify jMv2jM.
Cancel the common factor of j.
Cancel the common factor.
jMv2jM=FrjM
Rewrite the expression.
Mv2M=FrjM
Mv2M=FrjM
Cancel the common factor of M.
Cancel the common factor.
Mv2M=FrjM
Divide v2 by 1.
v2=FrjM
v2=FrjM
v2=FrjM
v2=FrjM
Take the square root of both sides of the equation to eliminate the exponent on the left side.
v=±FrjM
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite FrjM as FrjM.
v=±FrjM
Multiply FrjM by jMjM.
v=±FrjM⋅jMjM
Combine and simplify the denominator.
Multiply FrjM and jMjM.
v=±FrjMjMjM
Raise jM to the power of 1.
v=±FrjMjMjM
Raise jM to the power of 1.
v=±FrjMjMjM
Use the power rule aman=am+n to combine exponents.
v=±FrjMjM1+1
Add 1 and 1.
v=±FrjMjM2
Rewrite jM2 as jM.
Use axn=axn to rewrite jM as (jM)12.
v=±FrjM((jM)12)2
Apply the power rule and multiply exponents, (am)n=amn.
v=±FrjM(jM)12⋅2
Combine 12 and 2.
v=±FrjM(jM)22
Cancel the common factor of 2.
Cancel the common factor.
v=±FrjM(jM)22
Divide 1 by 1.
v=±FrjMjM
v=±FrjMjM
Simplify.
v=±FrjMjM
v=±FrjMjM
v=±FrjMjM
Combine using the product rule for radicals.
v=±FrjMjM
v=±FrjMjM
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
v=FrjMjM
Next, use the negative value of the ± to find the second solution.
v=-FrjMjM
The complete solution is the result of both the positive and negative portions of the solution.
v=FrjMjM
v=-FrjMjM
v=FrjMjM
v=-FrjMjM
v=FrjMjM
v=-FrjMjM
Solve for v F=(jMv^2)/r

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