- #1
Quadrat
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Homework Statement
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In a rotation of rigid bodies-problem there's a question regarding the speed of a falling block, attached to a solid cylinder which can rotate frictionless around its axis. I have a question regarding the algebraic operations.
Homework Equations
So I have this expression: ##mgh=1/2mv^2+1/2(1/2MR^2)(v^2/R^2)##.
The Attempt at a Solution
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I can operate on the expression to solve for v. So I eventually get that ##2mgh=v^2(m+1/2M)##. And from here I just want to divide both sides by ##(m+1/2M)## and take the square root of both sides.
Which would leave me with ##v=sqrt((2mgh)/(m+(1/2)M)##
My textbook expresses this result as ##v=sqrt((2gh)/(1+(M/2m))##
Are those the same results? If so, what operations were made to end up with that result? If not, what did I do wrong?