- #1

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To figure out total kinetic energy of a rotating object:

K translational + K rotational

[tex]\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2[/tex]

Then the book gives an alternate formula:

[tex]\frac{1}{2}mv^2(1+\frac{I}{mr^2})[/tex]

So I wanted to see how they get from one to the other. So I tried

[tex]\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2[/tex]

factor out the 1/2v^2

[tex]\frac{1}{2}v^2 (m+\frac{I}{r^2})[/tex]

almost there. But how do I get a 1 in place of the m? I could divide by m, but then I get

[tex]\frac{v^2}{2m} (1+\frac{I}{mr^2})[/tex]

It works for the right term, but not the left. What am I doing wrong?