marcia888
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This isn't a homework question, but I'm just wondering how the text in the book gets from one formula to the next.
To figure out total kinetic energy of a rotating object:
K translational + K rotational
\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2
Then the book gives an alternate formula:
\frac{1}{2}mv^2(1+\frac{I}{mr^2})
So I wanted to see how they get from one to the other. So I tried
\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2
factor out the 1/2v^2
\frac{1}{2}v^2 (m+\frac{I}{r^2})
almost there. But how do I get a 1 in place of the m? I could divide by m, but then I get
\frac{v^2}{2m} (1+\frac{I}{mr^2})
It works for the right term, but not the left. What am I doing wrong?
To figure out total kinetic energy of a rotating object:
K translational + K rotational
\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2
Then the book gives an alternate formula:
\frac{1}{2}mv^2(1+\frac{I}{mr^2})
So I wanted to see how they get from one to the other. So I tried
\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2
factor out the 1/2v^2
\frac{1}{2}v^2 (m+\frac{I}{r^2})
almost there. But how do I get a 1 in place of the m? I could divide by m, but then I get
\frac{v^2}{2m} (1+\frac{I}{mr^2})
It works for the right term, but not the left. What am I doing wrong?