Question

I'm trying to derive the power needed to change the speed of a rotating body. What happens to the (1/2) in the derivation? See next post.

Answer 1

\[P=\frac{ dW }{dt }= (\frac{ d }{ dt })\left\{\frac{ 1 }{ 2 }I \omega^{2}\right\}= I\left\{ (\frac{ d \omega }{ dt })\right\} \omega=\left\{ I \alpha\right\} \omega=\tau \omega \]

Answer 2

why do we lose the 1/2 going from work to the angular acceleration?

Answer 3

Because you took the derivative, using the power rule 2*1/2 = 1.

Answer 4

Thank you, i wasn't thinking that i =had to include the second omega

Answer 5

Np, we all have those moments :)