- #1
Totally
- 26
- 2
Homework Statement
Force represented by F(t)=20+t+5t^2 [N] acts upon the rim of a disk. How much time has to pass before the disk has angular velocity of 200 revs\sec? R and I are known.
Homework Equations
\begin{equation*}
\tau=I\alpha
\end{equation*}
\begin{equation*}
\tau=R \times F
\end{equation*}
\begin{equation*}
I=\frac{1}{2}mR^2
\end{equation*}
The Attempt at a Solution
\begin{equation*}
\alpha=\frac{R}{I}F
\end{equation*}
\begin{equation*}
\omega=\frac{R}{I}\int_{0}^{t} F(t)dt
\end{equation*}
I have same variable in my upper integration limit as in the function. So I'm thinking of integrating F(t) twice to get the distance and instead of writing it as θ, write it as ωt so it looks like the following
\begin{equation*}
\omega t=\frac{R}{I}∫∫F(t)dt
\end{equation*}
Then divide by t and solve the cubic. Does that seem like a legitimate move?