- #1

AbigailM

- 46

- 0

**Problem**

A thin homogeneous plate lies in the x-y plane. Its moment of inertia tensor in the x,y,z basis is given by

[itex]\textbf{I}=σl^{4}\begin{pmatrix} 2 & -2 &0 \\ -1 & 2 & 0 \\ 0 & 0 & 4\end{pmatrix}[/itex]

If the plate is rotated about the [itex]\hat{x}[/itex]-axis with constant angular velocity ω, what torque must be applied to the plate to keep the roation axis pointing in the x direction?

**The attempt at a solution**

We are given [itex]\textbf{I}[/itex] and we know that [itex]\textbf{ω}=(ω,0,0)[/itex].

[itex]\textbf{L}=\textbf{Iω}=σl^{4}\begin{pmatrix} 2 & -2 &0 \\ -1 & 2 & 0 \\ 0 & 0 & 4\end{pmatrix}\begin{pmatrix}ω \\ 0\\ 0\end{pmatrix}=σl^{4}ω(2,-1,0)[/itex]

[itex]L_{x}=2σl^{4}ω[/itex]

[itex]\Gamma_{x}=\frac{dL_{x}}{dt}=2\sigma l^{4}\dot{\omega}[/itex]

Thanks for the help.