1 A uniform lamina is in the form of a sector of a circle with centre \(O\), radius 0.2 m and angle 1.5 radians. The lamina rotates in a horizontal plane about a fixed vertical axis through \(O\). The centre of mass of the lamina moves with speed \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Show that the angular speed of the lamina is \(3.30 \mathrm { rad } \mathrm { s } ^ { - 1 }\), correct to 3 significant figures.

## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $R = 2 \times 0.2\sin 0.75/(3 \times 0.75)$ | M1 | For using $R = 2r\sin\alpha / 3\alpha$ |
| $[0.4 = 0.12118\ldots\omega]$ | A1 | |
| Angular speed is $3.30\ \text{rads}^{-1}$ | M1, A1 [4] | For using $v = r\omega$ |

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1 A uniform lamina is in the form of a sector of a circle with centre $O$, radius 0.2 m and angle 1.5 radians. The lamina rotates in a horizontal plane about a fixed vertical axis through $O$. The centre of mass of the lamina moves with speed $0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Show that the angular speed of the lamina is $3.30 \mathrm { rad } \mathrm { s } ^ { - 1 }$, correct to 3 significant figures.

\hfill \mbox{\textit{CAIE M2 2009 Q1 [4]}}