CAIE M2 2002 November — Question 1 3 marks

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2002
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeCentre of mass of rotating body
DifficultyModerate -0.5 This is a straightforward application of circular motion kinematics (v = rω) combined with basic center of mass location for a right-angled isosceles triangle. Students need to find the distance from the rotation axis to the center of mass (which is 4 cm from the midpoint of the hypotenuse) and multiply by the angular speed. The geometry is standard and the calculation is direct, making this slightly easier than average but still requiring proper understanding of the setup.
Spec6.04b Find centre of mass: using symmetry6.05a Angular velocity: definitions

1 \includegraphics[max width=\textwidth, alt={}, center]{fcf239a6-6558-43ec-b404-70aa349af6a9-2_373_552_260_799} A uniform isosceles triangular lamina \(A B C\) is right-angled at \(B\). The length of \(A C\) is 24 cm . The lamina rotates in a horizontal plane, about a vertical axis through the mid-point of \(A C\), with angular speed \(5 \mathrm { rad } \mathrm { s } ^ { - 1 }\) (see diagram). Find the speed with which the centre of mass of the lamina is moving.
[0pt] [3]

AnswerMarks Guidance
\(r = 4\)cmB1
Uses \(v = wr\)M1
Speed is 20cm s\(^{-1}\)A1 3 marks
$r = 4$cm | B1 |
Uses $v = wr$ | M1 |
Speed is 20cm s$^{-1}$ | A1 | 3 marks |
1\\
\includegraphics[max width=\textwidth, alt={}, center]{fcf239a6-6558-43ec-b404-70aa349af6a9-2_373_552_260_799}

A uniform isosceles triangular lamina $A B C$ is right-angled at $B$. The length of $A C$ is 24 cm . The lamina rotates in a horizontal plane, about a vertical axis through the mid-point of $A C$, with angular speed $5 \mathrm { rad } \mathrm { s } ^ { - 1 }$ (see diagram). Find the speed with which the centre of mass of the lamina is moving.\\[0pt]
[3]

\hfill \mbox{\textit{CAIE M2 2002 Q1 [3]}}