OCR M2 2007 January — Question 1 3 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2007
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeToppling and sliding of solids
DifficultyModerate -0.3 This is a straightforward toppling problem requiring only basic moment principles: the cylinder topples when the vertical line through its center of mass passes outside the base. The calculation involves simple geometry (tan α = radius/half-height = 6/10) with no complications from friction or sliding conditions. Slightly easier than average due to being a single-step problem with standard setup.
Spec6.04e Rigid body equilibrium: coplanar forces

1 A uniform solid cylinder has height 20 cm and diameter 12 cm . It is placed with its axis vertical on a rough horizontal plane. The plane is slowly tilted until the cylinder topples when the angle of inclination is \(\alpha\). Find \(\alpha\).

AnswerMarks Guidance
com directly above lowest pointB1
\(\tan \alpha = 6/10\)M1
\(\alpha = 31.0\) or \(0.540\) radsA1 3
com directly above lowest point | B1 |
$\tan \alpha = 6/10$ | M1 |
$\alpha = 31.0$ or $0.540$ rads | A1 | 3 |
1 A uniform solid cylinder has height 20 cm and diameter 12 cm . It is placed with its axis vertical on a rough horizontal plane. The plane is slowly tilted until the cylinder topples when the angle of inclination is $\alpha$. Find $\alpha$.

\hfill \mbox{\textit{OCR M2 2007 Q1 [3]}}