Edexcel M5 — Question 6 11 marks

Exam BoardEdexcel
ModuleM5 (Mechanics 5)
Marks11
PaperDownload PDF ↗
TopicImpulse and momentum (advanced)
TypeRod and particle collision
DifficultyChallenging +1.8 This M5 question requires conservation of angular momentum about an off-center axis (parallel axis theorem), followed by analyzing forces on a rotating system with both gravitational and centripetal components. While the techniques are standard for M5, the combination of impact mechanics, moment of inertia about a tangent, and force analysis at a specific instant requires careful multi-step reasoning and is significantly harder than typical A-level mechanics questions.
Spec6.02i Conservation of energy: mechanical energy principle6.03f Impulse-momentum: relation6.04b Find centre of mass: using symmetry

A uniform circular disc has mass \(m\), centre \(O\) and radius \(2a\). It is free to rotate about a fixed smooth horizontal axis \(L\) which lies in the same plane as the disc and which is tangential to the disc at the point \(A\). The disc is hanging at rest in equilibrium with \(O\) vertically below \(A\) when it is struck at \(O\) by a particle of mass \(m\). Immediately before the impact the particle is moving perpendicular to the plane of the disc with speed \(3\sqrt{ag}\). The particle adheres to the disc at \(O\).
  1. Find the angular speed of the disc immediately after the impact. [5]
  1. Find the magnitude of the force exerted on the disc by the axis immediately after the impact. [6]

A uniform circular disc has mass $m$, centre $O$ and radius $2a$. It is free to rotate about a fixed smooth horizontal axis $L$ which lies in the same plane as the disc and which is tangential to the disc at the point $A$. The disc is hanging at rest in equilibrium with $O$ vertically below $A$ when it is struck at $O$ by a particle of mass $m$. Immediately before the impact the particle is moving perpendicular to the plane of the disc with speed $3\sqrt{ag}$. The particle adheres to the disc at $O$.

\begin{enumerate}[label=(\alph*)]
\item Find the angular speed of the disc immediately after the impact.
[5]
\end{enumerate}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the magnitude of the force exerted on the disc by the axis immediately after the impact.
[6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M5  Q6 [11]}}