| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2013 |
| Session | June |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Energy methods for rotation |
| Difficulty | Challenging +1.2 This M5 question requires applying rotational dynamics (moment of inertia, angular acceleration) and impulse-momentum principles to a disc rotating about an off-center axis. Part (a) involves finding reaction forces using Newton's second law in both linear and rotational forms, requiring knowledge that I = (3/2)mr² for rotation about a point on the circumference. Part (b) requires angular impulse-momentum theorem. While conceptually demanding for A-level (M5 is advanced mechanics), the solution follows standard procedures without requiring novel insight—students familiar with the parallel axis theorem and rotational dynamics formulas can solve it methodically. |
| Spec | 3.03d Newton's second law: 2D vectors6.03f Impulse-momentum: relation |
A uniform circular disc, of radius r and mass m, is free to rotate in a vertical plane about a fixed smooth horizontal axis. This axis is perpendicular to the plane of the disc and passes through a point A on the circumference of the disc. The disc is held with AB horizontal, where AB is a diameter of the disc, and released from rest.
**(a)** Find the magnitude of
(i) the horizontal component,
(ii) the vertical component
of the force exerted on the disc by the axis immediately after the disc is released.
(11 marks)
When AB is vertical the disc is instantaneously brought to rest by a horizontal impulse which acts in the plane of the disc and is applied to the disc at B.
**(b)** Find the magnitude of the impulse.
(6 marks)7. A uniform circular disc, of radius $r$ and mass $m$, is free to rotate in a vertical plane about a fixed smooth horizontal axis. This axis is perpendicular to the plane of the disc and passes through a point $A$ on the circumference of the disc. The disc is held with $A B$ horizontal, where $A B$ is a diameter of the disc, and released from rest.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of
\begin{enumerate}[label=(\roman*)]
\item the horizontal component,
\item the vertical component\\
of the force exerted on the disc by the axis immediately after the disc is released.
When $A B$ is vertical the disc is instantaneously brought to rest by a horizontal impulse which acts in the plane of the disc and is applied to the disc at $B$.
\end{enumerate}\item Find the magnitude of the impulse.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 2013 Q7 [17]}}