| Exam Board | OCR |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments of inertia |
| Type | Conservation of angular momentum |
| Difficulty | Standard +0.3 This is a straightforward M4 rotational dynamics question requiring standard formulas: part (i) uses the rotational equation of motion (ω² = ω₀² + 2αθ) and τ = Iα with the standard disc moment of inertia; part (ii) applies conservation of angular momentum. Both parts are direct applications of bookwork formulas with no problem-solving insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r |
A flywheel takes the form of a uniform disc of mass 8 kg and radius 0.15 m. It rotates freely about an axis passing through its centre and perpendicular to the disc. A couple of constant moment is applied to the flywheel. The flywheel turns through an angle of 75 radians while its angular speed increases from 10 rad s$^{-1}$ to 25 rad s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\item Find the moment of the couple about the axis. [5]
\end{enumerate}
When the flywheel is rotating with angular speed 25 rad s$^{-1}$, it locks together with a second flywheel which is mounted on the same axis and is at rest. Immediately afterwards, both flywheels rotate together with the same angular speed 9 rad s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the moment of inertia of the second flywheel about the axis. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M4 2006 Q2 [8]}}