| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2013 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rotation about fixed axis: angular acceleration and velocity |
| Difficulty | Challenging +1.2 This is a standard M5 rotation problem requiring application of Newton's second law to both particles, the rotational equation of motion to the pulley, and the no-slip condition. While it involves multiple connected components and careful bookkeeping of forces/torques, the setup is typical for this topic with no novel insights required—just systematic application of learned techniques. |
| Spec | 6.04e Rigid body equilibrium: coplanar forces |
A light inextensible string has a particle of mass m attached to one end and a particle of mass 4m attached to the other end. The string passes over a rough pulley which is modelled as a uniform circular disc of radius a and mass 2m. The pulley can rotate in a vertical plane about a fixed horizontal axis which passes through the centre of the pulley and is perpendicular to the plane of the pulley. As the pulley rotates, a frictional couple of constant magnitude 2mga acts on it.
The system is held with the string vertical and taut on each side of the pulley and released from rest. Given that the string does not slip on the pulley, find the initial angular acceleration of the pulley.
(10 marks)
---6.
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\caption{Figure 2}
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A light inextensible string has a particle of mass $m$ attached to one end and a particle of mass $4 m$ attached to the other end. The string passes over a rough pulley which is modelled as a uniform circular disc of radius $a$ and mass $2 m$, as shown in Figure 2.
The pulley can rotate in a vertical plane about a fixed horizontal axis which passes through the centre of the pulley and is perpendicular to the plane of the pulley. As the pulley rotates, a frictional couple of constant magnitude $2 m g a$ acts on it.
The system is held with the string vertical and taut on each side of the pulley and released from rest. Given that the string does not slip on the pulley, find the initial angular acceleration of the pulley.
\hfill \mbox{\textit{Edexcel M5 2013 Q6 [10]}}