| Exam Board | OCR |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments of inertia |
| Type | Conservation of angular momentum |
| Difficulty | Standard +0.3 This is a standard angular momentum conservation problem with straightforward application of formulas. Students apply conservation of angular momentum (I₁ω₁ = I₂ω₂) to find the particle mass, then calculate kinetic energies before and after using rotational KE formula. While it involves rotational dynamics (M4 content), the solution path is direct with no conceptual tricks or novel problem-solving required—slightly easier than average due to clear setup and routine calculations. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| By conservation of angular momentum: \(I_2 \times 15 = 0.9 \times 16\) | M1 | Using \(I\omega\) |
| \(I_2 = 0.96\) | A1 | |
| \(I_2 = 0.9 + m \times 0.4^2\) | M1 | |
| Mass is 0.375 kg | A1 [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| KE before is \(\frac{1}{2} \times 0.9 \times 16^2\) | M1 | Using \(\frac{1}{2}I\omega^2\) |
| KE after is \(\frac{1}{2} \times 0.96 \times 15^2\) | A1 ft | Both expressions correct |
| Loss of KE is \(115.2 - 108 = 7.2\) J | A1 [3] |
# Question 3:
## Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| By conservation of angular momentum: $I_2 \times 15 = 0.9 \times 16$ | M1 | Using $I\omega$ |
| $I_2 = 0.96$ | A1 | |
| $I_2 = 0.9 + m \times 0.4^2$ | M1 | |
| Mass is 0.375 kg | A1 [4] | |
## Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| KE before is $\frac{1}{2} \times 0.9 \times 16^2$ | M1 | Using $\frac{1}{2}I\omega^2$ |
| KE after is $\frac{1}{2} \times 0.96 \times 15^2$ | A1 ft | Both expressions correct |
| Loss of KE is $115.2 - 108 = 7.2$ J | A1 [3] | |
---3 A circular disc is rotating in a horizontal plane with angular speed $16 \mathrm { rad } \mathrm { s } ^ { - 1 }$ about a fixed vertical axis passing through its centre $O$. The moment of inertia of the disc about the axis is $0.9 \mathrm {~kg} \mathrm {~m} ^ { 2 }$. A particle, initially at rest just above the surface of the disc, drops onto the disc and sticks to it at a point 0.4 m from $O$. Afterwards, the angular speed of the disc with the particle attached is $15 \mathrm { rad } \mathrm { s } ^ { - 1 }$.\\
(i) Find the mass of the particle.\\
(ii) Find the loss of kinetic energy.
\hfill \mbox{\textit{OCR M4 2010 Q3 [7]}}