1 A particle \(P\) of mass 0.6 kg is on the rough surface of a horizontal disc with centre \(O\). The distance \(O P\) is 0.4 m . The disc and \(P\) rotate with angular speed \(3 \mathrm { rad } \mathrm { s } ^ { - 1 }\) about a vertical axis which passes through \(O\). Find the magnitude of the frictional force which the disc exerts on the particle, and state the direction of this force.

## Question 1:

| Working/Answer | Mark | Guidance |
|---|---|---|
| $F = 0.6 \times 3^2 \times 0.4$ | M1 | Uses $a = \omega^2 r$ |
| $F = 2.16\text{ N}$ | A1 | |
| Radial, direction PO | B1 | Do not allow direction OP |

**Total: 3 marks**

---

1 A particle $P$ of mass 0.6 kg is on the rough surface of a horizontal disc with centre $O$. The distance $O P$ is 0.4 m . The disc and $P$ rotate with angular speed $3 \mathrm { rad } \mathrm { s } ^ { - 1 }$ about a vertical axis which passes through $O$. Find the magnitude of the frictional force which the disc exerts on the particle, and state the direction of this force.

\hfill \mbox{\textit{CAIE M2 2015 Q1 [3]}}