Vectors in circular motionAQA A-Level Further Maths: Mind map

Exam questions on Vectors in circular motion

1. A particle $P$ moves anticlockwise on a circle of radius $2$ m with centre at the origin $O$. At time $t$ seconds its position vector, in metres, is $\mathbf{r}=2\cos3t\,\mathbf{i}+2\sin3t\,\mathbf{j}$.
   Find the acceleration of $P$, as a vector, when $t=\frac{\pi}{6}$.2 marks
2. A particle $Q$ moves on a circle of radius $4$ m with centre at the origin $O$. At time $t$ seconds its position vector, in metres, is $\mathbf{r}=4\sin2t\,\mathbf{i}+4\cos2t\,\mathbf{j}$.
   Show that the speed of $Q$ is constant and state its value.2 marks
3. A particle $P$ moves anticlockwise with constant speed $4$ m s⁻¹ on a circle of radius $6$ m with centre at the origin $O$. At time $t=0$ it is at the point $(6,0)$. Position vectors are in metres relative to $O$ and $t$ is in seconds.
   Find the angular speed of $P$ and write down its position vector at time $t$.3 marks