Motion in a vertical circleEdexcel International A Level Further Maths: Mind map

Exam questions on Motion in a vertical circle

1. A particle of mass $0.5$ kg is attached to one end of a light inextensible string of length $1$ m. The other end of the string is fixed at a point $O$. The particle is at rest at the lowest point and is then projected horizontally with speed $8$ m s$^{-1}$. It moves in a complete vertical circle. Take $g=9.8$ m s$^{-2}$.
   Find the tension in the string when the particle is at the highest point.2 marks
2. A bead $B$ of mass $0.1$ kg is threaded on a smooth circular wire of radius $0.5$ m, fixed in a vertical plane with centre $O$. $B$ is projected from the lowest point of the wire with speed $5$ m s$^{-1}$. Take $g=9.8$ m s$^{-2}$.
   Find the magnitude and direction of the force exerted on $B$ by the wire when $B$ is at the highest point of the wire.2 marks
3. A smooth sphere of radius $0.5$ m is fixed with its centre at $O$. A particle $P$ of mass $0.4$ kg is projected horizontally with speed $1$ m s$^{-1}$ from the highest point $A$ of the sphere, and moves on the outer surface. Take $g=9.8$ m s$^{-2}$.
   Find the speed of $P$ when $OP$ makes an angle of $30^\circ$ with the upward vertical and $P$ is still on the sphere.3 marks