Vertical circular motionEdexcel A-Level Further Maths: Mind map

Exam questions on Vertical circular motion

1. A particle $P$ of mass 0.5 kg is attached to one end of a light inextensible string of length 2 m. The other end of the string is fixed at a point $O$. $P$ moves in a vertical circle with centre $O$, with the string taut. At the lowest point $A$ of the circle, $P$ has speed 12 m s⁻¹. Take $g=9.8$ m s⁻².
   Find the tension in the string when $P$ is at $A$.2 marks
2. A smooth circular wire of radius 0.9 m is fixed in a vertical plane with centre $O$. A small bead $B$ of mass 0.2 kg is threaded on the wire and is projected from the lowest point $A$ of the wire with speed $u$ m s⁻¹. Take $g=9.8$ m s⁻².
   Given that $u=7$, find the magnitude of the force exerted by the wire on $B$ when $OB$ is horizontal.2 marks
3. A particle $P$ of mass 0.4 kg is attached to one end of a light inextensible string of length 0.6 m. The other end of the string is fixed at a point $O$. $P$ is at rest at the point $A$ vertically below $O$ and is projected horizontally with speed 4 m s⁻¹. $P$ then moves along a circular path until the string becomes slack. Take $g=9.8$ m s⁻².
   Find the tension in the string when $OP$ is horizontal.3 marks