Circular motion in a vertical planeAQA A-Level Further Maths: Mind map

Exam questions on Circular motion in a vertical plane

1. A particle of mass $0.3$ kg is attached to one end of a light inextensible string of length $0.8$ m. The other end of the string is fixed at $O$. The particle moves in a vertical circle with centre $O$ and its speed at the lowest point $A$ is $7$ m s⁻¹. 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 small bead $B$ of mass $0.05$ kg is threaded on a smooth circular wire of radius $0.4$ m, fixed in a vertical plane with centre $O$. The bead is projected from the lowest point of the wire with speed $4$ m s⁻¹. Take $g=9.8$ m s⁻².
   Find the least speed at the lowest point for which the bead reaches the highest point of the wire.2 marks
3. A particle of mass $0.2$ kg is attached to one end of a light inextensible string of length $1.5$ m. The other end of the string is fixed at $O$. The particle hangs at rest at the lowest point and is then given a horizontal speed $u$ m s⁻¹. Take $g=9.8$ m s⁻².
   Find the least value of $u$ for which the particle completes the vertical circle with the string always taut.3 marks