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

What these 12 flashcards ask

Height above the lowest point at angle \theta from the downward vertical?
Energy equation for speed at angle \theta?
Speed at the top in terms of u?
Radial equation at angle \theta?
Tension at the lowest point?
Tension at the highest point?
Condition at the top for a string?
Condition on u for a string to complete the circle?
Condition on u for a bead on a wire to complete the circle?
Why does a wire have a different condition from a string?
When does the particle oscillate rather than leave the circle?
Where does the string go slack if 2gr<u^2<5gr?

Exam questions on Circular motion in a vertical plane

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).