Conical pendulumsAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

Forces on a conical pendulum particle?
Radius of the circle for string length L at angle \theta?
Vertical equation for a conical pendulum?
Horizontal equation for a conical pendulum?
Relationship between \theta, v and r?
Tension in terms of \omega and L?
Expression for \cos\theta in terms of \omega?
Condition on \omega for horizontal circular motion on one string?
Period of a conical pendulum?
Two strings, A above B: vertical equation?
Two strings: horizontal equation?
What does TB=0 mean for the lower string?

Exam questions on Conical pendulums

A particle of mass $0.4$ kg is attached to a fixed point $O$ by a light inextensible string of length $0.8$ m. The particle moves in a horizontal circle below $O$ with constant speed, with the string taut and making an angle of $30^\circ$ with the downward vertical. Take $g=9.8$ m s⁻².
Find the angular speed of the particle.2 marks
A particle of mass $0.6$ kg is attached to a fixed point $O$ by a light inextensible string of length $0.5$ m. It moves in a horizontal circle below $O$ , with the string taut and making an angle $\theta$ with the downward vertical, where $\cos\theta=0.8$ . Take $g=9.8$ m s⁻².
Find the time taken for one complete revolution.2 marks
A particle of mass $m$ kg is attached to a fixed point $O$ by a light inextensible string of length $L$ m. It moves in a horizontal circle below $O$ with constant angular speed $\omega$ rad s⁻¹, with the string taut and making an angle $\theta$ with the downward vertical. Take $g=9.8$ m s⁻².
Show that $\cos\theta=\frac{g}{\omega^2L}$ .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).