Motion in a vertical circleEdexcel International A Level Further Maths: Flashcards

What these 13 flashcards ask

What is conserved in vertical circular motion on a string or smooth surface?
Height gained from the lowest point to the top of a circle of radius r?
Radial equation with \theta from the downward vertical?
Tension at the lowest point?
Tension when the string is horizontal?
Tension at the highest point?
Where is the tension greatest and least?
Condition for a particle on a string to complete a vertical circle?
Condition for a bead on a wire to reach the top?
What happens when the tension reaches zero?
Why does a bead on a wire not need v^2\ge gr at the top?
When does a particle leave the outside of a sphere?
A particle slides from rest at the top of a smooth sphere. Where does it leave?

Exam questions on Motion in a vertical circle

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
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
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

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).