Why is there an acceleration when the speed is constant?

The direction of the velocity is changing.

Define angular speed.

The rate of change of angle, \omega in rad s⁻¹ (\omega=\frac{\theta}{t} at constant speed).

Which has the greater speed on a rotating turntable: a point near the centre or near the rim?

Near the rim: v=r\omega with the same \omega.

Angular speed and circular motionAQA A-Level Further Maths: Flashcards

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In which direction is the acceleration of a particle in uniform circular motion?

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In which direction is the acceleration of a particle in uniform circular motion?: Towards the centre of the circle.
Why is there an acceleration when the speed is constant?: The direction of the velocity is changing.
Define angular speed.: The rate of change of angle, $\omega$ in rad s⁻¹ ( $\omega=\frac{\theta}{t}$ at constant speed).
How many radians in one revolution?: $2\pi$
Convert $n$ revolutions per minute to rad s⁻¹.: Multiply by $\frac{2\pi}{60}$ .
State the relationship between speed and angular speed.: $v=r\omega$
State the two formulae for the magnitude of acceleration in circular motion.: $a=r\omega^2=\frac{v^2}{r}$
State the period of circular motion.: $T=\frac{2\pi}{\omega}$
A particle moves at $3\text{ m s}^{-1}$ on a circle of radius 0.6 m. Find $a$ .: $\frac{9}{0.6}=15\text{ m s}^{-2}$
A turntable rotates at 30 rev/min. What is $\omega$ ?: $\pi=3.14\text{ rad s}^{-1}$
Which has the greater speed on a rotating turntable: a point near the centre or near the rim?: Near the rim: $v=r\omega$ with the same $\omega$ .
How do you find the time to turn through angle $\theta$ ?: $t=\frac{\theta}{\omega}$

Exam questions on Angular speed and circular motion

A particle moves in a horizontal circle of radius 0.6 m with a constant speed of $3\text{ m s}^{-1}$ .
Find the number of revolutions the particle makes per minute.2 marks
A fairground ride rotates at a constant 12 revolutions per minute. A rider sits at a distance of 4.5 m from the axis of rotation.
Find the magnitude and direction of the acceleration of the rider.2 marks
A car of mass 900 kg travels at a constant speed of $15\text{ m s}^{-1}$ around a circular bend of radius 50 m.
Find the acceleration of the car and the magnitude of the resultant horizontal force acting on it.3 marks

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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).