In which direction is the centripetal acceleration?

Towards the centre of the circle.

The angle subtended at the centre of a circle by an arc equal in length to the radius.

Define angular speed.

The angle turned through per unit time, \omega = \theta / t, in rad s⁻¹.

Why does the centripetal force do no work?

It acts perpendicular to the velocity, so there is no displacement in the direction of the force.

If the speed of an object in circular motion doubles at constant radius, what happens to the force needed?

It increases by a factor of four, since F \propto v^2.

Circular motionAQA A-Level Physics: Flashcards

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Why does an object moving in a circle at constant speed accelerate?

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Why does an object moving in a circle at constant speed accelerate?: Its velocity, a vector, changes direction continuously, so there is a rate of change of velocity.
In which direction is the centripetal acceleration?: Towards the centre of the circle.
What is a radian?: The angle subtended at the centre of a circle by an arc equal in length to the radius.
How many radians are in a full circle?: $2\pi$ rad.
Define angular speed.: The angle turned through per unit time, $\omega = \theta / t$ , in rad s⁻¹.
Give three expressions for angular speed.: $\omega = v/r = 2\pi f = 2\pi/T$
State the link between linear speed and angular speed.: $v = \omega r$
State two expressions for centripetal acceleration.: $a = v^2/r = \omega^2 r$
State two expressions for centripetal force.: $F = mv^2/r = m\omega^2 r$
What provides the centripetal force for a stone whirled on a string?: The tension in the string.
Why does the centripetal force do no work?: It acts perpendicular to the velocity, so there is no displacement in the direction of the force.
If the speed of an object in circular motion doubles at constant radius, what happens to the force needed?: It increases by a factor of four, since $F \propto v^2$ .
Convert 600 revolutions per minute to a frequency in hertz.: 600 / 60 = 10 Hz

Exam questions on Circular motion

A stone of mass 0.15 kg is whirled in a horizontal circle of radius 0.80 m on a light string. It moves at a constant speed and completes 2.5 revolutions every second.
Explain why the stone is accelerating although its speed is constant.2 marks
A car of mass 1200 kg travels at a constant speed of 18 m s⁻¹ round a flat circular bend of radius 60 m. The only horizontal force on the car is the sideways friction between the tyres and the road.
The maximum friction force that the tyres can provide on a wet road is 8.0 kN. Calculate the maximum constant speed at which the car can take the bend.2 marks
A laboratory centrifuge spins sample tubes about a vertical axis at 6000 revolutions per minute. The base of each tube is 0.12 m from the axis of rotation.
Calculate the angular speed of the tubes and the speed of the base of a tube.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).