17 Motion in a circle AQA Physics A level pp 274-285

Uniform circular motion Speed unchanged Speed = |Velocity| = v Where r = radius and T = period Velocity changes since direction is changing Frequency = 1/T

Angular velocity, ω Rotational frequency f = 1/T Angular frequency = 360o per second We like to have simple units We like equations without (too many) constants Define So Also

Radians Units of ω are radians per second 2π radians = 1 rotation = 360o 1 rad = 360/2π = 57.296o Often c used in Maths but use “rad” in Physics 1 radian is also the angle which subtends an arc of a circle of length r, the radius

Centripetal acceleration The change in velocity = acceleration time Acceleration is perpendicular to motion Speed is unchanged – only changes direction Acceleration is always towards the centre of the circle It is called the Centripetal Acceleration

Centripetal acceleration Change in velocity Change in position But if is small Also

Centripetal force Force = mass x acceleration Force is in the direction of the acceleration

On the road – bridges and hills If R=0 so only just holding road mg Path of car

On the road - roundabouts Friction provides centripetal force If frictional force not enough, car continues in a straight line or curved path – not sideways!

On the road - banking Banking provides a natural force – cars move in a circle! Centripetal force Reaction force

At the fairground – the big dipper At the bottom of the dip In this case...

At the fairground – the long swing Like “Rush” at Thorpe Park Potential energy Kinetic energy

At the fairground – the big wheel At the top No force on rider due to chair At the bottom Maximum force on chair so feels heaviest

Ride safety Rides regularly checked for safety Incidents investigated by HSE – Health and Safety Executive G-forces experienced by riders Max 1.9g into head Max 5.1g into feet Maximum g-forces on top are at the back on Stealth Calculations for different sized People

Orbits Real orbits Ellipses Sun is at a focus Nearer the sun less Potential so more Kinetic energy Force not completely perpendicular Speeds up and slows down as well as changing direction

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