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2D Motion


Circular Motion 1


position vector



vertical circle




Summary of equations





Describing the circle - position vector R



circle position vector R



i & j are unit vectors along the x and y-axis respectively.


The position vector R of a particle at P from O, at time t, is given by:



circle - position vector equationo



As the position vector R rotates anti-clockwise, the particle at P traces out a circle of radius r .



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The velocity vector V


The velocity vector V at an instant is given by differentiating the position vector R with respect to t .


Here the unit vectors i & j, parallel to the x and y-axes, are centred on the particle at P.



vector equation for velocity




circle vector V




the magnitude of the velocity is given by:



circle velocity equation



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The acceleration vector A


The acceleration of the particle at P is given by differentiating V with respect to t .



circle - the acceleration vector



circle - equation for acceleration





A satellite is moving at 2000 ms-1 in a circular orbit around a distant moon.


If the radius of the circle followed by the satellite is 1000 km, find:

i) the acceleration of the satellite
ii) the time for the satellite to complete one full orbit of the moon in minutes(2d.p.).



circle problem#01


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Non-uniform circular motion(vertical circle)


A more in-depth treatment of motion in a vertical circle is to be found in 'kinetics/more circular motion'.


Here we look at the more general case of the acceleration component along the circle and the component towards the centre varying.


circle - non-uniform acceleration





A particle starts to move in a circular direction with an angular speed of 5 rad s-1 .
The radius of the circle of motion is 4 m, and the angular speed at time t is given by,


circle - non-uniform acceleration problem #01


What is,


i) the linear speed of the particle 6 secs. after it starts moving?

ii) the resultant particle acceleration?

(answers to 1 d.p.)


circle - non-uniform acceleration problem #01b



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