![]() ![]() ![]() In the frame of reference of the centre of the circle the real force acting is the centripetal force, however in the frame of reference of the person in the car the centrifugal force is equally real, and is used in centrifugation to separate compounds of different masses. However by Newton's third law you apply an equal and opposite force on the car, which you perceive as a centrifugal force pushing you against the side of the car. To make you turn the corner the car must supply the centripetal force, otherwise you would carry on in a straight line (not desirable). This is a manifestation of Newton's third law. The student will no doubt be familiar with centrifugal force, which seems to fling a person outwards when a car turns a corner. Similarly the force required to make a satellite move in a circular orbit can only be gravitational attraction to the central planet. That the force is towards the centre of the circle should also not be a surprise, the force required to whirl a conker on the end of a bit of string can only be supplied from the string linking the conker to the center of the circle. If there were no force Newton's first law tells us that the particle would travel in a straight line. It should not be a surprise that a force is required to make a particle go round in a circle. The force is also parallel to the acceleration (i.e. The magnitude of the centripetal acceleration is rω 2.Īccording to Newton's second law, where there is an acceleration, there is also a force. The acceleration is directed towards the centre of the circle, and is often called centripetal (centre seeking) acceleration. Notice that this is perpendicular to v, but antiparallel to r. In the same way, the acceleration of the particle can be seen to have the coordinates The magnitude of the tangential velocity is rω. Since the position vector is in the radial direction the velocity must be directed along the tangent of the circular motion, and for this reason it is often referred to as the tangential velocity. The velocity of the particle is easily found by differentiationĬheck that this is perpendicular to the position vector of the particle by taking the scalar product of the two vectors. Hence we find for the cartesian coordinates If a particle is going round a circle with a constant angular speed, integrating the above equation gives The SI units of ω are radians per second. Having defined angular position it is also useful to define the corresponding angular speed, θ therefore defines the angular position of the rotating particle. The characteristic feature of circular motion is that the radius is fixed and only the angle θ moves as time proceeds. (If you are in doubt, remember that a full circle is 2π radians and that the circumference is 2π r. If θ is measured in radians, then the distance travelled by the particle from the x axis, measured round the arc of the circle is s = rθ. It is much more convenient to use polar coordinates, r representing the distance to the centre of the circle and θ representing the angle measured anticlockwise from the x axis. Which has an unfortunate ambiguity of sign. We can use Cartesian coordinates, but these are not very convenient, the relationship between x and y on a circle of radius r is We first need a way of defining the position of a particle in its circular motion. ![]() We initially start with this simplified version, but it will need to be generalised because some problems in chemistry require a more sophisticated analysis. This topic deals with a single mass performing a circular motion. ![]()
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