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. Yet, with the inward net force directed perpendicular to the velocity vector, the object is always changing its direction and undergoing an inward acceleration.įor more information on physical descriptions of motion, visit The Physics Classroom Tutorial.This topic deals with a single mass performing a circular motion. Without such an inward force, an object would continue in a straight line, never deviating from its direction. The net force is said to be an inward or centripetal force. The net force acting upon such an object is directed towards the center of the circle. The final motion characteristic for an object undergoing uniform circular motion is the net force. The animation at the right depicts this by means of a vector arrow. The direction of the acceleration is inwards. Nonetheless, it is accelerating due to its change in direction. An object undergoing uniform circular motion is moving with a constant speed. Accelerating objects are objects which are changing their velocity - either the speed (i.e., magnitude of the velocity vector) or the direction. The animation at the right depicts this by means of a vector arrow.Īn object moving in a circle is accelerating. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well. At all instances, the object is moving tangent to the circle. As an object moves in a circle, it is constantly changing its direction. Uniform circular motion can be described as the motion of an object in a circle at a constant speed. Multimedia Studios » Circular, Satellite, and Rotational Motion » Uniform Circular Motion
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