Circular Motion

• Angular speed describes the circular motion of a body in terms of the rate of change of the angle at the centre of its path.
• There are 2 pi radians in a whole circle, so dividing 2 pi by pi gives the period (T), the time taken to complete one revolution.
• Period: the time taken to complete one revolution or one complete oscillation.
• Circumference of a circle is 2 pi r.
• Angles are now described in terms of radians.
• There are 2 pi radians in one complete rotation (360).
• Angular displacement: the angle through which rotation has occurred in radians.
• Angular speed: the rate of change of angular displacement (the angle through which the object rotates per unit time).
• The period can also be found by dividing the distance around the circular path (circumference) by the linear speed of the object.
• Bodies can have the same angular speed but different linear speeds depending on how far they are from the centre of the circle.
• The linear speed increases with path radius for objects with the same angular speed.
• A body moving around a circular path is continually changing its direction of motion.
• The body’s velocity is continually changing although its speed remains constant.
• Since the direction of the object’s velocity is changing, it is always accelerating.
• Centripetal acceleration: rate of change of velocity of a body following a circular path, directed towards the centre of the circle.
• There is a centripetal force acting in the same direction as the centripetal acceleration.
• Centripetal force: resultant force that must act towards the centre of a circle to make a body follow a circular path.
• a = centripetal acceleration (ms-2).
• v = velocity (ms-1).
• r = radius of circular path (m).
• F = Resultant force on object (N).
• m = mass of object (kg).
• No work is done by the centripetal force as there is no displacement in the direction of the resultant force.
• The centripetal force does not change the speed of the object and therefore does not change its kinetic energy, only is direction of motion.
• When a body is undergoing uniform circular motion, it travels right round the circumference, a distance, in a time T.
• Since speed is distance/time.