UNIFORM CIRCULAR MOTION

1. UNIFORM CIRCULAR MOTION THE MOTION OF AN OBJECT moving IN A CIRCLE AT CONSTANT SPEED Averagespeed= distance/time=arc/time = =*R/time=2R/T(period) where R is the radius of the circumference and T iscalled the period of the circularmotion

2. Relatedformulas Angular Speed Formula calculates the distance traveled by the body in terms of rotations to the time taken. It is represented by ω and is given asangular speed=/tDistance traveled is in terms of angle θ is measured in radians and time taken is in seconds. Hence the Angular speed is expressed in radians per seconds or rad/s.Angular speed for one complete rotation is given as 2/TThe relation between Linear speed and Angular speed is v=Where v = Linear speed andr = radius of circular path.

3. Does constant speed mean constant velocity? • Speed and velocity refer to two distinctly different quantities. Speed is a scalar quantity and velocity is a vector quantity. Velocity, being a vector, has both a magnitude and a direction. The magnitude of the velocity vector is the instantaneous speed of the object. The direction of the velocity vector is directed in the same direction that the object moves. Since an object is moving in a circle, its direction is continuously changing. At one moment, the object is moving northward such that the velocity vector is directed northward. One quarter of a cycle later, the object would be moving eastward such that the velocity vector is directed eastward. As the object rounds the circle, the direction of the velocity vector is different than it was the instant before. So while the magnitude of the velocity vector may be constant, the direction of the velocity vector is changing. The best word that can be used to describe the direction of the velocity vector is the word tangential. 

4. SPEED and VELOCITY • To summarize, an object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. While the speed of the object is constant, its velocity is changing. Velocity, being a vector, has a constant magnitude but a changing direction. The direction is always directed tangent to the circle and as the object turns the circle, the tangent line is always pointing in a new direction

5. ACCELERATION? • Sure! • the fact is that an accelerating object is an object that is changing its velocity. And since velocity is a vector that has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity. For this reason, it can be safely stated that an object moving in a circle at constant speed is indeed accelerating. It is accelerating because the direction of the velocity vector is changing.

6. An object moving in a circle is experiencing an acceleration. Even if moving around the perimeter of the circle with a constant speed, there is still a change in velocity and subsequently an acceleration. This acceleration is directed towards the center of the circle. And in accord with Newton's second law of motion, an object which experiences an acceleration must also be experiencing a net force. The direction of the net force is in the same direction as the acceleration. So for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. This is sometimes referred to as the centripetal force requirement. The word centripetal (not to be confused with the F-wordcentrifugal) means center seeking. For object's moving in circular motion, there is a net force acting towards the center which causes the object to seek the center.

7. Mathematics of Circular Motion • There are three mathematical quantities that will be of primary interest to us as we analyze the motion of objects in circles. These three quantities are speed, acceleration and force. • Averagespeedv=2R/T • Acceleration=/R • Force=m/R