Physics Notes - Circular Motion

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2.6.1 Draw a vector diagram to show that the acceleration of a particle moving with uniform speed in a circle is directed toward the centre of the circle. Review of basic kinematics: If the acceleration and velocity of an object are parallel (or anti-parallel) then the object's speed will increase (decrease). If the acceleration and velocity of an object are perpendicular then only the direction of the velocity will change and the speed (i.e. the magnitude of the velocity) will remain constant. If a ball is attached to the end of string and swung at a constant speed (i.e. only the direction of the velocity is changing not the magnitude) then there must still be an acceleration. The acceleration is directed towards the center of the motion. This acceleration is call centripetal acceleration!

2.6.2 State the expression for centripetal acceleration.
The acceleration of any object moving in a circle at a constant speed is given by the equation: (1)
a⃗ =v2r
It is important to note that centripetal acceleration is very special. It is the acceleration required for an object to move in a circle at a constant speed. The reverse is also true if an object's acceleration is equal to v2r (and perpendicular to the velocity) then the object must be going in a circle. If an object is moving in a circle at with a changing velocity, then the overall acceleration is not equation to the centripetal acceleration. However the acceleration perpendicular to the velocity (that is the part changing the direction) is still equal to v2r 2.6.3 Identify the force producing circular motion in various situations Sometimes people will make reference to the "centripetal force." This is not a real force, its a pseudo-force. In general the centripetal force is made up of many other forces and is the sum of those forces. This is not unlike the idea of a net force which is also generally the sum of multiple forces. If you have a ball on the end of a string and you swing it in a vertical circle...
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