Saturday, September 21, 2013

Law of Conservation

When a roller skater rotates on her scates, she travels faster is she makes a circle in a smaller radius. This is because a quantity termed as Angular Momentum (AM, ang Mom) is conserved in the process. Angular momentum is given by the equation = I * w * w. I is termed as the Moment of inertia. The angular velocity is a vector quantity implying that localised direction of travel is important in a circular motion.

When a scater suddenly reduces her radius of motion, her moment of inertia decreases. In order for the angular momentum of travel to be conserved the velocity increases. In other words if she goes around in a smaller circle her speed increases.

Let us take the case when she travels in a bigger circle than before. In this case too, angular momentum is conserved. In this case the moment of inertia increases. So in order for the total AM to be conserved her speed decreases.

This law is termed as the law of conservation of ang mom it applies to all objects that are rotating in a circular motion.

An analogy to the same law is the law of conservation of momentum which applies to motion in straight lines. In this case the momentum of the system of bodies that are colliding is conserved. So the momentum before the collision is MV + M1V1 where M and M1 are two different masses which travel at different speeds. So the total momentum of the system is conserved. AM and linear momentum are vectors implying that the quantity is dependent upon the direction.