Sat, May 14, 2005 at 3:03 PM

This is yet another discovery I made in the process of making a

G.E.G. All copyright reserved by me.

We all learn from the physics textbook that energy is conserved in

any situation. An excellent example would be a falling object: At any

moment of its descending, the sum total of its kinetic energy and

potential energy should be equal. This does not bother my intellect at

all. What I found interesting is the energy exchange of the case of

swinging or rotational motion. Does they obtain the same law of

conservation of energy as the case of falling object?

The reason I think why falling object is chosen for textbook

example is because of the linearity of the motion. During the whole

trajectory, the velocity remain on the same straight line as the

acceleration as well as the line which we calculate the level of

potential energy. Now consider the case of swinging object. As we

apply a pulse force to distrub the equilibrium, what the object

respond is by displacement in two dimension. Due to the restraint of a

rope, the object must SWING instead of moving in a plane parallel to

the ground. It is easy to see that as the object is swinging, it should

have its own set of angular momentum, angular velocity and rotational

energy. Although the conventional calculation require us to calculate

the velocity at different height, in what sense does these velocity

meant? Since the object is moving in a circular trajectory, it follows

that the object is changing its direction of movement in every

moment(with centipendal acceleration). So if that velocity have any

meaning, it should refer to the instantaneous velocity in the direction

of its movement. However, as far as I understand the teaching of

Physics, it doesn’t appear that velocity refer to the velocity at the

direction of its movement. It is most situably refer to the direction

of the vertical component of the movement since it is linear.(How

meaningful/useful is this calculation is another matter.) Moreover,

any conservation of energy formula would require a condition that NO

external force is acting on the system. This condition is VIOLATED

since a varying tension of the rope is CONTINUOUSLY acting on the

system to neutralize/reduce or even overcome the gravity. It would be

a better analogy to consider this system as an object is continuously

acting by a fixed and a variable force in the opposition direction.

Now, taken these considerations into account. The following

conclusion is of a closer description of reality: At any moment, the

sum of Rotational Kinetic Energy, Work done by the centripetal force

and gravitational Potential energy should be a constant. We can apply

this formula into calculate the exact Angular Velocity of the object,

then use sine and cosine of its value to obtain the vertical and

horizontal velocity of this object.