Physics: Bifilar Pendulum
Dimensional Analysis: Investigation on bifilar suspension
Ho Yuk Him (Date of experimentation :20th and 29th October, 2010) This paper presents a study on the application of dimensional analysis on the formulation of an equation concerning the periodic time of a rod rotating at an angle about the vertical axis suspended by two strings at each end. We find that period is inversely related to distance between the strings parallel to each other and directly proportional to the both the square root of length of string and the length of suspension, (i.e. ｄ ). Although discrepancy is found when the equation proposed
by eminent scholars is compared against with ours, our findings can hardly pale into insignificance as errors and the cause of uncertainty are discussed and ways to improve the experiment are suggested, which can possibly spur further studies on this realm of knowledge.
I. Introduction In physics, there are mainly two ways from which useful equations can be derived. One from them is to make good use of the mathematical expression of the theories formulated by our predecessors. An archetype to this notion is the Newton’s second law, which states without ambiguity that “ The rate of change of momentum of an object is directly proportional to the net force acted on it, and the motion occurs along the direction of the force”. This statement can be paraphrased using mathematical terms, i.e. , (1) where F denotes force, m mass and a acceleration. This equation has a formative impact on the realm of physics, as it helps the derivation of other equations. For instance, answering a question concerning the force acting on a ball of mass m being in a circular motion requires the use of (1). Given the centripetal acceleration, , (2) where a denotes acceleration, v velocity and angular velocity, no additional equation is needed, as (1) suffices the requirement. Obviously, the force acting on the ball in its circular path is, . (3) Encouragingly, this method has yielded
Ho Yuk Him (Date of experimentation :20th and 29th October, 2010) This paper presents a study on the application of dimensional analysis on the formulation of an equation concerning the periodic time of a rod rotating at an angle about the vertical axis suspended by two strings at each end. We find that period is inversely related to distance between the strings parallel to each other and directly proportional to the both the square root of length of string and the length of suspension, (i.e. ｄ ). Although discrepancy is found when the equation proposed
by eminent scholars is compared against with ours, our findings can hardly pale into insignificance as errors and the cause of uncertainty are discussed and ways to improve the experiment are suggested, which can possibly spur further studies on this realm of knowledge.
I. Introduction In physics, there are mainly two ways from which useful equations can be derived. One from them is to make good use of the mathematical expression of the theories formulated by our predecessors. An archetype to this notion is the Newton’s second law, which states without ambiguity that “ The rate of change of momentum of an object is directly proportional to the net force acted on it, and the motion occurs along the direction of the force”. This statement can be paraphrased using mathematical terms, i.e. , (1) where F denotes force, m mass and a acceleration. This equation has a formative impact on the realm of physics, as it helps the derivation of other equations. For instance, answering a question concerning the force acting on a ball of mass m being in a circular motion requires the use of (1). Given the centripetal acceleration, , (2) where a denotes acceleration, v velocity and angular velocity, no additional equation is needed, as (1) suffices the requirement. Obviously, the force acting on the ball in its circular path is, . (3) Encouragingly, this method has yielded