WJEC Physics for A2: Study and Rev Guide

Pointer Remember that ‘ y against x ’ means that y is on the vertical axis and x on the horizontal. pivot centre of mass y Fig. M1 Compound pendulum b Suggest a unit for k in the compound pendulum equation. Explain your answer. QUICKFIRE c For the compound pendulum graph, state: a) the gradient b) intercept on the T 2 l axis. QUICKFIRE M Mathematics and data The A level quali cation requires you to manipulate more complex mathematical relationships than AS and to analyse data sets which are related by such relationships. This section builds upon the Section 3 of Year 1 & AS Study and Revision Guide. M.1 Graphs and error bars with non-linear functions You are expected to plot linear graphs for non-linear relationships, which could be more complicated than those at AS level, and also to include error bars. This section is essentially a brief recap on the AS book with a more complicated example. M.1.1 Linearising graphs Remember that the trick is to convert the equation into the form y = mx + c , where x and y are the variables. Then a graph of y against x has a gradient m and an intercept c on the y axis. As an example, consider Fig. M1. A compound pendulum is a freely suspended distributed mass. In this case the mass is a uniform bar. Using the symbol on the diagram, the period, T , of the oscillation is given by: T = 2 p k 2 + l 2 gl where k is a constant and g the acceleration due to gravity. We’ll use this as an example of a more complex (but still algebraic) relationship which we need to manipulate. This is as complicated as it gets! Example The period of the compound pendulum in Fig. M1 is measured for a range of values of l , in order to verify the relationship above. What plot will give a straight line? Answer Squaring gives T 2 = 4 p 2 k 2 + l 2 gl Rearranging gives T 2 l = 4 p 2 k 2 g + 4 p 2 g l 2 Comparing this with the linear equation y = mx + c suggests that a graph of T 2 l against l 2 should be linear. 196 A Level Physics: Study and Revision Guide