Andrew May

Work, power and energy

When an elastic string, natural length a, modulus of elasticity λ, is stretched by a distance x, the tension in the string is \( T = \lambda \frac{x}{a} \).

Confidence intervals/samples/hypothesis testing

Take many samples, size n, from a population and find their means. The Central Limit Theorem proves that these means form a Normal distribution with mean μ (that of the population) and standard deviation \( \frac{\sigma }{{\sqrt n }} \) (called the standard error):

Variable acceleration and SHM

\bar X \sim N\left( {\mu ,\frac{{{\sigma ^2}}}{n}} \right)

Miscellaneous statistics topics

For small samples (n < 30) see Chapter 19.

Motion in a circle

If r A and r B are the position vectors of A and B then ṙ A = v A and ṙ B = v B are the velocities of A and B.

Basic algebra and arithmetic

For straight-line motion

Miscellaneous pure topics

F = m\ddot x{\kern 1pt} so{\kern 1pt} \ddot x{\kern 1pt} = \frac{F}{m}