## UY1: Centre Of Mass Of A Cone

Find the centre of mass of an uniform cone of height $h$ and radius $R$. Let the density of the cone be $\rho$. It is obvious from the diagram that the x and y components of the centre of mass of a cone is 0: \begin{aligned} x_{CM} &= 0 \\ y_{CM} &= 0 \end{aligned} Hence, we just need to find …

## UY1: Concept Of Work

In classical mechanics, we are concerned with the concepts of work and energy. Work-energy concepts are based on Newton’s laws and do not involve any new physical principles. The work-energy concept can therefore be applied to the dynamics of a mechanical system without resorting to Newton’s laws. This is useful in complex situation (e.g. variable forces) and applicable to a …

## UY1: Uniform Circular Motion & Non-uniform Circular Motion

Uniform Circular Motion A particle moving with uniform speed $v$ in a circular path of radius $r$ experiences an acceleration $\vec{a}_{r}$ that has a magnitude: $$a_{r} = \frac{v^{2}}{r}$$ $\vec{a}_{r}$ is directed towards the center of the circle (centripetal acceleration) $\vec{a}_{r}$ is always perpendicular to $\vec{v}$ Applying Newton’s Second Law along the radial direction: $$\sum F_{r} = ma_{r} = m\frac{v^{2}}{r}$$ A …