# Archive | M3

## Particle Moving in a Horizontal Circle Attached to Two Rods

A particle attached to two rods, moving in a horizontal circle, will produce forces in the rods which balance vertically and produce a force directed towards the centre of the circle which keep the partilce moving in the circle. We can find the forces in the rods by resolving vertically and horizontally. Resolving vertically for […]

## Circular Horizontal Motion of a Ring Threading an Inelastic String

When a car is travelling on a banked surface, if it does not slip, this is due to the force of friction acting at the wheels. Suppose the car moves in a horizontal circle of radius r with a speed v. The forces acting on the car are shown in the diagram below. Resolving vertically […]

## Bodies on Slopes – Toppling

A body will topple when the vertical through the centre of gravity lies just outside the base. A particle on a slope is typically more susceptible to toppling because the vertical is closer to the point where it would lie just outside the base. The triangular prism above is on a slope which makes an […]

## The Centre of Mass of a Scalene Triangle

Equilateral and isosceles triangles of constant mass per unit area have symmetry, and this symmetry can be used to find the centre of mass of a triangle. The centre of mass of an equilateral triangle is quickly found to be two thirds of the distance from the vertex to the centre of the the opposite […]

## Basics of Simple Harmonic Motion

Simple harmonic motion occurs when motion in a circle with uniform acceleration is projected on a line through the centre of the circle. The motion is most naturally projected onto the x and y axes. Suppose the motion is projected onto the– axis. Then (1) We can differentiate to obtain the velocity: (2) and again […]

## Simple Harmonic Motion for a Particle Suspended on an Elastic String

Suppose we suspend a particle of mass m from an elastic spring. The tension in the string isThe particle will be in equilibrium when the tension is equal to the weight. We havewhere x-e labels the equilibrium extension. If the particle is pulled down a further small distanceso that the resultant force on the particle […]

## Elastic Strings

Elastic strings are similar to springs. Both strings and springs obey Hooke’s Law when being extended, but when being compressed, there is no tension in the string while the spring experiences a force tending to increase the length. (Springs obey Hooke’s Law whether extended or compressed, but strings only obey Hooke’s Law when extended). The […]

## Particle on String Executing Circular Horizontal Motion

When analysing the motion of the particle we should resolve vertically and horizontally. Resolving vertically we obtain(1) Resolving horizontally, we have to use the fact that the acceleration for a particle moving in a circle is of magnitudeorand directed towards the centre of the circle. We apply (2) (2) divided by (1) gives Then Unlike […]

## Circular Vertical Motion

A moving particle general has two sorts of energy – kinetic and potential. If conservation of energy can be applied to the particle – if no or other external forces eg friction acts – then the total energy will remain constant. Motion in a circle is a special case. There is an external force – […]

## Centres of Mass, Summation Method

For a uniform regular body with symmetry eg a cube, flat triangle, sphere, the centre of mass is in the middle. Unfortunately, most bodies are not regular or uniform. To find the centre of mass of an arbitrary body we must use one of the formulae, or or same variation of one of these formulae. […]