# Archive | M2

## Non Uniform Rod Suspended by Two Non Vertical Strings

We can find the centre of mass and tension in the strings holding a non uniform rod of known length and mass by resolving and taking moments in the usual way. Consider the non uniform rod shown below. Take the tension in the string at end A to beand the tension in the string at […]

## The Difference Between Centre of Mass and Centre of Gravity

The centre of mass is not the same as the centre of gravity. To take the simplest example, a body consisting of two point masses A and B, 1 kg each, placed 1 m apart. The centre of mass C is halfway between the two masses. If however the body is placed in the vicinity […]

## Climbing a Ladder Safely

Unfortunately, a ladder is most likely to slip when the climber is at the top. This is because the moment of the climber in the direction in which the ladder would slip is at its maximum when the climber is at the top. We can analyse the forces on a ladder as it leans against […]

## Introduction to Frameworks

A framework is a connected network of rods. Each rod is assumed to be weightless, inflexible or rigid and inextensible, with thickness of zero. We typically want to find the forces in each rod, and these assumptions means the equations we write down are easy to solve. Assuming the rod is weightless means the only […]

## Bouncing Balls

When a ball is dropped from a height and hits the ground, it bounces and starts moving up. The speed with which it bounces up is not quite as big as the speed with which it hits the ground, If the ball hits the ground with a speedand the coefficient of restitution between the ball […]

## Centre of Mass of a System of Particles

We can find the centre of mass of a system of particles by taking moments about a point for each particle, treating the position of each particle as a position vector, and summing the results, then equating this sum to the position vector of the whole system of particles. For example, consider the system of […]

## Hinges

A hinge attached to one end of a body fixes that end of the body in space. The body may have any orientation in one plane relative to the hinge: Because of this, a reaction at the hinge will have components both parallel and perpendicular to the surface. We may model the hinge as being […]

## The Work Energy Principle

The Work Energy Principle is a version of the Law of Conservation of Energy. It takes into account that energy is not conserved, or at least that useful energy is not conserved. In almost any process in practice, work must be done to overcome friction, and this work that is done cannot be recovered. The […]

## Impulse in Two Dimensions

Impulse in a vector. An object may experience an impulse acting at any angle to it’s path, forcing it to change direction by any angle. We should always represent impulse by a vector. This may be strictly unnecessary if the impulse acts along the path of the velocity, but it becomes essential if the impulse […]