Standard Models in Mechanics

Standard Models in Mechanics

Particle Model

• A particle model assumes that an object is a point mass situated at the centre of mass of the object.
• This model is used when the shape, size and orientation of the object are irrelevant to the problem.
• Ideal for problems involving linear motion and dynamics.

Rigid Body Model

• A rigid body is a model where the size and shape of the object are considered but the object does not deform under the forces applied to it.
• This model is particularly useful for rotational motion problems.
• Rotation of rigid bodies is often related to moments, where the moment of a force about a point is given by the force multiplied by the perpendicular distance from the point to the line of action of the force.

Light Model

• A light model considers the object to be massless.
• This is relevant in string and pulley systems where the mass of the string or pulley is insignificant compared to other masses in the problem.
• One key implication of the light model is that tension along the light object (such as a string) is uniform.

Smooth Model

• A smooth model assumes that there is no friction occurring between the surfaces of objects.
• This model is often used to simplify problems where friction is thought to have negligible effect on the outcome.

Rough Model

• A rough model assumes that there is friction between the contacts of objects.
• This is model is important in problems where friction plays a significant role, often affecting the motion of objects or the forces acting on them.

Hook’s Law Model

• Hook’s Law describes the behavior of springs. Under this model, the force exerted by a spring is proportional to the displacement from its natural length.
• It is typically used in problems involving elastic potential energy, damping, and oscillation.

Important Concepts

• Be familiar with when to apply each model. Part of problem solving in mechanics is identifying the correct model to use based on the information given and simplifying assumptions.
• Understand that actual physical situations are approximations of these ideal models.
• Practise problems using these models. This will improve your ability to identify when to use a particular model and how to apply it to solve problems.