mechanics stuff

What does a light string mean, and what changes if the string is not light?

A light string has negligible mass, so the tension is the same throughout the string.

If the string is not light, its weight cannot be ignored, so the tension may be different in different parts of the string.

What does an inextensible string mean in connected particles questions?

An inextensible string does not stretch, so connected particles have the same magnitude of acceleration.

What does modelling an object as a particle ignore?

A particle has mass but no size, so its dimensions, shape, rotation and air resistance effects due to surface area are ignored.

Use this when they ask for a limitation of modelling something like a stone, ball, car, or block as a particle.

What does a smooth pulley mean?

A smooth pulley has no friction, so the tension is the same on both sides of the pulley.

If the pulley is rough, there may be different tensions on each side.

What does a uniform rod mean in moments questions?

A uniform rod has its mass evenly distributed, so its weight acts at the midpoint of the rod.

What does a rigid rod mean?

A rigid rod does not bend or stretch, so the distances between points on the rod stay fixed.

When do you use F <= mu R and when do you use F = mu R?

Use F <= mu R when the object is simply in equilibrium, resting, not slipping, or the question asks you to show an inequality for mu.

Use F = mu R when the object is in limiting equilibrium, on the point of slipping, just about to move, or when finding the minimum value of mu needed for equilibrium.

Key idea: friction adjusts up to a maximum. It only equals mu R at the slipping threshold.

Projectile model improvements other than air resistance

Use mark-scheme-safe answers: allow for wind effects, account for spin of the ball, or use a more accurate value of g.
“Take account of dimensions / don’t model as a particle” may be reasonable, but wind/spin are safer.