Free-Body Diagrams and Equilibrium
Particle equilibrium requires sum F_x = sum F_y = 0; rigid bodies may additionally require sum tau = 0.
Why this shows up in the exam
String junctions · Frame members · Equilibrant forces
Learn the idea
Isolate one body and resolve only the forces acting on it. A complicated arrangement becomes component equations when each object is isolated.
🧠 Memory hook: Isolate, resolve, balance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum F_x = 0; sum F_y = 0 — particle equilibrium
- R = sqrt((sum F_x)²+(sum F_y)²) — resultant magnitude
- sum tau = 0 — rigid-body rotational equilibrium
How to approach it
- 1Draw one FBD
- 2Choose useful axes
- 3Solve components and check signs
Common slip-ups that cost marks
- •Drawing forces by the body
- •Wrong angle reference
- •Ignoring torque for beams
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
More from Laws of Motion
Newton's laws of motion
Understand and apply Newton's first, second, and third laws to analyze forces, motion, and interactions in various physical situations.
Circular motion and centripetal force
Analyze the forces involved in uniform and non-uniform circular motion, including centripetal force, tension, and friction.
Friction and its applications
Study the types of friction (static and kinetic), their effects on motion, and how friction interacts with other forces in different scenarios.
Impulse, momentum, and conservation laws
Explore the principles of linear momentum, impulse, and their conservation in collisions and explosions.
Inertia and Inertial Frames
In an inertial frame, sum F_ext = 0 implies a = 0. Earth-fixed frames are approximate when rotational effects are negligible.
Newton’s Second Law in Vector Form
In an inertial frame sum F_ext = dp/dt; for constant mass this becomes m dv/dt = ma.