Laws of Motion Class 11 Notes: Free Body Diagrams, Friction and Pulley Problems

Laws of Motion is where many Class 11 students first get scared of physics. The fix is one skill: drawing a correct free body diagram (FBD). These notes teach that skill and the standard problems built on it.

Newton’s laws in one line each

1. A body stays at rest or in uniform motion unless a net external force acts (inertia).
2. F = dp/dt = ma (for constant mass).
3. Action and reaction are equal and opposite and act on different bodies.

How to draw a free body diagram (4 steps)

1. Isolate one body. Draw it as a dot or box.
2. Draw weight mg downward.
3. Draw every contact force: normal (perpendicular to surface), tension (along the string, pulling), friction (along surface, opposing motion).
4. Choose axes along the motion; write ΣF = ma on each axis.

Friction

• Static friction adjusts itself up to a limit: f_s ≤ μ_sN
• Kinetic friction: f_k = μ_kN (μ_k < μ_s)
• Angle of repose: tan θ = μ_s

Standard problems

1. Block on a rough incline (angle θ): along the incline mg sin θ − f = ma; perpendicular N = mg cos θ. If it just starts to slide, μ = tan θ.

2. Atwood machine (masses m₁ > m₂ over a light pulley): a = (m₁ − m₂)g/(m₁ + m₂); T = 2m₁m₂g/(m₁ + m₂). Example: 5 kg and 3 kg → a = 2 × 10/8 = 2.5 m/s², T = 37.5 N.

3. Two blocks pushed together on a smooth floor: treat both as one system for a = F/(m₁ + m₂), then isolate one block to find the contact force.

4. Lift problems: apparent weight N = m(g + a) going up, m(g − a) going down, zero in free fall.

Circular motion

Centripetal force F = mv²/r towards the centre. Banking of road: tan θ = v²/rg (no friction). Maximum speed on a flat curve: v = √(μrg).

Impulse and momentum

Impulse J = FΔt = Δp. Conservation of momentum when no external force: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

Common mistakes

• Drawing “ma” as a force on the FBD (it is the result, not a force).
• Assuming friction always equals μN — static friction is only what is needed.
• Putting action and reaction on the same body.

Revise the base first: Motion Class 9 notes.

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Frequently asked questions

Is friction always μN?

No. Kinetic friction is μk N. Static friction takes only the value needed to prevent motion, up to μs N.

Why does a body in a lift feel heavier when it accelerates up?

Normal reaction N = m(g + a) is more than mg, and you feel N as your weight.

What is the most important skill in this chapter?

Drawing a correct free body diagram and writing ΣF = ma along chosen axes.