Class 11 Physics · Gujarat Board, CBSE, GUJCET and JEE
Laws of motion turns a described situation into an equation. Almost every mark in this chapter comes from one skill: drawing the free-body diagram correctly before writing anything. Friction, which sits inside this chapter, is the single most searched topic of Class 11 mechanics.
21 formulas, 4 memory hooks, and the 5 mistakes that cost the most marks.
| What | Formula | Symbols and notes |
|---|---|---|
| Second law | F = ma = dp/dt | p = mv is linear momentum; the vector form is what the law actually says |
| Impulse | J = FΔt = Δp | a large force for a short time, or a small force for long, can give the same change |
| Conservation of momentum | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | holds when the net external force is zero |
| Recoil of a gun | vgun = −(mbullet/mgun)vbullet | the minus sign is the recoil direction |
| What | Formula | Symbols and notes |
|---|---|---|
| Static friction | fs ≤ μsN | static friction is whatever it needs to be, up to this maximum |
| Limiting friction | fmax = μsN | the value just before sliding starts |
| Kinetic friction | fk = μkN | constant once sliding, and μk < μs |
| Angle of friction | tanλ = μs | λ is the angle the total contact force makes with the normal |
| Angle of repose | tanα = μs | the incline angle at which a body just begins to slide; numerically equal to the angle of friction |
| Body on a rough incline | a = g(sinθ − μcosθ) | when it slides down; it stays put while tanθ ≤ μ |
| Stopping distance | d = v²/(2μg) | independent of mass, which is why a loaded truck does not stop later for this reason |
| What | Formula | Symbols and notes |
|---|---|---|
| Centripetal force | F = mv²/r = mω²r | directed towards the centre; it is a requirement, not a new force |
| Flat road, maximum speed | vmax = √(μrg) | friction alone supplies the centripetal force |
| Banked road, no friction | tanθ = v²/rg | the ideal speed needs no friction at all |
| Banked road with friction | vmax = √(rg(μ + tanθ)/(1 − μtanθ)) | the full result used in entrance papers |
| Vertical circle, top | vtop ≥ √(gr) | the minimum speed to keep the string taut |
| Vertical circle, bottom | vbottom ≥ √(5gr) | follows from energy conservation between top and bottom |
| What | Formula | Symbols and notes |
|---|---|---|
| Two masses over a pulley | a = (m₁ − m₂)g/(m₁ + m₂) | for an ideal pulley and a light inextensible string |
| Tension in that string | T = 2m₁m₂g/(m₁ + m₂) | the same throughout a light string over a frictionless pulley |
| Lift going up with acceleration a | apparent weight = m(g + a) | reading of a weighing machine inside the lift |
| Lift going down with acceleration a | apparent weight = m(g − a) | zero in free fall, which is weightlessness |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Memory hooks
“Draw before you write”
Every laws of motion question
Free-body diagram first: weight down, normal perpendicular to the surface, friction along the surface opposing relative motion, then tension. Most lost marks in this chapter are a missing force, not a wrong formula.
“Static is lazy, kinetic is fixed”
Telling the two frictions apart
Static friction only supplies as much as is needed to prevent sliding, up to μsN. Kinetic friction is a fixed μkN once sliding has begun.
“Repose equals friction”
Angle of repose and angle of friction
Both have tangent equal to μs, so the two angles are numerically the same. One is measured from the incline, the other from the normal.
“Centripetal is a job, not a force”
What supplies the centripetal force
Nothing is labelled centripetal on a free-body diagram. Friction, tension, gravity or the normal does that job. Write which one before using mv²/r.
Where marks go
Test yourself
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