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Class 11 Physics Notes

Laws of Motion Class 11 Physics Notes

Complete, exam-ready notes on Newton's laws of motion: inertia and momentum, the three laws, impulse, the law of conservation of momentum, friction, and circular motion with banking of roads — written for CBSE, JEE and NEET revision.

Class11SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is Newton's second law in one line?

Newton's second law states that the net force on a body equals the rate of change of its momentum: F = ma, or more generally F = dp/dt.

Newton's Laws of Motion

  • First law (inertia): a body at rest stays at rest and a body in motion stays in uniform motion unless acted on by a net external force.
  • Second law:
  • F⃗=dp⃗dt=ma⃗\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a}
  • .
  • Third law: every action has an equal and opposite reaction; forces act on different bodies.
F⃗=ma⃗=dp⃗dt\vec{F} = m\vec{a} = \frac{d\vec{p}}{dt}
Newton's second law

Impulse and Conservation of Momentum

Impulse

J=∫F dt=ΔpJ = \int F\,dt = \Delta p

Impulse is the change in momentum produced by a force acting over a time interval. For a constant force, J=FΔt=ΔpJ = F\Delta t = \Delta p.

Conservation of momentum

m1u1+m2u2=m1v1+m2v2m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

In the absence of external force, the total momentum of a system is conserved. This is used in collision analysis and rocket propulsion.

Long impulse = less force

Airbags and landing pads extend the collision time, reducing the average force (same impulse Δp spread over longer t).

Friction

  • Static friction acts on bodies at rest (up to a maximum
  • fs=μsNf_s = \mu_s N
  • ).
  • Kinetic friction acts on moving bodies:
  • fk=μkNf_k = \mu_k N
  • .
  • Static friction is generally greater than kinetic friction (
  • μs>μk\mu_s > \mu_k
  • ).
  • Friction is a necessity for walking, driving and holding objects.
fmax=μsN,fk=μkNf_{\text{max}} = \mu_s N,\quad f_k = \mu_k N
Friction formulas

Circular Motion

Centripetal force

Fc=mv2r=mω2rF_c = \frac{mv^2}{r} = m\omega^2 r

The force needed to keep a body moving in a circle of radius r at speed v, directed toward the centre. It is not a new kind of force but the resultant of real forces.

Banking of roads

Banking a curve with angle θ allows a vehicle to negotiate it without relying on friction: tan⁡θ=v2rg\tan\theta = \frac{v^2}{rg}. This is essential at high v where friction alone is insufficient.

Solved Examples

Example: A ball of mass 0.5 kg0.5\,\text{kg} moving at 10 m/s10\,\text{m/s} is stopped in 0.02 s0.02\,\text{s}. Find the average force.

Solution: Δp=0−0.5×10=−5 kg m/s\Delta p = 0 - 0.5\times10 = -5\,\text{kg m/s}. F=ΔpΔt=−50.02=−250 NF = \frac{\Delta p}{\Delta t} = \frac{-5}{0.02} = -250\,\text{N} (negative = opposite the motion).

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Second law

F=dpdt=maF = \frac{dp}{dt} = ma

Impulse

J=FΔt=ΔpJ = F\Delta t = \Delta p

Conservation of momentum

m1u1+m2u2=m1v1+m2v2m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

Static friction

fs=μsNf_s = \mu_s N

Centripetal force

Fc=mv2rF_c = \frac{mv^2}{r}

Banking angle

tan⁡θ=v2rg\tan\theta = \frac{v^2}{rg}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • F = ma = dp/dt.
  • Impulse = change in momentum.
  • Conservation of momentum applies when net external force is zero.
  • Centripetal force is a resultant, not a separate force.
  • Banking angle tanθ = v²/(rg).

FAQ

Common questions

What is Newton's third law?

For every action there is an equal and opposite reaction. Action and reaction act on different bodies, so they do not cancel each other out.

What is impulse?

Impulse is the product of force and the time it acts, equal to the change in momentum: J = FΔt = Δp.

Why are airbags effective in collisions?

They increase the collision time, which spreads the same momentum change over a longer interval and reduces the average force on the passenger.

Why are roads banked at curves?

Banking provides a horizontal centripetal component from the normal force, so a vehicle can turn at high speed even with little or no friction (tanθ = v²/rg).

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Related notes

All Class 11 NotesClass 11 Units and Measurements NotesClass 11 Motion in a Plane NotesPhysics Tutor in Mohali

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