Laws of Motion — Physics Class 11 Notes (CBSE & HBSE)
Free NCERT Physics notes for Laws of Motion (Class 11) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Laws of Motion (CBSE & HBSE)
This chapter builds the foundation of dynamics by introducing Newton's three laws of motion, inertia, linear momentum and impulse. It then applies these laws to real situations involving friction (static, kinetic and rolling) and the dynamics of uniform circular motion, including the banking of roads. For both CBSE and HBSE Class 11, this is a high-weightage chapter that combines conceptual reasoning with numerical problem solving.
Newton's Laws, Inertia, Momentum and Impulse
Force and Inertia
Force is a push or pull that can change the state of rest or of uniform motion of a body, change its shape, or change its direction of motion. The SI unit of force is the newton (N), where 1 N = 1 kg m s⁻².
Inertia is the inherent property of a body by virtue of which it resists any change in its state of rest or of uniform motion. Mass is the quantitative measure of inertia — a heavier body has greater inertia.
- Inertia of rest — a body at rest stays at rest (a coin on a card flicks away while the card moves).
- Inertia of motion — a body in motion stays in motion (a passenger lurches forward when a bus stops).
- Inertia of direction — a body resists change in direction (mud flies off tangentially from a spinning wheel).
Newton's First Law (Law of Inertia)
Every body continues in its state of rest or of uniform motion in a straight line unless compelled by an external net force to change that state. The first law defines force qualitatively and introduces the concept of an inertial frame.
Newton's Second Law
The rate of change of linear momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
$$\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a} \quad (\text{for constant mass})$$
This law gives the quantitative measure of force.
| Quantity | Symbol | SI Unit |
|---|---|---|
| Linear momentum | p = mv | kg m s⁻¹ |
| Force | F | newton (N) |
| Impulse | J = F·t | N s |
Linear Momentum and Impulse
Linear momentum p = mv is a vector quantity directed along the velocity.
Impulse is the product of force and the time for which it acts, and equals the change in momentum:
$$\vec{J} = \vec{F}\,\Delta t = \Delta \vec{p} = m\vec{v} - m\vec{u}$$
This impulse–momentum theorem explains why follow-through (large Δt) reduces the force in catching a ball, and why airbags and crumple zones save lives.
Newton's Third Law
To every action there is an equal and opposite reaction. Action and reaction act on different bodies, are equal in magnitude, opposite in direction, and act simultaneously — so they never cancel out.
CBSE/HBSE trap: Action and reaction act on two different bodies, so they can never be added to give zero net force on a single body. Students wrongly cancel them — beware!
Friction: Static, Kinetic and Rolling
Nature of Friction
Friction is the force that opposes the relative motion (or tendency of relative motion) between two surfaces in contact. It arises from interlocking of surface irregularities and molecular adhesion. Friction always acts tangential to the surfaces and opposes relative sliding.
Types of Friction
| Type | When it acts | Key relation |
|---|---|---|
| Static | Surfaces at rest, tendency to move | fₛ ≤ μₛN |
| Limiting | Just before sliding begins | (fₛ)max = μₛN |
| Kinetic | Surfaces in relative motion | f_k = μ_k N |
| Rolling | One body rolls over another | f_r = μ_r N |
Generally μₛ > μ_k > μ_r, which is why rolling is preferred over sliding (ball bearings) and why it is harder to start motion than to keep it going.
Laws of Limiting Friction
- Limiting friction is independent of the area of contact (for given materials).
- It depends on the nature of the surfaces in contact.
- It is directly proportional to the normal reaction: (fₛ)max = μₛN.
Angle of Friction and Angle of Repose
The angle of friction θ is the angle between the resultant of friction and normal reaction and the normal reaction, with tan θ = μₛ.
The angle of repose α is the minimum angle of an inclined plane at which a body just begins to slide down. At this angle:
$$\tan\alpha = \mu_s$$
So the angle of repose equals the angle of friction.
Motion on an Inclined Plane
For a block on an incline of angle θ:
- Component of weight along incline = mg sin θ
- Normal reaction N = mg cos θ
- Friction (up the incline, opposing downward slide) = μ mg cos θ
Tip: Friction is a self-adjusting force in the static regime — it equals exactly the applied force up to a maximum of μₛN. Do not write fₛ = μₛN unless motion is impending.
CBSE/HBSE trap: μ is dimensionless and has no unit. Many students wrongly assign it units of force.
Dynamics of Circular Motion and Banking of Roads
Centripetal Force
For a body of mass m moving in a circle of radius r with speed v, a net inward force called the centripetal force is required:
$$F_c = \frac{mv^2}{r} = m\omega^2 r$$
This force is directed toward the centre and is provided by tension, gravity, friction, or the normal reaction depending on the situation. There is no real outward 'centrifugal' force in an inertial frame — it is a pseudo-force felt only in a rotating frame.
Motion of a Car on a Level Circular Road
On an unbanked road, friction alone supplies the centripetal force:
$$\frac{mv^2}{r} \le \mu_s mg \;\Rightarrow\; v_{max} = \sqrt{\mu_s r g}$$
This is the maximum safe speed on a flat road. Exceeding it makes the car skid outward.
Banking of Roads
To reduce dependence on friction, the outer edge of a curved road is raised by an angle θ. The horizontal component of the normal reaction then provides centripetal force.
Without friction, the optimum (design) speed satisfies:
$$\tan\theta = \frac{v^2}{rg} \;\Rightarrow\; v_0 = \sqrt{rg\tan\theta}$$
With friction, the maximum safe speed is:
$$v_{max} = \sqrt{rg\left(\frac{\mu_s + \tan\theta}{1 - \mu_s\tan\theta}\right)}$$
| Situation | Centripetal force provided by |
|---|---|
| Flat road | Static friction |
| Banked, frictionless | Horizontal component of N |
| Banked, with friction | Friction + horizontal component of N |
Conical Pendulum / Vertical Circle
For a vertical circle, the minimum speed at the top is v_top = √(gr) so the string stays taut, and at the bottom v_bottom = √(5gr).
Tip: At the design (optimum) speed on a banked road, no friction is needed at all — the road does the work geometrically.
CBSE/HBSE trap: Centrifugal force is a pseudo-force; never include it when analysing motion from the ground (inertial) frame.
Frequently asked questions
Are these Laws of Motion notes free?
Yes — the Laws of Motion notes for Physics (Class 11) on Siksha Sarovar are completely free to read, with no account required.
Do these notes follow CBSE and HBSE?
Yes. The Laws of Motion notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.
What does the Laws of Motion chapter cover?
Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Laws of Motion.