Class 11 Physics: Laws of Motion

Laws of Motion

Below is an organized explanation of Newton’s Laws of Motion, complete with formulas, theory, and real-world context.

1. Newton’s First Law (Law of Inertia)

Theory: A body remains at rest or in uniform motion along a straight path unless acted upon by a net external force.

This law defines inertia: the property of an object to resist changes to its motion. No net force means no acceleration.

Implication: If net force (F_net) = 0, then velocity is constant.
Equation (conceptual): $F$ _net = 0 → v = constant

2. Newton’s Second Law

Theory: The rate of change of momentum of an object is directly proportional to the net external force applied and occurs in the direction of the force.

This law forms the basis of dynamics. It explains how motion changes when forces act.

Formula: $F = =m a$
Where:
- $F$ is force (Newtons, N)
- $m$ is mass (kilograms, kg)
- $a$ is acceleration (m/s²)
Alternate form using momentum ( $p = m v$ ): $F = \frac{d}{d t} p$

3. Newton’s Third Law

Theory: For every action, there's an equal and opposite reaction.

This means forces occur in pairs—one force from object A on B, and another from B on A.

Formula: $F$ ₁₂ = −F₂₁

4. Momentum & Conservation

Theory: Momentum is a measure of an object's motion. In the absence of external forces, momentum of a system is conserved.

Conservation of momentum applies in isolated systems—e.g., collisions or explosions.

Momentum formula: $p = m v$
Conservation (2-body): $m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$

5. Frictional Forces

Theory: Friction opposes motion between two surfaces in contact. There are two main types: static (before motion) and kinetic (during motion).

Static friction adjusts to match applied force up to its limit. Kinetic friction is typically constant once sliding begins.

Static friction limit: $f ≤ μ$ _sN
Kinetic friction: $f = μ$ _kN
Where:
- $μ$ _s is coefficient of static friction
- $μ$ _k is coefficient of kinetic friction
- $N$ is normal force (N)

6. Circular Motion & Centripetal Force

Theory: An object moving in a circle constantly accelerates toward the center, requiring a centripetal force to maintain the motion.

Even though speed is constant, direction changes—so velocity changes, and hence there's acceleration.

Centripetal force: $F$ _c = m v2 r
Where:
- $F$ _c = Centripetal force (N)
- $m$ = Mass (kg)
- $v$ = Speed (m/s)
- $r$ = Radius of circle (m)
(Alternatively, you might see $F$ _c = (m v²)/r.)

7. Free Body Diagrams (FBD)

Theory: An FBD depicts all external forces acting on an isolated object—like gravity, normal force, friction, tension, etc.—to analyze forces and motion effectively.

It helps visualize how forces cancel or add, making problem-solving clearer.

Common forces to include:
- Weight: $W = m g$
- Normal reaction ( $N$ )
- Frictional force ( $f$ )
- Applied force ( $F$ )

Note: All formulas involve vector quantities—consider both magnitude and direction when applying these laws.