Learning Objectives
- State and apply Newton's three laws of motion
- Understand the concept of inertia and momentum
- Solve problems involving free body diagrams
- Understand friction and its types
- Apply concepts of circular motion dynamics
Key Concepts
Newton's First Law (Law of Inertia)
A body continues in its state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.
Inertia: The natural tendency of a body to resist a change in its state of rest or motion. Mass is a measure of inertia.
Types of inertia: Inertia of rest, Inertia of motion, Inertia of direction.
Newton's Second Law
The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
F = dp/dt = d(mv)/dt
For constant mass: F = ma
Momentum: p = mv (a vector quantity, SI unit: kg m/s)
Impulse: J = FΔt = Δp (change in momentum). Impulse equals the area under force-time graph.
Newton's Third Law
For every action, there is an equal and opposite reaction. Action and reaction act on different bodies simultaneously.
F₁₂ = -F₂₁ (Force on body 1 by body 2 = negative of force on body 2 by body 1)
Action-reaction pairs never cancel each other as they act on different bodies.
Conservation of Linear Momentum
If no external force acts on a system, the total momentum remains constant: p_total = constant.
For two-body system: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Applications: recoil of gun, rocket propulsion, explosions.
Free Body Diagrams (FBD)
A diagram showing all forces acting on a single body. Steps: isolate the body, identify all forces (gravity, normal, tension, friction, applied), resolve forces along convenient axes, apply Newton's second law along each axis.
Friction
Static Friction: f_s ≤ μ_s N (self-adjusting, up to a maximum value). Opposes tendency of relative motion.
Kinetic Friction: f_k = μ_k N (constant). Acts during actual relative motion. μ_k < μ_s.
Rolling Friction: f_r = μ_r N. Much smaller than kinetic friction.
Angle of Friction: tan λ = μ_s
Angle of Repose: tan θ = μ_s (minimum angle of an inclined plane at which a body begins to slide).
On an inclined plane of angle θ: Component of gravity along plane = mg sin θ, Normal force N = mg cos θ.
Circular Motion Dynamics
Centripetal Force: F_c = mv²/r = mrω² (directed toward centre)
Banking of roads: tan θ = v²/rg (without friction)
With friction: v_max = √[rg(μ + tan θ)/(1 - μ tan θ)]
Summary
Newton's laws of motion form the foundation of classical mechanics. The first law defines inertia and equilibrium. The second law relates force to rate of change of momentum (F = ma). The third law states action-reaction pairs. Conservation of momentum applies to isolated systems. Friction is a contact force that opposes relative motion. Circular motion requires centripetal force directed toward the centre.
Important Terms
- Inertia: Resistance to change in state of motion
- Momentum: Product of mass and velocity (p = mv)
- Impulse: Product of force and time interval (J = FΔt)
- Normal Force: Perpendicular contact force from a surface
- Tension: Force transmitted through a string or rope
- Coefficient of Friction: Ratio of frictional force to normal force (μ = f/N)
- Centripetal Force: Net force directed toward centre in circular motion
Quick Revision
- F = ma = dp/dt; valid in inertial frames only
- Impulse = FΔt = change in momentum
- Action and reaction are equal, opposite, and act on different bodies
- f_s ≤ μ_s N, f_k = μ_k N, μ_k < μ_s
- Angle of repose: tan θ = μ_s
- Centripetal force: F = mv²/r; Banking: tan θ = v²/rg
- Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂