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Physics Fundamentals: Scalars, Vectors, Momentum

Jun 10, 2025

Overview

This lecture introduces the foundational physics concepts of scalars, vectors, units, momentum, and impulse, including their definitions, calculations, and practical examples.

Scalars, Vectors, and Units

  • Scalars have magnitude only (amount), e.g., speed, time, mass, distance, energy.
  • Vectors have both magnitude and direction, e.g., velocity, acceleration, force, momentum.
  • Vector notation uses an arrow over the symbol and direction in square brackets (e.g., v [East]).
  • Positive directions: North, East, forward, up, right; negative: South, West, backward, down, left.
  • SI units used in physics: meters (m), seconds (s), kilograms (kg); all others are derived units.
  • Derived units example: force (Newton, N = kg·m/s²), energy (Joule, J = kg·m²/s²), power (Watt, W = kg·m²/s³).
  • Common metric conversions: kilo = 1,000 base units; 1 km/h = 1 m/s ÷ 3.6; 1 hour = 3,600 seconds.

Momentum

  • Momentum (p) = mass (m) × velocity (v); unit: kg·m/s, and it is a vector.
  • Direction of momentum matches direction of velocity.
  • Large momentum can come from large mass at low speed or small mass at high speed.
  • Example: Elephant (1,800 kg at 0.21 m/s) and bullet (0.050 kg at 2,000 m/s) have similar momentum.

Impulse

  • Impulse = Force (F) × time interval (Δt); unit: Newton-seconds (N·s).
  • Δ (Delta) means "change in" (e.g., Δv = change in velocity).
  • Impulse equals the change in momentum: FΔt = mΔv.
  • Newton-seconds (N·s) and kg·m/s are interchangeable units.
  • Example: Tennis ball receives 0.425 N·s impulse in 0.025 s → Force = 17 N.

Applications and Examples

  • Airbags increase collision time (Δt) to reduce force on the head, since FΔt = mΔv and mΔv is constant.
  • Collision example: Conservation of momentum used to find post-collision velocity of objects.
  • In a two-puck collision, momentum change of one puck is equal and opposite to the other; use p = m × v for calculations.

Key Terms & Definitions

  • Scalar — a quantity with magnitude only.
  • Vector — a quantity with magnitude and direction.
  • Momentum (p) — the product of mass and velocity; a vector.
  • Impulse — the product of force and the time interval during which the force acts.
  • Derived Unit — a unit made up of base SI units, e.g., Newton, Joule, Watt.
  • Δ (Delta) — symbol indicating change in a quantity.

Action Items / Next Steps

  • Practice converting between units (km/h ↔ m/s, hours ↔ seconds).
  • Solve momentum and impulse problems using provided formulas.
  • Review SI base and derived units.