Aspirant Academy

Science and Technology

Motion, Laws of Motion and Gravitation

Physics: Motion, Work/Power/Energy, Gravitation, Light, Heat, Electricity, Magnetism, Sound, EM Waves, Medical Diagnostics, Nuclear Fission/Fusion, Radiation Safety

Paper II · Unit 2 Section 3 of 13 0 PYQs 31 min
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Motion, Laws of Motion and Gravitation

2.1 Kinematics — Equations of Motion

For uniform acceleration (a):

  • v = u + at (velocity after time t)
  • s = ut + ½at² (displacement)
  • v² = u² − 2as

Scalar vs. Vector: Scalars have magnitude only (speed, distance, mass, energy). Vectors have magnitude and direction (velocity, displacement, force, acceleration, momentum).

Circular Motion: A body in uniform circular motion has constant speed but changing direction — thus has centripetal acceleration a = v²/r directed toward the centre. Centripetal force = mv²/r.

2.2 Newton's Laws of Motion

Law Statement Application
First (Law of Inertia) Body remains in rest or uniform motion unless external force acts Seatbelts, headrests in cars
Second F = ma; rate of change of momentum = net force Rocket propulsion, braking distance
Third Every action has equal and opposite reaction Gun recoil, swimming, rocket engines

Momentum (p = mv): conserved in absence of external forces.

Impulse = F·t = change in momentum. This explains why airbags save lives — they increase collision time, which reduces the force exerted on the body.

2.3 Work, Power, and Energy

  • Work (W) = F·s·cosθ (joules). If force is perpendicular to displacement, W = 0.
  • Kinetic Energy (KE) = ½mv²
  • Potential Energy (PE) = mgh (gravitational) = ½kx² (spring)
  • Power (P) = W/t = Fv (watts). 1 horsepower (HP) = 746 watts.
  • 1 kWh = 3.6 MJ (SI unit of electrical energy = "unit" on electricity bill)

Efficiency = (Useful output energy / Input energy) × 100%

2.4 Gravitation

Newton's Universal Law of Gravitation (1687): F = Gm₁m₂/r²
where G = 6.674 × 10⁻¹¹ N·m²/kg² (Universal Gravitational Constant, measured by Cavendish 1798).

Key values:

  • Acceleration due to gravity (g): 9.8 m/s² at Earth's surface; decreases with altitude; less at equator than poles (Earth is flattened at poles — closer to centre at poles).
  • Escape velocity: √(2GM/R); for Earth = 11.2 km/s; Moon = 2.4 km/s (reason Moon has no atmosphere — gas molecules exceed escape velocity); Sun = 617 km/s.
  • Orbital velocity (circular orbit at surface) = √(GM/R) = 7.9 km/s for Earth.

Kepler's Laws (1609–1619):

  1. Elliptical Orbits — planets orbit the Sun in ellipses with the Sun at one focus.
  2. Equal Areas — line joining Sun to planet sweeps equal areas in equal times (implies planets move faster when closer to Sun).
  3. T² ∝ r³ — period² proportional to semi-major axis³ (allows calculation of planetary periods).