Last Minute Lecture

Physics of Gravitation Explained | Chapter 13 of University Physics Chapter 13 of University Physics unifies Newton’s laws with celestial mechanics to reveal how gravitation governs everything from falling apples to orbiting planets and black holes. In this summary, we explore the universal law of gravitation, weight and gravitational acceleration, potential energy and escape speed, satellite motion, Kepler’s laws, and the physics of extreme objects like black holes. Newton’s Universal Law of Gravitation Every mass attracts every other mass with a force given by: F g = G (m 1 m 2 ) / r² G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²). The force acts along the line connecting the masses and obeys Newton’s Third Law. Superposition lets you sum gravitational forces from multiple bodies. Weight & Acceleration Due to Gravity On or near Earth’s surface, the gravitational force on a mass m is: w = G m E m / R E ² = m g g ≈ 9.80 m/s² but varies slig...

Potential Energy & Conservation Explained | Chapter 7 of University Physics Chapter 7 introduces potential energy as stored energy due to position or configuration and develops the principle of conservation of mechanical energy—an indispensable tool for solving physics problems with elegance and efficiency. Potential Energy Potential energy (U) represents energy stored within a system. Two key forms appear in this chapter: Gravitational Potential Energy For an object of mass m at height y above a reference level: U grav = m g y As the object moves under gravity, its potential energy converts to kinetic energy. The work done by gravity relates to the change in potential: W grav = –ΔU grav When only gravity does work, K + U remains constant. Elastic Potential Energy Springs store energy when displaced by x , following Hooke’s Law ( F = k x ): U el = ½ k x² Work done by or against a spring between positions x₁ and x₂ is: W = ½ k x₂² – ½ k x₁² In pure spr...