Last Minute Lecture

Equilibrium, Elasticity & Material Properties Explained | Chapter 11 of University Physics Chapter 11 examines how rigid bodies remain in balance under forces and how materials deform under stress. You’ll learn the conditions for static equilibrium, locate the center of gravity, construct free-body diagrams, and explore stress-strain behavior including Young’s, shear, and bulk moduli, as well as elastic versus plastic deformation. Conditions for Rigid-Body Equilibrium For a rigid body to be in equilibrium (static or dynamic), two requirements must hold: ΣF = 0 — No net external force (no translation) Στ = 0 — No net external torque about any axis (no rotation) These ensure the object remains at rest or moves with constant velocity without spinning. Center of Gravity & Stability The center of gravity is the point where an object’s weight can be assumed to act. Under uniform gravity, it coincides with the center of mass. Locating this point is crucial when ca...

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...

Applying Newton’s Laws – Force & Motion Explained | Chapter 5 of University Physics Chapter 5 applies Newton’s laws to real-world scenarios, guiding you through equilibrium, dynamics, friction, circular motion, and the fundamental forces that govern interactions. Using free-body diagrams and vector components, you’ll learn systematic strategies to solve both static and accelerated systems. Watch the full video summary here for step-by-step problem-solving examples. Equilibrium of Particles Under Newton’s First Law, systems in equilibrium have zero net force and zero acceleration. To solve equilibrium problems—such as hanging masses, objects on inclined planes, or ropes under tension—follow these steps: Draw a free-body diagram isolating the particle. Identify and label all forces (weight, tension, normal). Resolve forces into components and set ΣF x = 0, ΣF y = 0. Solve algebraically for the unknown forces. Dynamics: Non-Equilibrium Systems When forces ...