Last Minute Lecture

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 ...

Motion in Two and Three Dimensions Explained | Chapter 3 of University Physics Chapter 3 of University Physics advances kinematics into the realm of two- and three-dimensional motion. Using vectors to describe position, velocity, and acceleration, this chapter lays the mathematical foundation for understanding parabolic trajectories, circular motion, and the critical role of frames of reference in real-world physics. Position, Displacement, and Velocity Vectors To describe motion in space, we use the position vector r⃗ , which specifies an object’s location relative to an origin. Displacement ( Δr⃗ ) is the change in position, and is itself a vector with both magnitude and direction. Average velocity is displacement divided by time, while instantaneous velocity is the derivative of position with respect to time—always tangent to the path of motion. The speed is simply the magnitude of velocity, regardless of direction. Acceleration in Two and Three Dimensions Accelerati...