Fundamentals of Dynamics for Engineering Students

Explore position, displacement, velocity, and acceleration as functions of time; derive velocity and acceleration from position; and solve for average velocity, average speed, and instantaneous acceleration in a straight-line motion.

Learn how plots of acceleration, velocity, and position relate under constant acceleration, and how velocity is the slope of position while position is the area under the velocity-time curve.

Study motion along a curved line in three dimensions using a position vector r and velocity and acceleration components in I, J, K, and compute the acceleration magnitude.

Apply the displacement equation to projectile motion by separating horizontal and vertical components, using x: v0x t with no acceleration and y: y0 + v0y t − 1/2 g t^2.

Explore normal and tangential acceleration through a curved road example, calculating tangential acceleration from Δv/Δt and normal acceleration from v^2/r, and determining the acceleration magnitude.

Compute relative velocity in one dimension for two moving vehicles, using v_B relative to A equals v_B minus v_A, and extend to two dimensions with position vectors and relative acceleration.

Explore relative motion in two dimensions by adding A and B to get A relative to B; use a two-boat example and the cosine rule to find magnitude and direction.

Explore kinetics by introducing mass, forces, and free body diagrams, and apply Newton's second law, work and energy, and impulse and momentum to solve dynamics problems.

Apply Newton's second law to a kinetics problem with a free-body diagram of 100 kg crate pulled by 1500 N at 30 degrees, computing gravity, normal force, friction, and acceleration.

Apply Newton's second law in cylindrical coordinates to a three-dimensional particle, summing forces in radial, theta, and z directions and computing accelerations r'', (r theta'' + 2 r' theta'), and z''.

Explore the principle of work and energy as a tool to solve kinetics problems, linking kinetic energy to work and analyzing positive/negative work from gravity, springs, and constant forces.

Apply the principle of work and energy to a mass-spring-bucket system, calculating the marble’s exit velocity from the bucket using the spring work and gravity, with explicit values and assumptions.

Understand the energy conservation principle: in an isolated system, kinetic and potential energies sum constant, with gravitational and elastic potentials, as energy transfers between them, illustrated by a bouncing ball.

Explore how a roller coaster from 20 meters high converts potential energy into kinetic energy at point b, illustrating energy conservation for a 300 kg mass while ignoring friction.

Explore the impulse–momentum principle and its difference from work and energy, defining impulse as force applied over time and momentum change from V1 to V2 under constant or variable forces.