Engineering Dynamics course & examples, 15+hours mechanical

This lecture covers sign conventions for rectilinear motion, defines velocity and acceleration directions, and derives a displacement–velocity–acceleration relation by eliminating time, with tangent slopes on the displacement–time curve.

Relate velocity to the slope of the displacement-time curve at any point. Compute displacement as the area under the velocity-time curve between two times.

Demonstrate acceleration as a function of time using dv/dt and show that the area under the acceleration-time curve equals the change in velocity from t1 to t2.

Explore how velocity as a function of displacement is derived from the S-curve, using tangent and normal lines to relate velocity and acceleration at points along the curve.

Derive displacement as a function of time by integrating acceleration to obtain velocity, then integrating velocity to get displacement, while exploring how s(t) and its derivatives relate in kinetics.

Explore how acceleration as a function of time, velocity, and displacement is analyzed through integration to obtain s(t) and v(t).

Explore plane curvilinear motion in two dimensions, contrasting it with rectilinear motion and velocity. See how displacement delta r and average velocity describe motion along a path in engineering.

Explore average velocity and average speed in curvilinear motion, defining instantaneous velocity as the time derivative of the position vector and its magnitude as speed, tangent to the path.

Explain instantaneous acceleration in plane curvilinear motion by using velocity vectors tangent to the curve and plotting them from a common origin in a hodograph.

Explore rectangular coordinates to describe motion using velocity and acceleration vectors, with x and y components and time derivatives, and determine magnitudes and curve slopes from instantaneous velocity.

Compute magnitudes of velocity and acceleration from their x and y components using triangle methods. Relate instantaneous velocity to the curve’s tangent and derive the slope from vy and vx.

Describe curvilinear motion using normal and tangential coordinates along and normal to the particle's path, with T aligned to velocity and N toward the center of curvature.

Introduce velocity in normal and tangential coordinates using unit vectors, relate ds to the radius of curvature, and express instantaneous velocity in the tangent and normal directions.

Explore acceleration in rectangular coordinates as the time derivative of velocity, decomposing into a_T (change in speed) and a_N (change in direction) along the unit tangent.

Analyze acceleration in normal and tangential coordinates along a curved path, deriving the tangential and normal components from velocity, unit vectors ET and EN, and radius of curvature.

Differentiate the polar position vector to obtain radial and tangential velocity components along e_r and e_theta, then combine them to express the total velocity.

Differentiate velocity to derive acceleration in polar coordinates, separating it into radial and tangential components a_r and a_theta, with circular motion and curvature context.

Explore space curvilinear motion in three dimensions, deriving velocity and acceleration in rectangular and cylindrical (polar) coordinates, and learn coordinate transformations to express motion components across frames.

Explore a chapter two kinematics example of a rocket in a vertical tracking radar, computing velocity, radius, and theta dot using gravity and vector components.

examine the kinematics of a power screw, deriving the velocity and acceleration of the ball center as it moves along a helical path on a cylinder.

Chapter 2 presents a relative-velocity problem: observers in a moving frame determine plane B’s true velocity using vector addition, components, and trigonometry to resolve its magnitude and direction.

Explore the kinetics of particles by linking unbalanced forces to motion through Newton's second law, work and energy, and impulse–momentum methods, with integrated statics and kinematics foundations.

Apply Newton's second law by showing how force relates to acceleration and inertia, verify F proportional to m a, and derive the vector form F = m a.

Apply the equation of motion by summing vector forces equal to mass times acceleration, using free body diagrams to solve constrained and unconstrained motion.

Explore curvilinear motion and its analysis in rectangular and polar coordinates. Learn to decompose acceleration and force into coordinate components and compute total force magnitude via vector addition.

Explore the work-energy principle by linking net force and acceleration to velocity and displacement, using F·dr and the spring example F = kx.

The work–energy principle and kinetic energy are explained, defining kinetic energy and the work–energy theorem W = ΔK, and showing how forces cause velocity changes without explicit acceleration.

Explore power as the time rate of doing work, distinguish energy delivery by machines, and analyze mechanical and overall efficiency with units like watts and horsepower.

This lecture defines potential energy as the work done against gravity and spring forces to raise a mass m by height h, expressed as m g h, to simplify analysis.

Introduce potential energies in the work-energy equation, including elastic spring work, and show two approaches: isolate the particle versus isolate the system, focusing on endpoint positions and delta potential energy.

Explore conservative force fields where work depends only on end positions, not path, and derive forces from a potential function. Learn how gradients relate to force and path independence.

Explore how impulse and momentum arise from time-based equations of motion, linking velocity change to work and energy, and apply them to impact problems.

Explore linear impulse and linear momentum in three-dimensional curvilinear motion; derive p = m v, and show sum of forces equals time rate of change of momentum in component form.

Apply the impulse–momentum principle to relate momentum changes to the time integral of all forces, using vector components and free-body diagrams for time-varying forces.

Explore how linear momentum is conserved in multiple directions, and how impulse and equal-and-opposite forces govern interacting bodies, using free-body diagrams, with angular impulse and angular momentum explored.

Define angular momentum as the cross product of position and linear momentum about the origin, with magnitude |L| = r p sin theta and direction normal to the plane.

Relate the moment of forces to angular momentum using the cross product and the time rate of change. Apply the angular impulse momentum principle to particles and rigid-body systems.

Explore the angular impulse and impulse-momentum principle, showing how the total angular impulse equals the change in angular momentum, via the vector cross product and component integration.

Explore angular momentum in plane motion, applying moments about a normal axis and angular impulse between points, and note conservation and the role of free body diagrams.

A 75 kg man on a scale in an accelerating elevator shows how acceleration affects scale readings, with 3 seconds of motion yielding 1.25 m/s^2 and a 84.6 kg reading.

This example analyzes a sliding block at speed v past point a without losing contact; loss occurs when the normal force vanishes, shown via a free-body diagram and curvature constraints.

Apply conservation of energy to an engineering dynamics inclined plane problem, analyzing work by weight and friction and the resulting kinetic energy change from 4 m/s to 3.15 m/s.

Using conservation of energy in a frictionless vertical slider with weight and spring, determine the velocity at position B as 283 inches per second.

Explore chapter 3 quiz problems: coupler force of 0.2 lb, train acceleration, chain on rough surface with mu_k friction, and a 10 lb/in spring linking displacement, velocity, and acceleration.

Compute the kinetic energy of a system by splitting it into the center-of-mass translation and the internal motion of particles about the center of mass.

This lecture introduces impulse and momentum, defining linear momentum as the system mass times the center-of-mass velocity, and shows the time rate of change equals external forces under constant mass.

Explore angular momentum of a mass about the origin, center of mass, and an arbitrary point P with acceleration a, and show dL/dt equals external moments about a fixed point.

Explore angular momentum about the origin and about the center of mass, distinguishing absolute and relative angular momentum and their governing equations for all rigid or non-rigid systems.

Derive the angular momentum about an arbitrary point p and relate it to the center of mass momentum, including the system's linear momentum and external-force moments.

Explain the conservation of energy and momentum in conservative systems, noting that internal friction and inelastic components dissipate energy, while no work by external forces keeps mechanical energy constant.

Analyze the plane kinematics of a four-particle rigid system to compute the center of mass, particle velocities, and the system’s total kinetic energy using cross-product relations.

a three-ball frame of negligible mass under a sudden force, deriving the center of mass acceleration from the net force and the angular acceleration from torque and angular momentum concepts.

Analyzing a 20 kg shell fired at 100 m/s that explodes into three fragments mid-flight, this dynamics example uses projectile motion and momentum conservation to determine fragment c's velocity.

Examine the rotation of a rigid body in a plane, defining angular position theta, angular velocity omega, and angular acceleration alpha, and apply rectilinear motion analogies to planar kinematics.

Explain rotation about a fixed axis for a rigid body, relating angular velocity and acceleration to linear velocity via cross products, and using normal and tangent coordinates.

Explore relative velocity in rigid body plane motion by treating motion as translation plus rotation about a reference point, with v_A = v_B + omega cross r_A/B.

Analyze the kinematics of a flywheel under a variable counterclockwise torque, compute angular velocity and displacement, determine reversal time, and total revolutions over 14 seconds.

Examine the plane motion of a rigid triangle under rotation, derive velocity and acceleration relations for points A, B, and C, and determine angular velocity and acceleration.

Compute the angular velocities CB and AB via the relative velocity equation and cross products, yielding omega_CB and omega_AB in rad/s for a kinematics example.

an velocity analysis of a linkage shows a and b moving tangentially on circular paths, with centers at the intersection of velocity normals, and bc angular velocity computed from velocities.

Solve section 5 quiz problems on relative velocity and angular velocity for rotating bars and wheels, applying velocity addition, angle relations, and rolling without slipping.

Explore the moment of inertia as a tensor, relate torque to angular acceleration around a rotational axis, and derive I for plane motion.

Calculate the moment of inertia of a three-dimensional body about an arbitrary axis by integrating dm = rho dV and using I = ∫ r^2 dm.

The lecture explains rigid-body rotation about a fixed axis, derives plane-motion equations and free body/kinetic diagrams, and identifies a point q where the resultant force passes and moments vanish.

Compute the kinetic energy of a rigid body in plane motion from center-of-mass motion and angular velocity, yielding T = 1/2 I ω^2 via the moment of inertia.

Compute angular momentum about the center of mass of a rigid body by integrating r cross (omega cross r) and derive L = I omega, simplifying when inertia is symmetric.

Analyze a 150 kg vertical bar with midspan center of mass, derive angular acceleration versus theta, and compute forces in the B-D link via free-body and moment summations.

Solve a moment-of-inertia and torque problem for a hoisting drum system lifting a concrete block, deriving angular acceleration and block acceleration from a free-body diagram and system equations.

Analyze a rolling wheel driven by a 100 N force, applying work-energy and power concepts to relate torque, angular velocity, and kinetic energy, noting friction does no work without slipping.

Explore a planar rigid-body mechanism with two wheels and a spring, applying conservation of energy to compute velocities and the spring's maximum deformation, while neglecting friction losses.

Analyze a 7.5 kg pendulum with center of mass at G and radius of gyration 295 mm, deriving normal and tangential forces and angular acceleration via moment equations.

Solve section 6 quiz problems on tipping, calculating maximum applied force to prevent crate overturning, center of mass considerations on an incline, and normal forces with friction.