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 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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.