Engineering Mechanics: Dynamics (EN PH 131) lessons and practice

Model rectilinear, curvilinear, relative, polar-coordinate, and constrained motion.

Draw free-body and kinetic diagrams, apply Newton’s second law, and analyze tangential–normal and polar components.

Connect force, displacement, kinetic energy, potential energy, power, and efficiency.

Analyze force pulses, collisions, particle systems, angular momentum, and conservation laws.

Relate translation, fixed-axis rotation, angular motion, and the velocity and acceleration of points on planar rigid bodies.

Describe particle position, displacement, velocity, and acceleration with consistent reference frames and units.

• 1.1 · Define particles, reference frames, coordinates, units, and assumptions (written lesson not published)
• 1.2 · Relate position, path length, and displacement (published written lesson)
• 1.3 · Differentiate position to obtain velocity and acceleration (published written lesson)
• 1.4 · Solve rectilinear motion with constant acceleration (published written lesson)
• 1.5 · Solve rectilinear motion with variable acceleration (published written lesson)

Analyze two-dimensional particle motion using suitable coordinates and relative-motion relationships.

• 2.1 · Analyze particle motion in Cartesian components (published written lesson)
• 2.2 · Model projectile motion under uniform gravity (published written lesson)
• 2.3 · Use normal and tangential components along a curved path (published written lesson)
• 2.4 · Use radial and transverse components for planar motion (published written lesson)
• 2.5 · Relate positions, velocities, and accelerations between translating frames (published written lesson)

Create kinetic diagrams and apply Newton’s second law to particle motion.

• 3.1 · Draw consistent free-body and kinetic diagrams (published written lesson)
• 3.2 · Apply Newton’s second law in Cartesian components (published written lesson)
• 3.3 · Apply force–acceleration equations in normal and tangential coordinates (published written lesson)
• 3.4 · Apply force–acceleration equations in radial and transverse coordinates (published written lesson)
• 3.5 · Analyze constrained and connected particle systems (written lesson not published)

Apply universal gravitation and central-force ideas to introductory orbital motion.

• 4.1 · Apply Newton’s law of universal gravitation (published written lesson)
• 4.2 · Relate gravitational force, field strength, mass, and distance (published written lesson)
• 4.3 · Analyze uniform circular orbits (published written lesson)
• 4.4 · Relate kinetic, potential, and total energy in an orbit (published written lesson)
• 4.5 · Use angular momentum in introductory central-force motion (written lesson not published)

Use work–energy methods to relate forces, displacement, speed, and power.

• 5.1 · Calculate work done by constant and variable forces (published written lesson)
• 5.2 · Apply the particle work–energy principle (published written lesson)
• 5.3 · Use gravitational and elastic potential energy (written lesson not published)
• 5.4 · Apply conservation of mechanical energy with nonconservative work (written lesson not published)
• 5.5 · Relate force, velocity, power, and efficiency (written lesson not published)

Use linear impulse–momentum and conservation laws for particles and short-duration interactions.

• 6.1 · Calculate particle linear momentum (written lesson not published)
• 6.2 · Apply the linear impulse–momentum equation (written lesson not published)
• 6.3 · Apply conservation of linear momentum to a particle system (written lesson not published)
• 6.4 · Analyze direct central impact with restitution (written lesson not published)
• 6.5 · Analyze introductory oblique impact (written lesson not published)

Extend force, momentum, and energy methods to systems of particles and their mass centres.

• 7.1 · Locate the centre of mass of a particle system (written lesson not published)
• 7.2 · Relate external force to mass-centre acceleration (written lesson not published)
• 7.3 · Apply work–energy to a system of particles (written lesson not published)
• 7.4 · Apply impulse–momentum to a system of particles (written lesson not published)
• 7.5 · Distinguish internal and external forces in system balances (published written lesson)

Relate moments, angular impulse, and angular momentum for particles and particle systems.

• 8.1 · Calculate particle angular momentum about a point (published written lesson)
• 8.2 · Relate moment to the rate of angular momentum (published written lesson)
• 8.3 · Apply angular impulse–momentum (published written lesson)
• 8.4 · Apply conservation of angular momentum (published written lesson)
• 8.5 · Analyze angular momentum for a system of particles (published written lesson)

Introduce planar rigid-body kinematics and kinetics without extending into advanced three-dimensional dynamics or vibrations.

• 9.1 · Distinguish translation and rotation about a fixed axis (published written lesson)
• 9.2 · Relate angular position, velocity, and acceleration (published written lesson)
• 9.3 · Relate velocities of points on a planar rigid body (published written lesson)
• 9.4 · Relate accelerations of points on a planar rigid body (published written lesson)
• 9.5 · Apply introductory planar rigid-body equations of motion (published written lesson)

University of Alberta

A later course that extends into rigid-body motion, impact, energy and momentum methods, and mechanical vibrations.

University of Calgary

Overlaps in particle and planar rigid-body kinematics and kinetics, work–energy, and impulse–momentum, then introduces three-dimensional rigid-body dynamics.

Concordia University

Overlaps in particle and rigid-body kinematics, force–acceleration, work–energy, impulse–momentum, and systems; it also introduces vibrations.

University of Waterloo

Related Waterloo variants cover particle motion, energy and momentum, systems of particles, planar rigid bodies, and—in some versions—vibrations.

UBC Vancouver

Focuses on systems of particles, planar rigid-body kinematics and kinetics, energy and momentum, and rotating coordinates.

University of Toronto

Overlaps in two-dimensional particle and rigid-body motion, force, work, momentum, energy, planetary motion, and simple harmonic motion.

University of Ottawa

Overlaps in Newtonian mechanics, particle and rigid-body motion, moving coordinates, impulse–momentum, and work–energy.

A car slows from 24 m/s to 8 m/s in 4.0 s with constant acceleration. Find the acceleration and displacement.

Worked method: a = (8 − 24)/4 = −4.0 m/s². Using average velocity, Δx = [(24 + 8)/2](4) = 64 m. The negative acceleration is opposite the chosen positive direction.

A 5.0 kg slider starts from rest and moves down through a vertical drop of 3.0 m on a smooth track. Find its speed.

Worked method: Conservation of mechanical energy gives mgh = ½mv², so v = √(2gh) = √[2(9.81)(3.0)] = 7.67 m/s. Mass cancels, as expected for a smooth gravitational descent.

A 2.0 kg cart initially moves at 3.0 m/s to the right. A net 10 N force acts to the left for 0.50 s. Find the final velocity.

Worked method: Choose right as positive. m(v₂ − v₁) = FΔt gives 2(v₂ − 3) = −10(0.50), so v₂ = 0.50 m/s to the right.

A particle moves in a circle of radius 2.0 m at 6.0 m/s. Find its normal acceleration.

A 0.40 kg ball moving at 12 m/s is brought to rest. Find the impulse on the ball.