ECE 105: Classical Mechanics

Sources and References

Equivalent UW courses — PHYS 121 (Mechanics), PHYS 111 (Physics 1) Primary textbook — Robert Hawkes, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter Williams, Physics for Scientists and Engineers: An Interactive Approach, 2nd ed., Nelson, 2018. Supplementary references — Hugh D. Young and Roger A. Freedman, University Physics with Modern Physics, 15th ed., Pearson, 2019; Halliday, Resnick, and Walker, Fundamentals of Physics, 11th ed., Wiley, 2018.

Equivalent UW Courses

ECE 105 is the engineering version of first-term university mechanics; its closest Math/Phys equivalent is PHYS 121 (Mechanics), with PHYS 111 (Physics 1) being the lighter life-sciences variant. All three cover kinematics, Newton’s laws, work and energy, momentum, rotation, and simple harmonic motion. PHYS 121 tends to push the calculus a little harder and includes slightly more formal treatment of conservation laws, while PHYS 111 softens the mathematics. ECE 105 sits roughly between these — full calculus throughout but with a problem-solving emphasis tuned to engineering applications.

What This Course Adds Beyond the Equivalents

Compared with PHYS 121, ECE 105 spends more time on problem-solving strategy and on the kinds of combined-topic problems that show up in engineering practice (e.g., a rotating rigid body attached to a spring, or rolling-plus-friction scenarios). Rotational dynamics and rolling motion get careful attention because they are less familiar from high school. What ECE 105 omits compared with a full PHYS 121/PHYS 122 sequence is most of wave mechanics beyond the SHM section, any significant discussion of thermodynamics, and the laboratory component — physics lab work is deferred to later engineering courses rather than being integrated here.

Topic Summary

Kinematics in 1D and Free Fall

Position, velocity, and acceleration as time derivatives; constant-acceleration equations; free fall with \( g \approx 9.81\ \text{m/s}^2 \). Foundation for everything else because forces ultimately produce accelerations.

Kinematics in 2D, Circular Motion, and Relative Motion

Vector decomposition of motion, projectile trajectories, uniform circular motion with centripetal acceleration \( a_c = v^2/r \), and Galilean velocity addition between reference frames. Shows that motion problems become vector problems in more than one dimension.

Forces: Normal, Tension, Friction

Newton’s three laws, free-body diagrams, and the common contact forces. Static and kinetic friction are modelled as \( f \le \mu_s N \) and \( f = \mu_k N \), and coupled-body problems introduce systems of equations.

Elastic Force and Dynamics of Circular Motion

Hooke’s law \( F = -kx \) and its role as a linear restoring force; centripetal force supplied by tension, friction, or gravity. Prepares the way for SHM at the end of the course.

Work, Energy, and Conservation of Energy

Work as \( W = \int \vec{F}\cdot d\vec{r} \), kinetic energy, potential energy for gravity and springs, and the work-energy theorem. Conservation of mechanical energy gives a powerful shortcut that avoids solving the full dynamics.

Linear Momentum and Impulse

Momentum \( \vec{p} = m\vec{v} \), impulse as \( \int \vec{F}\, dt \), and conservation of momentum in collisions. Elastic and inelastic collisions are worked in one and two dimensions.

Centre of Mass, Rotational Kinematics, and Moment of Inertia

Centre-of-mass formulas for discrete and continuous distributions; angular position, velocity, and acceleration; rotational kinetic energy and moment of inertia computed by integration for standard shapes. Torque \( \vec{\tau} = \vec{r}\times\vec{F} \) is the rotational analogue of force.

Angular Momentum and Rolling Motion

Conservation of angular momentum \( \vec{L} = I\vec{\omega} \), and rolling-without-slipping constraints linking translational and rotational motion. The classic rolling-cylinder-down-an-incline problem combines energy conservation with moment-of-inertia bookkeeping.

Static Equilibrium

Conditions \( \sum \vec{F} = 0 \) and \( \sum \vec{\tau} = 0 \) for rigid bodies, with applications to ladders, beams, and trusses. A direct bridge to engineering statics.

Simple Harmonic Motion

Mass-spring systems obey

\[ m\ddot{x} + kx = 0 \]

with angular frequency \( \omega = \sqrt{k/m} \); energy oscillates between kinetic and potential. Ideal and physical pendulums are treated as small-angle SHM.