Mechanics

Upon completion of the course, successful students will be able to:

• apply dimensional analysis to deduce the form of an equation and to check an equation for dimensional consistency;
• use vector components, unit vector notation, and vector algebra to solve problems that involve vector quantities related to forces and motion in 2D and 3D;
• use the dot product or cross product to calculate physical quantities such as: work, power, torque, and angular momentum;
• use derivatives and antiderivatives to solve problems involving topics and concepts such as: kinematics, work, power, force, potential energy, torque, impulse, and PV diagrams;
• interpret graphs of position, velocity, and acceleration as functions of time;
• solve 1D, 2D, and 3D kinematics problems with constant and time-dependant accelerations;
• analyze problems that involve relative motion in 1D and 2D;
• apply Newton’s laws to solve problems in 1D and 2D that involve constant and time-dependant forces acting on objects;
• distinguish between inertial and non-inertial reference frames;
• solve problems that involve objects undergoing circular motion;
• calculate the work done and power expended by a force acting on a moving body;
• apply the law of conservation of energy and/or the work-energy theorem to solve problems that involve forces acting on objects;
• apply the law of conservation of momentum to solve problems that involve collisions or explosions in 1D and 2D;
• define and determine the center of mass for a system of particles and solve problems that involve forces acting on the system;
• use the parallel axis theorem to determine the moment of inertia of a rigid body about a specified axis;
• solve problems that involve forces and torques acting on objects that can translate and rotate (for example, rolling objects or massive pulleys) using the rotational analogue of Newton’s second law and/or conservation of energy;
• apply the law of conservation of angular momentum to solve problems that involve rotating bodies and inelastic collisions;
• solve problems that involve simple harmonic motion such as: mass-spring systems, simple pendulums, and physical pendulums;
• solve problems that involve heat transfer and thermal equilibrium;
• calculate the internal energy of a system given the state variables;
• apply the first law of thermodynamics to systems undergoing a change of state variables;
• distinguish between the following thermodynamic processes, and sketch them on a PV diagram: isobaric, isochoric, isothermal, and adiabatic;
• calculate the work done on or by a system during a single thermodynamic process and/or a cyclical process;
• explain how heat engines produce mechanical work, and calculate the work done by and the efficiency of a heat engine;
• state and discuss the precision and accuracy of measurements;
• determine the uncertainty on a quantity calculated from measured values by propagating uncertainty through a calculation;
• present data using computer generated plots and determine physical quantities using linear and non-linear regressions;
• discuss the outcome of an experiment in order to provide appropriate context for the results;
• communicate details of an experiment (for example, the objective, data, calculations, discussion, and conclusion) in a written report.