# PHYS 121 General Engineering Physics I • 6 Cr.

## Description

First in a three-course survey of physics for science and engineering majors. Course presents fundamental principles of mechanics, including motion, Newton's laws, work, energy, momentum, rotation, and gravity. Conceptual development and problem solving have equal emphasis. Laboratory work presents methods of experimental and analysis (modeling, errors, graphical analysis, etc.) and prepares students for upper-division research. Prerequisite: High School physics or equivalent, and MATH& 151 or permission of instructor.

## Outcomes

After completing this class, students should be able to:

Laboratory Skills
• Use standard laboratory instruments appropriately, based on a sufficient understanding of their function;
• Measure physical quantities in the laboratory with appropriate attention to minimizing possible sources of random and systematic error;
• Make reasonable estimates of the uncertainties associated with each measurement;
• Evaluate a hypothesis in terms of its testability and determine the kind and amount of data required to test it;
• Summarize the properties of a set of data to facilitate analysis, using standard statistics such as mean and standard deviation;
• Determine the uncertainty of a computed quantity that arises from the uncertainties in the measured values of the quantities from which it is computed;
• Analyze an appropriate set of measurements for consistency with a hypothesis, form and justify a conclusion regarding the fit between the data and the hypothesis;
• Recognizes that measurement uncertainty is estimated as an act judgment on the part of the observer and that judgment does not imply arbitrariness.
Communication Skills
• Produce a compact and unambiguous verbal description of an experimental procedure and of the observations/data obtained using it;
• Produce a compact and unambiguous verbal description of a chain of theoretical or experimental reasoning, including clarity regarding assumptions, accuracy regarding logical connections, specificity regarding conclusions, and clarity regarding the scope (and limitations) of applicability.
Kinematics objectives
• Students can distinguish acceleration from velocity in diverse settings, can distinguish accelerated motions from non accelerated motions, recognize that this is a significant distinction, and can correctly determine the direction of acceleration.
• The student will demonstrate competence with verbal, graphical, algebraic and vector algebraic representations of motions as described below.
• Verbal
• Correctly describe the position velocity and acceleration of an object with attention to proper use of "increasing", "decreasing" or "constant" (steady).
• Given a verbal description of the motion the student can correctly deduce the values (if given) or relative magnitudes, and signs for the position velocity and acceleration.
• Graphical
• Given a verbal description or an observation of the motion the student can produce qualitatively correct graphs for the position velocity and acceleration.
• From graphs of the position velocity and acceleration (and appropriate initial conditions) students can describe the motion and the graphs with proper use of slope vs. value and "increasing", "decreasing" or "constant" (steady)
• Students are able to obtain quantitative information from graphs utilizing slope, value, area under the curve, and intersections of graph curves or intersections with the axes.
• Students can produce any two of the position velocity or acceleration graphs from the remaining graph and appropriate initial conditions.
• Algebraic
• Given a verbal description, graph, or an observation of the motion the student can write an appropriate equation for the motion correctly choosing signs and values if this information is available.
• Students can re-arrange or combine equations algebraically before the substitution of values to solve for the desired quantities.
• Vector Algebraic
• Students can represent the position, velocity, relative velocity or acceleration vectorially and decompose the vectors into components where appropriate.
• Students can perform vector arithmetic and find resultant vectors in one and two dimensions.
• Students can solve end of chapter problems involving one or two objects in one or two dimensions. Students will demonstrate the ability to apply representations to this process, including proper use of coordinates, selection of equations, interpretation of implicitly given information, and symbolic (rather than numeric) algebra steps.
• Dynamics
• The student has formed a concept of Newtonian force and distinguishes force from closely related or more primitive concepts of impetus, momentum, velocity, and "the force of inertia" (which is not a Newtonian force at all).
• For small numbers of interacting objects, the student can identify the forces of interaction, properly assign them to the system that experiences the force, and identify the object that makes the force.
• The student can distinguish between inertial and non-inertial reference frames, and understands that Newton's Second Law only applies to the former.
• The student is able to describe an operational (and non circular) method of defining mass and force using Newton's Second Law.
• The student correctly identifies the net force (rather that any particular force) as the cause of the acceleration (rather than causing velocity).
• The student can apply vector concepts to describe the effects of competing forces acting on a system.
• The student can correctly determine the net vector force acting on a system when three or more forces act, and can express the net force in both common vector forms.
• The student can apply Newton's Second law to a body in the context of end of chapter problems, utilizing Free Body Diagrams, appropriate coordinates, and any required Kinematics equations.
• The student can recognize action reaction pairs among the forces acting in common situations, and distinguishes these from "cause/effect" pairs of forces.
• The student Distinguishes weight from mass, and distinguishes weight from the supporting force supplied to objects by objects in the environment.
• The student can determine from the problem whether to go from dynamics to kinematics or the other way.
• Friction and Circular Motion
• The student has a conceptual understanding of frictional forces as demonstrated by the ability to distinguishes and properly identify cases of static friction from cases of kinetic friction, the ability to predict the behavior of objects that are acted on by frictional forces, and by correctly distinguishing the physical meanings of the terms found in the expressions used to describe friction.
• The student can apply their understanding of frictional forces to the solution of end of chapter problems involving a small number of objects.
• The student has a conceptual understanding of the dynamics of circular motion as demonstrated by the ability to properly identify the centripetal force and centripetal acceleration in a variety of settings*, the ability to predict the behavior of objects that are acted on by centripetal forces when these forces are removed, and by the absence of the appearance of incorrect centrifugal forces and centrifugal accelerations in their subsequent coursework (through the end of the quarter).*Particularly cases where the centripetal force is the net of several forces acting on the object.
• Students can apply their understanding of the dynamics of circular motion to the solution of end of chapter problems.
Conservation
• The student is able to make intellectually fruitful choices of system and clearly identify what elements are contained in the system and what parts of the problem are in the environment.
• The student can describe general principles that guide the physicist in making the choices above for each of the three potentially conserved quantities addressed in the course: energy, linear momentum and angular momentum.
• The student can apply the non-conservation test (see each section below) for each of the three potentially conserved quantities at the system boundary to detect whether the quantity is conserved, gained, or lost, by the system.
• The student can make appropriate choices of states to compare that will produce an equation that is useful in analyzing the problem.
• The student can apply conservation methods to solve for a variable that links to an associated dynamics problem and the reverse. (The student can integrate these two methods in a single compound problem).
Energy objectives
• The student can compute the work done by a force, applies the definition of work correctly to this question in a variety of settings, and can use the concept of Work as the test applied to the system boundary to check for conservation of energy in the system.
• The student identifies work as a scalar quantity and treats it as a scalar in solving problems.
• The student can identify conservative forces, demonstrate that these forces meet the definition of a conservative force, and define a potential energy function for such forces.
• The student can compute dot products between vectors, can represent this computation in both common forms, can describe how the dot product acts as a projection operator, and can apply the dot product to the calculation of the work done by a force.
• The student can derive the work energy theorem for the one dimensional case, compute the translational and rotational kinetic energy of an object or system of objects, and describes the work energy theorem as the embodiment of the program outlined above for the conservation of energy.
• The student can compute the total energy for a state of a system typically found in end of chapter problems, including translational and rotational kinetic energies, gravitational potential energy, and spring potential energy.
Momentum objectives
• The student can compute the impulse of a force, applies the definition of impulse correctly to this question in a variety of settings, and can use the concept of impulse as the test applied to the system boundary to check for conservation of momentum in the system.
• The student identifies impulse as a vector quantity and treats it as a vector in solving problems.
• The student can derive the impulse momentum theorem for the one dimensional case, compute the momentum of an object or system of objects, and describes the impulse momentum theorem as the embodiment of the program outlined above for the conservation of momentum .
• the student can demonstrate the ability to solve momentum conservation problems in one and two dimensions.
• The student can distinguish elastic from inelastic collisions, apply appropriate conservation principles to the appropriate problems, and describe qualitatively the implications of the general solution to the two body elastic collision problem, and solve problems involving this solution.
Angular Momentum
• The student can compute the angular momentum for a rotating object or for a translating object when viewed from a particular axis.
• The student can compute the angular impulse of a torque, applies the definition of angular impulse correctly to this question in a variety of settings, and can use the concept of angular impulse as the test applied to the system boundary to check for conservation of angular momentum in the system.
• The student can solve end-of chapter problems involving conservation of angular momentum.
• The student can compute cross products between vectors, can represent this computation in both common forms, can describe the resulting vector in relation to the two input vectors in three dimensions, and can apply the cross product to the calculation of angular momentum (and torque - see below).
• The student can correctly apply the definitions of torque, angular impulse and angular momentum in the analysis of precession (the so-called Gyroscopic Effect).
Rotational Dynamics
• Students can compute the torque of a force using each of the three principle methods: The cross product, Fperp x R, or as Rperp x F (moment arm), and determine the direction of the torque using the Right Hand Rule.
• Students can demonstrate a conceptual understanding of torque as the measure of how effective a force is at producing angular acceleration and consequently make a distinction between torque and force through short written responses concerning observations. Students also employ appropriate methods to visualize the effects of torque on a system that use twisting motions rather than following the direction of the torque vector.
• For small numbers of interacting objects, the student can identify the torques of interaction, properly assign them to the system that experiences the torque, identify the object that makes the torque.
• Given an object or system acted upon by several forces, the student can compute the net torque about any specified axis, and can make appropriate choices of axes to solve static equilibrium problems.
• The student can apply Newton's Second law for rotations to a body in the context of end of chapter problems, utilizing Free Body Diagrams, appropriate coordinates, and any required Kinematics equations.
• The student can combine rotational Dynamics and the translational Dynamics previously described to systems involving two or three objects in the context of end-of-chapter problems.