• | Apply conservation of energy to the flow of a fluid in a pipe to develop Bernoulli's equation. |
• | Apply the equipartition theorem to a gas problem. |
• | Apply the ideal gas equation to an ideal gas problem. |
• | Associate ropes and strings with tension forces that exert a pull. |
• | Calculate an object's linear or angular speed as it rolls without slipping down an inclined plane or a curved track. |
• | Calculate the average power of a wave on a string. |
• | Calculate the center of mass of a collection of individual, point-like objects where each object may have a different mass and position. |
• | Calculate the center of mass of an extended object with a constant linear, area, or volume density. |
• | Calculate the change in a quantity using the final value minus the initial value. |
• | Calculate the change in a spacecraft's kinetic energy as it falls toward or moves away from a celestial object of known mass. |
• | Calculate the fractional change in an object's length, volume, or shape when it is subjected to a given tensile, bulk, or shear stress. |
• | Calculate the magnitude of the vector (cross) product using the definition of the cross product. |
• | Calculate the properties of a standing wave on a string. |
• | Calculate the scalar (dot) product of two vectors using its definition and the component method. |
• | Calculate the velocity of an object in different reference frames. |
• | Calculate the velocity or acceleration by differentiating position given as a function of time. |
• | Categorize the sum of all radial forces and radial components of forces acting on an object in circular motion as the centripetal force. |
• | Choose (or write or match) the equations of rotational kinematics in exact analogy to the equations of one-dimensional accelerated motion. |
• | Choose the correct system boundary in a diagram containing objects that collide or interact via forces. |
• | Cite examples or describe situations in which a force (acting on a group of objects) originates from outside the system boundary. Recognize when forces acting between objects are internal to the system. |
• | Compare the behavior of a traveling wave reflected at a fixed end and at an open end. |
• | Compare the range, maximum height, and elevation angle between two given projectile trajectories or vice versa. |
• | Convert a quantity from one unit of measure to another. |
• | Convert between the number of moles of gas and the mass of the gas. |
• | Convert temperatures between Celsius, Fahrenheit, and Kelvin. |
• | Correctly interpret Newton's second law as a statement of cause (on the right side of the equal sign) and effect (on the left side). |
• | Correctly use either velocity (a vector) or speed (a scalar) depending on the circumstances of the problem. |
• | Deduce a graph of force versus distance from the corresponding graph of potential energy versus distance. |
• | Demonstrate that a sinusoidal function of time solves the equation obtained by applying Newton's second law to an object connected to a spring. |
• | Derive the expression for kinetic energy from Newton's second law. |
• | Describe an object's displacement vector verbally, graphically, in terms of compass headings, or in terms of components and unit vectors. |
• | Describe collisions or explosions as if observed from the objects' center of mass. Recognize that only forces external to the system of colliding or exploding objects will change the momentum of the system's center of mass. |
• | Describe Newton's second law for rotation in terms of the rate of change of an object's angular momentum. |
• | Describe situations in which the velocity of an object is a nonzero constant when no net force acts on the object. |
• | Describe the damage to an object when it is subject to sufficient stress to reach or exceed its proportional limit, yield point, or fracture point. |
• | Determine the correct number of significant figures in a problem. |
• | Determine the direction of the vector (cross) product using the right-hand rule. |
• | Determine the equation for gravitational potential energy by integrating the work done by gravity on a test particle as it moves in a gravitational field. |
• | Determine the sum or difference of two (or more) vectors by adding (or subtracting) like components. |
• | Determine the units of a final result by multiplying and dividing units as if they were variables (correctly perform "unit algebra"). |
• | Determine the work done by a nonconservative or external force on a system. |
• | Determine whether momentum is or is not conserved when the system boundary includes objects that ordinarily move. Explain why momentum is always conserved if the system includes everything in the universe. |
• | Determine whether or not momentum and/or kinetic energy are conserved during a collision or explosion. |
• | Develop an equation for the escape speed of an object on the surface of a planet or orbiting the planet. |
• | Distinguish between an object's mass and weight and the equivalence of inertial and gravitational mass. |
• | Distinguish between an object's net, initial-to-final displacement and the total length of the path it traveled. |
• | Explain how conservation of energy is theoretically absolute. Even if we cannot measure the amount of energy transferred to the environment, all of the energy supplied to a process is transferred into other types of energy. |
• | Explain the cause-and-effect relationship of Newton's second law as expressed in terms of momentum: A net force changes an object's momentum vector. |
• | Express a vector in terms of its magnitude and a unit vector that points in the direction of the vector. |
• | Express an object's total kinetic energy in separate terms for the translation of the center of mass and rotation about the center of mass. |
• | For an object in uniform circular motion, relate its centripetal/radial acceleration to its speed and radius. |
• | For an object in uniform circular motion, relate its tangential speed and radius to its angular speed and/or its period or frequency of revolution. |
• | For nonuniform circular motion, relate an object's tangential acceleration to its angular acceleration. |
• | Global: Demonstrate the ability to make connections between concepts across physics. |
• | Global: Demonstrate the ability to think critically and employ critical thinking skills. |
• | Global: Demonstrate the quantitative skills needed to succeed in Introductory Physics. |
• | Global: Read and interpret graphs and data. |
• | Graphically, combine vectors (drawn as arrows) to correctly demonstrate the head-to-tail rule for vector addition and subtraction. |
• | Identify Newton's third law (action/reaction) pairs of forces, and use these forces to specify the net force on an object. |
• | Identify pairs of forces that are equal in magnitude but opposite in direction using Newton's second law and not Newton's third law. |
• | Identify the centrifugal force as the reaction of Newton's third law to the centripetal force. |
• | Identify the units of pressure in the SI and customary system of units, and convert values for pressure from one system of units to the other. |
• | Identify whether a collision is elastic or inelastic. |
• | Interpret an object's linear, area, or volume density as an intrinsic property of that object and relate this value to the object's mass, length, area, or volume. |
• | Locate the triple point and the different phases of a substance on a phase diagram. |
• | Perform calculations relating the forces and torques on an extended object in static equilibrium. |
• | Perform calculations using estimates of order of magnitude. |
• | Predict sound frequencies or velocities of moving objects using the Doppler equations. |
• | Predict the gravitational force exerted on a space traveler who is just outside or just inside a very large hollow (Dyson) sphere. |
• | Predict the wave form due to the superposition of two overlapping waves. |
• | Recognize that a change in the direction of a velocity vector is sufficient for an acceleration to exist. |
• | Recognize that contact forces at the surface of objects are associated with normal forces that exert a push. |
• | Recognize that if objects A and B are in thermal equilibrium with object C, objects A and B are in thermal equilibrium with each other (the zeroth law of thermodynamics). |
• | Recognize that the mass flow rate of a fluid is a conserved quantity. |
• | Recognize that the period of a pendulum is independent of the bob's mass, and that the period of a mass/spring system is independent of the amplitude of oscillation. |
• | Recognize that the total work done by several forces acting on an object is equivalent to the work done by a single net force. |
• | Recognize that unlike a pendulum, the period of a mass/spring system does depend on the mass of the object oscillating. |
• | Recognize the vector nature of momentum. |
• | Reduce a two-dimensional problem into two coupled one-dimensional problems by resolving the components of velocity and acceleration into components along two perpendicular axes. |
• | Relate a frictional force to the (perpendicular) normal force. |
• | Relate a graph of a wave to the amplitude, wavelength, frequency, and/or phase constant of the wave. |
• | Relate a motion diagram to a verbal description of the motion. |
• | Relate a potential energy function to its corresponding force function. |
• | Relate a verbal statement of a problem to a mathematical statement of a problem. |
• | Relate an object's angular momentum to its angular speed and rotational inertia. |
• | Relate an object's angular momentum to its position and linear momentum. |
• | Relate an object's average acceleration to its change in velocity and the associated time interval. |
• | Relate an object's average velocity to its displacement and the associated time interval. |
• | Relate centripetal/radial acceleration to a change in direction of an object's velocity vector. |
• | Relate changes in internal energy of a system to the initial and final states of the system, independent of the path taken on a pV diagram. |
• | Relate Newton's second law to a free-body diagram. |
• | Relate position versus time, velocity versus time, and acceleration versus time graphs to one another. |
• | Relate rotational kinetic energy to the object's moment of inertia and its angular speed. |
• | Relate the amplitude, wavelength, and frequency of a wave to an equation of the form y(x,t) = Acos(Bx - Ct). |
• | Relate the angular acceleration to the time rate of change of the angular speed. |
• | Relate the angular velocity to the time rate of change of the angular position. |
• | Relate the angular velocity vector to the direction of rotation using the right-hand rule. |
• | Relate the area under a velocity versus time graph to the total distance traveled by the object |
• | Relate the average power supplied or consumed in a process to the duration of the process and the energy supplied or consumed. |
• | Relate the beat frequency of two interacting waves to the frequencies of the individual waves. |
• | Relate the buoyant force to the volume of fluid displaced and the density of the fluid. |
• | Relate the components of a force to the magnitude and direction of the force. |
• | Relate the displacement of air molecules and the pressure of air in a sound wave. |
• | Relate the frequency to the speed of sound and the length of a pipe in different pipe configurations, such as open-open, open-closed, and closed-closed. |
• | Relate the frequency, period, and/or amplitude of an object undergoing simple harmonic oscillations to the properties of the spring or pendulum to which it is connected. |
• | Relate the fundamental frequency to the harmonics of a standing wave. |
• | Relate the hydrostatic pressure at a point in the fluid to the depth of that point and the density of the fluid. |
• | Relate the impulse delivered to an object to the average applied force and duration of the force. |
• | Relate the magnitude and direction of an applied force and lever arm to the resulting torque. |
• | Relate the molecular velocities to the pressure, volume, and temperature of a gas. |
• | Relate the moment of inertia of a collection of point masses to the masses and location of the masses. |
• | Relate the moment of inertia of an object with a continuous mass distribution to the geometry of the object. |
• | Relate the momentum of an object to the velocity vector and mass. |
• | Relate the net (total) force exerted on each object to the sum of individual forces. |
• | Relate the net impulse delivered to an object to the momentum change of the object. |
• | Relate the net torque on an object to its angular acceleration and/or moment of inertia. |
• | Relate the period of a planet's orbit to the length of the semi-major axis of its orbit. |
• | Relate the physical dimensions of an object to the coefficients of expansion and the temperature changes during thermal expansion. |
• | Relate the properties of a standing wave to two counterpropagating waves. |
• | Relate the sign of work (positive or negative) to the direction of the force relative to the direction of motion. |
• | Relate the sound intensity level in decibels to the intensity of the wave. |
• | Relate the speed of a fluid's flow through a pipe to the diameter of the pipe and/or volume of fluid flowing through the pipe. |
• | Relate the speed of sound in a gas to the properties of the gas. |
• | Relate the speed of sound in a solid to the physical properties of the substance. |
• | Relate the speed on an object undergoing simple harmonic oscillation to the position and velocity of the object. |
• | Relate the speed or distance an object moves to the energy of a system using the work-energy theorem. |
• | Relate the stability of an object to the location of the center of mass of the system relative to a pivot point. |
• | Relate the stress (force per unit area) to the strain (fractional change in length, volume, or shape) of an object. |
• | Relate the time-dependent behavior to the rms value of an oscillating quantity. |
• | Relate the velocity of a wave on a string to the tension and mass per unit length of the string. |
• | Relate the velocity, wavelength, frequency, phase difference, and/or wave number of a wave. |
• | Relate the work done by a constant force to the magnitude and direction of the force, as well as the displacement of the object |
• | Relate the work done by a torque acting on an extended object to an object's change in rotational kinetic energy. |
• | Relate the work done by a variable force to the magnitude and direction of the force, as well as the displacement of the object |
• | Relate verbal description of all the forces exerted on an object to the corresponding free-body diagram. |
• | Rewrite the kinematic equations for one-dimensional projectile motion in two dimensions. Use them to solve for an unknown quantity. |
• | Solve an equation for an unknown quantity. |
• | Solve Newton's second law equations for quantities of interest. |
• | Solve one (or more) of the kinematic equations for an unknown quantity for motion involving constant acceleration. |
• | Solve one (or more) of the kinematic equations for an unknown quantity for motion involving constant velocity. |
• | Specify whether given physical quantities are scalars or vectors. |
• | State Kepler's second law in words and select the correct diagram to represent the idea of equal areas in equal times. |
• | Use a diagram to indicate the forces, lever arms, and torques exerted on an object. |
• | Use conservation of energy to solve a problem. |
• | Use conservation of momentum and conservation of mechanical energy to solve an elastic collision problem. |
• | Use conservation of momentum to solve a problem. |
• | Use graphs of motion to compare the motion of two (or more) objects. |
• | Use Hooke's law to relate the force exerted by a stretched spring to the displacement from equilibrium and the spring constant. |
• | Use information from the periodic table to determine the number of nucleons or mass of an element. |
• | Use motion diagrams to compare the motion of two (or more) objects. |
• | Use Newton's law of gravitation to solve a problem. |
• | Use radians to solve a problem. |
• | Use the conditions for constructive or destructive interference to relate the frequencies and locations of the wave sources to the location of nodes and antinodes. |
• | Use the gravitational potential energy equation to solve for an unknown quantity. |
• | Use the kinetic energy equation to solve for an unknown value. |
• | Use the rotational kinematic equations to solve for an unknown quantity. |
• | Use the spring potential energy equation to solve for an unknown quantity. |