PY 205 Learning Objectives
The student shall demonstrate, through performance in homework assignments,
in-class assessments, tests and a final exam, the ability to do the following:
Measurement and Units
1.1 Describe the base SI units meter and kilogram and compare them to the common British units foot and pound.
1.2 Use various conversion factors.
1.3 Analyze the units and dimensions of equations (dimensional analysis); use units in numerical calculations.
1.4 Quote numerical results to the correct number of significant figures.
Kinematics in One Dimension
2.1 State and use the definitions of 1D position x, displacement, average velocity, and average acceleration.
2.2 State and use the definitions of 1D instantaneous velocity v and acceleration a.
2.3 Sketch graphs of v versus t and a versus t given a graph of x versus t.
2.4 Apply the equations developed for constant acceleration (as in Table 2-1) to solve 1D motion problems.
2.5 Apply constant acceleration equations to free fall problems.
2.6 Use differential calculus to develop consistent equations for x, v, and a in terms of t including initial conditions (e.g.,
derive v(t)and x(t) when a = constant).
Vectors and Vector Addition
3.1 Explain the difference between vectors and scalars, giving examples of each.
3.2 Describe how to add vectors graphically.
3.3 Sketch vector diagrams showing sums and differences A + B and A – B.
3.4 Use properties of a right triangle to compute simple cases A + B and A – B.
3.5 Use components to combine vectors not conforming to right triangle cases.
3.6 Be able to express vectors in two or three dimensions in terms of Cartesian unit vectors i, j, and k. Carry out sums and differences
of vectors in unit vector form.
Kinematics in Two Dimensions
4.1 State and use the definitions of 2D position, displacement, average velocity, average acceleration.
4.2 State and use the definitions of 2D instantaneous velocity and acceleration.
4.3 Use calculus to develop or check equations for displacement, velocity, and acceleration.
4.4 Solve projectile motion problems using constant acceleration equations in 2D.
4.5 Define centripetal acceleration; describe uniform circular motion; derive the relation between the magnitude of centripetal
acceleration aR and speed v.
4.6 Describe the motion of an object from the point of view of a moving observer.
Newton’s Laws of Motion
5.1 Give examples of the law of inertia (1st law).
5.2 Use F = ma (2nd law) in some simple cases.
5.3 Explain the difference between mass and weight; calculate weight from mass and mass from weight.
5.4 Give examples of force pairs (3rd law).
5.5 Draw free body diagrams for problems involving these forces: weight, normal force, and various applied forces.
5.6 Use free body diagrams to set up Newton’s second law for the motion of objects in various 1D and 2D problems. Solve the
resulting equation(s) algebraically.
5.7 Apply Newton's second law to determine the motion of a single body; derive symbolic expressions and evaluate them.
5.8 Apply Newton’s second law to determine the motion of coupled masses; derive symbolic expressions and evaluate them.
Additional Applications of Newton’s Laws
6.1 State and use the empirical laws of friction between ordinary surfaces for static and kinetic situations.
6.2 Apply Newton’s second law to determine the motion of a single body including friction; derive symbolic expressions and evaluate
6.3 Apply Newton’s second law to determine the motion of coupled masses including friction; derive symbolic expressions and
6.4 Define “terminal speed”.
6.5 Apply Newton’s second law to a particle undergoing uniform circular motion.
6.6 Treat nonuniform circular motion using radial and tangential components.
13.1 Explain the meaning of “Universal” as used in “Universal Law of Gravitation”.
use Newton’s law of gravitation to calculate the gravitational force between two point masses (particles).
13.2 Use Newton’s law of gravitation and the superposition principle to calculate the net gravitational force (direction as well as
magnitude) on one particle due to other particles.
13.3 Derive and evaluate the gravitational acceleration g on the surface of the earth or another planet given that the mass of the planet
is distributed with spherical symmetry.
13.4 Explain the difference between the Universal Gravitation Constant (G) and the local acceleration of gravity (g).
13.5 Explain the term “weightlessness” as applied to satellites in orbit about the earth. Determine the speed of such satellites in terms
of the radius of the orbit. Compare weightlessness in a satellite to weightlessness in a freely falling elevator.
13.6 Derive Kepler’s Third Law from the Law of Universal Gravitation.
13.7 Apply Kepler’s Third Law to planets and satellites.
9.1 Define the center of mass of a group of point particles; define the center of mass of an extended rigid body.
9.2 Determine the center of mass of various systems of particles; use symmetry when appropriate.
9.3 Define the linear momentum, p, of a particle.
9.4 Express Newton’s second law for a single particle in terms of momentum.
9.5 Determine the velocity of the center of mass of various systems of particles using its connection to the total linear momentum of
9.6 State the relation between the rate of change of the total linear momentum and the net external force on the system.
9.7 Define “impulse”; state the momentum-impulse theorem.
9.8 Apply the impulse-momentum theorem in various situations.
9.9 Show how conservation of linear momentum follows from Newton’s second law.
9.10 Apply conservation of linear momentum to various situations.
Scalar Product of Two Vectors
3.7 State the rectangular and polar forms of the scalar product.
3.8 Calculate the scalar product of two vectors given in unit-vector form.
3.9 Calculate the scalar product of two vectors given their magnitudes and orientations.
Work and Kinetic Energy
7.1 Define the work done by a constant force F in a displacement d; define the joule.
7.2 Evaluate work in objective 7.1 as a scalar (dot) product.
7.3 Define work done by a variable force in a 1D displacement as an area and as an integral; apply to a spring force, other xn type
forces, or a force defined graphically by an F versus x plot.
7.4 Define and calculate the kinetic energy of a particle.
7.5 State and use the work-energy principle applied to a particle.
7.6 Define average and instantaneous power; calculate power in various situations.
Potential Energy and Conservation of Energy
8.1 Explain the difference between work and potential energy.
8.2 Explain the difference between conservative and non-conservative forces.
8.3 Calculate the gravitational potential energy of a particle in various situations (i.e., both near and far from the surface of the Earth).
8.4 Calculate the elastic potential energy of a particle attached to a stretched spring.
8.5 Define the mechanical energy of a particle.
8.6 State the relationship between the work done on a particle and the change in its potential energy; use this relation to show that
conservation of mechanical energy follows from the work-energy theorem.
8.7 Apply conservation of mechanical energy in various situations.
8.7 Explain why a particle’s mechanical energy always decreases when friction does work on the particle; apply the generalized
work-energy principle when friction is present in various cases.
Rotational Motion About a Fixed Axis
10.1 Give examples of objects in rotation about a fixed axis.
10.2 Define angle in radians; convert between radians, revolutions, and degrees.
10.3 State and use definitions of angular displacement, average angular velocity, and average angular acceleration.
10.4 State and use definitions of instantaneous angular velocity and angular acceleration.
10.5 Solve various constant angular acceleration problems.
10.6 Associate angular variables with their 1D linear motion counterparts.
10.7 Calculate the tangential velocity and the radial acceleration of a point on a body in rotation about a fixed axis; sketch directions of
10.8 Describe the vector nature of angular velocity and angular acceleration.
10.9 Define torque in terms of the moment arm. Calculate the net torque on a body.
10.10 Apply Newton’s second law for rotation to various cases.
10.11 Define the moment of inertia I of a body about a fixed axis of rotation by treating the body as a collection of (point) particles.
10.12 Apply the definition of I to various cases; use the parallel axis theorem; see Fig. 10-2 for some special cases.
10.13 Calculate the kinetic energy of rotation for a body rotating about a fixed axis.
Vector Product of Two Vectors
3.10 state the rectangular and polar forms of the vector product
3.11 calculate the vector product of two vectors given in unit-vector form.
3.12 calculate the vector product of two vectors given their magnitudes and orientations.
11.1 Describe rolling without slipping from two frames. Use the relation between linear speed and angular velocity.
11.2 Calculate the kinetic energy of a wheel rolling without slipping. Find the speed of a hoop, disk, or sphere that rolls down an
incline plane without slipping. Which one reaches the bottom first?
11.3 Define: vector cross product.
11.4 Apply the vector cross product to torque.
11.5 Apply the vector cross product to angular momentum.
11.6 Calculate the angular momentum of a single particle about some axis; give both direction and magnitude.
11.7 Discuss the relation between rate of change of L and net external torque for a system of particles.
11.8 State the relation between the angular momentum L of a rigid body in rotation about a fixed axis and its angular velocity vector.
11.9 Use angular momentum L for rotation about a fixed axis to derive conservation of angular momentum. Apply conservation of
angular momentum to various cases. Describe the direction of the vector L.
11.10 State the general law of conservation of angular momentum and apply it to various problems.
Simple Harmonic Motion
15.1 Give examples of bodies executing oscillatory motion; define the terms “amplitude”, “period”, “frequency” and “phase
15.2 Define simple harmonic motion (SHM) with reference to a mass on an ideal spring.
15.3 Show that Newton’s second law for 1D SHM of a particle on an ideal spring is solved by the sine or cosine functions; determine
the frequency and period in terms of the spring constant and mass; calculate frequency and period in various cases.
15.4 Given the position, x, as a function of time, determine the amplitude, frequency, angular frequency, period, and phase constant of
15.5 Given data about the particle at t = 0, determine the equation for position, x, as a function of time.
15.6 Apply conservation of mechanical energy to solve various SHM problems.
15.7 When is a pendulum’s motion equivalent to simple harmonic motion? Calculate the period and frequency of a simple pendulum.
Compare SHM and uniform circular motion.
Wave Motion, Transverse Waves
16.1 Give examples of waves; distinguish mechanical waves from radio (EM) waves and transverse waves from longitudinal waves.
16.2 Calculate the wave speed for the case of transverse waves on a stretched string.
16.3 Explain how the intensity of a point source varies with distance from it; how are plane waves related to spherical waves?
16.4 Describe the motion of a wave pulse on an infinite stretched string.
16.5 Write down the equation describing a sinusoidal traveling wave on an infinite stretched string; identify the direction of motion,
amplitude, frequency, period, and wavelength; calculate the wave speed from the frequency and wavelength.
16.7 Use the superposition principle to combine two overlapping waves and to explain reflection of a wave pulse from a fixed end of a
stretched string. Give examples of constructive and destructive interference.
16.8 Determine the allowed wavelengths and frequencies for standing waves on a stretched string with both ends fixed.
Longitudinal Waves and Sound
17.1 Contrast sound waves with waves on a stretched string; sketch sinusoidal sound waves in a pipe as if sound waves were
transverse; calculate sound wave speed from frequency and wavelength.
17.2 Calculate echo times for a pulse of sound; compare speeds in air (gas), water (liquid), and aluminum (solid).
17.3 Define sound level in decibels and compare sound levels from the same source at different distances from the source.
17.4 Calculate the allowed frequencies of standing sound waves in pipes open at one or at both ends.
17.5 Explain how are beats are produced; evaluate the beat frequency or use it to deduce individual frequencies.
17.6 Explain the Doppler effect.
17.7 Calculate the frequency heard by an observer when the source moves towards or away from the observer; repeat for the observer
in motion towards or away from the moving or stationary source.