Classroom topics
The table below lists the main topics taught at Physics Fundamentals. Each row gives the level, the central focus, and a representative experiment students actually perform.
| Topic | Level | Focus | Representative experiment |
|---|---|---|---|
| Kinematics | Foundation | Describing motion with position, velocity, and acceleration | Timing a ball rolling down a ramp |
| Forces and Newton's laws | Foundation | Net force, mass, and acceleration, F = m*a | Accelerating a trolley with a hanging mass |
| Energy and work | Foundation | Kinetic and potential energy, conservation of energy | Measuring height and speed of a pendulum bob |
| Momentum | Intermediate | Momentum conservation in collisions, p = m*v | Colliding carts on a low-friction track |
| Rotational motion | Intermediate | Torque, angular acceleration, and moment of inertia | Hanging masses to spin a rotating disc |
| Oscillations and waves | Intermediate | Simple harmonic motion and traveling waves | Measuring the period of a mass on a spring |
| Sound | Intermediate | Wave speed, frequency, and standing waves | Measuring wavelength with a resonance tube |
| Thermodynamics | Intermediate | Heat, temperature, and the ideal gas law | Verifying Boyle's law with a gas syringe |
| Electricity | Intermediate | Current, voltage, resistance, and circuits | Validating Ohm's law with a resistor |
| Magnetism and electromagnetic induction | Advanced | Magnetic fields and Faraday's law | Generating a current by moving a magnet in a coil |
| Optics | Advanced | Reflection, refraction, lenses, and interference | Measuring the focal length of a converging lens |
| Modern physics and relativity | Advanced | Photoelectric effect, mass-energy equivalence, relativity | Determining Planck's constant with LEDs |
| Astrophysics | Advanced | Gravity, stellar evolution, and cosmic distances | Analyzing spectra to identify elements in stars |
Projectile motion
A projectile launched with initial speed v0 at an angle uses independent horizontal and vertical motion. The horizontal velocity stays constant, while the vertical motion is uniformly accelerated by gravity.
Because there is no horizontal acceleration, the horizontal position grows at a steady rate, x = vx*t. Vertically the object accelerates downward at g, so its height is y = vy0*t - 0.5*g*t^2. The result is a parabola. The range, or horizontal distance traveled, is largest when the launch angle is 45 degrees for a fixed launch speed on level ground.
# typical numbers: v0 = 20 m/s, angle = 45 deg, g = 9.80 m/s^2
import math
v0 = 20.0
angle = math.radians(45.0)
g = 9.80
vx = v0 * math.cos(angle)
vy0 = v0 * math.sin(angle)
flight_time = 2.0 * vy0 / g # back to launch height
rng = vx * flight_time
print("time of flight:", round(flight_time, 2), "s")
print("range:", round(rng, 2), "m")
print("max height:", round(vy0**2/(2*g), 2), "m")
# output: 2.89 s, 40.82 m, 10.20 m
The series circuit
In a series circuit the same current passes through every component. The applied voltage is shared among the resistors, and the total resistance is the sum of the individual resistances.
For two series resistors the total resistance is R_total = R1 + R2, and Ohm's law gives the current as I = V / R_total. The voltage across each resistor is then V1 = I*R1 and V2 = I*R2, and these two voltages add to the battery voltage. This is the simplest circuit to analyze, and it underlies the way voltage dividers and protective resistors work.
# two series resistors with a 9 V battery
V = 9.0 # volts
R1 = 100.0 # ohms
R2 = 200.0 # ohms
R_total = R1 + R2
I = V / R_total # same current everywhere
V1 = I * R1
V2 = I * R2
print("current:", round(I*1000, 1), "mA")
print("V1:", round(V1, 2), "V, V2:", round(V2, 2), "V")
# output: 30.0 mA, 3.00 V, 6.00 V
The traveling sine wave
A wave transmits energy through a medium without transporting the material itself. A simple harmonic wave on a string can be described by displacement as a function of position and time.
The speed of a wave equals the product of its wavelength and frequency, v = f*lambda. Because frequency is the inverse of period, f = 1/T, this can be written v = lambda / T. For waves on a stretched string, the speed depends on the string's tension and linear density: v = sqrt(Tension / mu). A tighter string carries waves faster, which is why tuning an instrument changes its pitch.
# wave speed from tension and linear mass density
tension = 88.0 # N
mu = 0.0022 # kg per m, linear density
v = (tension / mu)**0.5
freq = 440.0 # Hz, the A above middle C
wavelength = v / freq
print("wave speed:", round(v, 1), "m/s")
print("wavelength:", round(wavelength, 3), "m")
# output: 200.0 m/s, 0.455 m