Φ Physics Course

Introductory course

Physics for Medicine, Biology, and Everyday Life

A practical web course that starts with motion and builds toward fluids, light, sound, ultrasound, electromagnetism, chemical bonds, and quantum physics.

View course map Start module 1
14

Core physics modules

28

Worked math examples

Web

Static site: HTML, CSS, JS

How to use this course

Each module gives the central idea, the key equations, real-world applications, and two worked examples. The math is shown step by step so students can see where each answer comes from.

Course scope: This introductory reference emphasizes the central idea, key equations, practical applications, and worked examples for each topic.

Course map

Modules

01

Acceleration

How velocity changes over time.

 02

Force

Pushes, pulls, and Newton’s laws.

 03

Work and Energy

How forces move objects and store energy.

 04

Momentum

Mass in motion and collisions.

 05

Rotation

Turning motion, torque, and angular speed.

 06

Gravity

Attraction between masses.

 07

Gases

Pressure, volume, temperature, and molecules.

 08

Liquids

Pressure, flow, and buoyancy.

 09

Light

Waves, photons, color, and refraction.

 10

Electricity

Charge, voltage, current, and resistance.

 11

Sound and Ultrasound

Mechanical waves, frequency, intensity, and medical imaging.

 12

Magnetism

Fields produced by moving charges.

 13

Chemical Bonds

Why atoms stick together.

 14

Quantum Physics

Particles, waves, photons, and atoms.
Module 1

Acceleration

Acceleration means a change in velocity over time. Velocity includes both speed and direction, so an object can accelerate by speeding up, slowing down, or changing direction.

Key equations

\[a=\frac{\Delta v}{\Delta t}\]

Acceleration is change in velocity divided by change in time.

\[v=v_0+at\]

Final velocity equals starting velocity plus acceleration times time.

Worked examples

Car speeding up

Problem. A car goes from rest to 30 m/s in 6 s. What is its acceleration?

  1. \[a=\frac{\Delta v}{\Delta t}\]
  2. \[a=\frac{30-0}{6}\]
  3. \[a=5\ \text{m/s}^2\]

Answer. The car accelerates at 5 m/s².

Falling ball

Problem. A ball falls from rest for 3 s. Ignoring air resistance, how fast is it moving?

  1. \[g=9.8\ \text{m/s}^2\]
  2. \[v=gt\]
  3. \[v=(9.8)(3)\]
  4. \[v=29.4\ \text{m/s}\]

Answer. The ball is moving 29.4 m/s downward.

Module 2

Force

A force is a push or pull. Forces change motion. Newton’s second law connects force, mass, and acceleration.

Key equations

\[F=ma\]

Force equals mass times acceleration.

\[F_g=mg\]

Weight is gravitational force near Earth.

Worked examples

Force needed to accelerate

Problem. A 10 kg object accelerates at 2 m/s². What force is needed?

  1. \[F=ma\]
  2. \[F=(10)(2)\]
  3. \[F=20\ \text{N}\]

Answer. The required force is 20 N.

Weight on Earth

Problem. What is the weight of a 70 kg person on Earth?

  1. \[F_g=mg\]
  2. \[F_g=(70)(9.8)\]
  3. \[F_g=686\ \text{N}\]

Answer. The person’s weight is 686 N.

Module 3

Work and Energy

Work happens when a force moves an object through a distance. Energy is the ability to do work. Kinetic energy is energy of motion.

Key equations

\[W=Fd\cos\theta\]

Work equals force times distance times the cosine of the angle between them.

\[KE=\frac{1}{2}mv^2\]

Kinetic energy depends on mass and the square of velocity.

Worked examples

Pushing a box

Problem. You push a box with 50 N of force for 4 m. How much work is done?

  1. \[W=Fd\]
  2. \[W=(50)(4)\]
  3. \[W=200\ \text{J}\]

Answer. The work done is 200 J.

Kinetic energy of a ball

Problem. A 2 kg ball moves at 10 m/s. What is its kinetic energy?

  1. \[KE=\frac{1}{2}mv^2\]
  2. \[KE=\frac{1}{2}(2)(10^2)\]
  3. \[KE=100\ \text{J}\]

Answer. The ball has 100 J of kinetic energy.

Module 4

Momentum

Momentum is mass in motion. In a closed system with no outside force, total momentum is conserved.

Key equations

\[p=mv\]

Momentum equals mass times velocity.

\[p_{\text{initial}}=p_{\text{final}}\]

Momentum is conserved when no external force acts.

Worked examples

Momentum of an object

Problem. A 5 kg object moves at 3 m/s. What is its momentum?

  1. \[p=mv\]
  2. \[p=(5)(3)\]
  3. \[p=15\ \text{kg}\cdot\text{m/s}\]

Answer. The momentum is 15 kg·m/s.

Carts sticking together

Problem. A 2 kg cart moving at 4 m/s sticks to a 2 kg cart at rest. What is their final speed?

  1. \[p_i=(2)(4)+(2)(0)=8\]
  2. \[m_f=2+2=4\ \text{kg}\]
  3. \[p_i=p_f\]
  4. \[8=4v\]
  5. \[v=2\ \text{m/s}\]

Answer. The carts move together at 2 m/s.

Module 5

Rotation

Rotation is motion around an axis. Rotational motion uses angle, angular velocity, and torque instead of distance, velocity, and force alone.

Key equations

\[\omega=\frac{\Delta\theta}{\Delta t}\]

Angular velocity is change in angle divided by time.

\[\tau=rF\sin\theta\]

Torque depends on lever arm, force, and angle.

Worked examples

Angular velocity of a wheel

Problem. A wheel turns through 12 radians in 3 s. What is its angular velocity?

  1. \[\omega=\frac{\Delta\theta}{\Delta t}\]
  2. \[\omega=\frac{12}{3}\]
  3. \[\omega=4\ \text{rad/s}\]

Answer. The angular velocity is 4 rad/s.

Torque from a wrench

Problem. You push perpendicular to a 0.3 m wrench with 20 N of force. What torque do you produce?

  1. \[\sin 90^\circ=1\]
  2. \[\tau=rF\]
  3. \[\tau=(0.3)(20)\]
  4. \[\tau=6\ \text{N}\cdot\text{m}\]

Answer. The torque is 6 N·m.

Module 6

Gravity

Gravity is the attractive force between masses. Near Earth, it gives objects an acceleration of about 9.8 m/s².

Key equations

\[F=G\frac{m_1m_2}{r^2}\]

Newton’s law of gravitation.

\[F_g=mg\]

Weight near Earth.

Worked examples

Weight of a person

Problem. What is the weight of a 60 kg person on Earth?

  1. \[F_g=mg\]
  2. \[F_g=(60)(9.8)\]
  3. \[F_g=588\ \text{N}\]

Answer. The person weighs 588 N.

Force between two masses

Problem. What is the gravitational force between two 10 kg masses separated by 2 m?

  1. \[F=G\frac{m_1m_2}{r^2}\]
  2. \[F=(6.67\times10^{-11})\frac{(10)(10)}{2^2}\]
  3. \[F=(6.67\times10^{-11})(25)\]
  4. \[F=1.67\times10^{-9}\ \text{N}\]

Answer. The force is 1.67 × 10⁻⁹ N, extremely small.

Module 7

Gases

Gases are collections of moving particles. Their behavior depends on pressure, volume, temperature, and the number of molecules.

Key equations

\[PV=nRT\]

The ideal gas law.

\[P_1V_1=P_2V_2\]

Boyle’s law when temperature is constant.

Worked examples

Pressure of an ideal gas

Problem. A gas has 1 mole, temperature 300 K, and volume 0.025 m³. Find pressure.

  1. \[PV=nRT\]
  2. \[P=\frac{nRT}{V}\]
  3. \[P=\frac{(1)(8.314)(300)}{0.025}\]
  4. \[P=99{,}768\ \text{Pa}\]

Answer. The pressure is about 1.0 × 10⁵ Pa, roughly atmospheric pressure.

Boyle’s law

Problem. A gas volume is 4 L at 1 atm. If pressure doubles to 2 atm and temperature stays constant, what is the new volume?

  1. \[P_1V_1=P_2V_2\]
  2. \[(1)(4)=(2)V_2\]
  3. \[V_2=2\ \text{L}\]

Answer. The volume decreases to 2 L.

Module 8

Liquids

Liquids flow and exert pressure. Pressure increases with depth because more liquid sits above you.

Key equations

\[P=\rho gh\]

Fluid pressure from depth.

\[F_b=\rho Vg\]

Buoyant force equals weight of displaced fluid.

Worked examples

Water pressure

Problem. What is the water pressure at 10 m depth, not including atmospheric pressure?

  1. \[P=\rho gh\]
  2. \[P=(1000)(9.8)(10)\]
  3. \[P=98{,}000\ \text{Pa}\]

Answer. The pressure is 98,000 Pa.

Buoyant force

Problem. An object displaces 0.02 m³ of water. What buoyant force acts on it?

  1. \[F_b=\rho Vg\]
  2. \[F_b=(1000)(0.02)(9.8)\]
  3. \[F_b=196\ \text{N}\]

Answer. The upward buoyant force is 196 N.

Module 9

Light

Light behaves like both a wave and a particle. As a wave, it has speed, frequency, and wavelength. Light bends when it enters a new medium.

Key equations

\[c=f\lambda\]

Wave speed equals frequency times wavelength.

\[n_1\sin\theta_1=n_2\sin\theta_2\]

Snell’s law for refraction.

Worked examples

Frequency of red light

Problem. Red light has wavelength 650 nm. What is its frequency?

  1. \[650\ \text{nm}=650\times10^{-9}\ \text{m}\]
  2. \[f=\frac{c}{\lambda}\]
  3. \[f=\frac{3.0\times10^8}{650\times10^{-9}}\]
  4. \[f=4.62\times10^{14}\ \text{Hz}\]

Answer. The frequency is 4.62 × 10¹⁴ Hz.

Refraction into glass

Problem. Light goes from air into glass with n₁ = 1.00, n₂ = 1.50, and θ₁ = 30°. Find θ₂.

  1. \[n_1\sin\theta_1=n_2\sin\theta_2\]
  2. \[(1.00)\sin30^\circ=(1.50)\sin\theta_2\]
  3. \[0.5=1.5\sin\theta_2\]
  4. \[\sin\theta_2=0.333\]
  5. \[\theta_2\approx19.5^\circ\]

Answer. The light bends toward the normal; θ₂ ≈ 19.5°.

Module 10

Electricity

Electricity is the movement or separation of electric charge. Voltage pushes charge, current is charge flow, and resistance opposes current.

Key equations

\[V=IR\]

Ohm’s law.

\[P=IV\]

Electrical power.

Worked examples

Current in a circuit

Problem. A circuit has resistance 10 Ω and voltage 20 V. What is the current?

  1. \[V=IR\]
  2. \[I=\frac{V}{R}\]
  3. \[I=\frac{20}{10}\]
  4. \[I=2\ \text{A}\]

Answer. The current is 2 A.

Power use

Problem. A device uses 3 A at 120 V. What power does it use?

  1. \[P=IV\]
  2. \[P=(3)(120)\]
  3. \[P=360\ \text{W}\]

Answer. The device uses 360 W.

Module 11

Sound and Ultrasound

Sound is a mechanical wave that travels through matter by compressing and expanding particles. Ultrasound uses sound waves above human hearing, making it useful for imaging, blood-flow measurement, and procedures in medicine.

Key equations

\[v=f\lambda\]

Wave speed equals frequency times wavelength.

\[I=\frac{P}{A}\]

Intensity is power spread over area.

\[f' = f\left(\frac{v+v_o}{v-v_s}\right)\]

The Doppler effect describes frequency shift from motion.

Worked examples

Wavelength of ultrasound

Problem. An ultrasound probe sends a 5.0 MHz sound wave through soft tissue. If sound travels through tissue at about 1540 m/s, what is the wavelength?

  1. \[v=f\lambda\]
  2. \[\lambda=\frac{v}{f}\]
  3. \[f=5.0\times10^6\ \text{Hz}\]
  4. \[\lambda=\frac{1540}{5.0\times10^6}\]
  5. \[\lambda=3.08\times10^{-4}\ \text{m}=0.308\ \text{mm}\]

Answer. The wavelength is about 0.31 mm, which helps explain why ultrasound can form detailed images.

Ultrasound intensity

Problem. An ultrasound beam delivers 0.020 W over an area of 0.00010 m². What is the intensity?

  1. \[I=\frac{P}{A}\]
  2. \[I=\frac{0.020}{0.00010}\]
  3. \[I=200\ \text{W/m}^2\]

Answer. The intensity is 200 W/m². In real ultrasound systems, intensity is carefully controlled for diagnostic safety.

Module 12

Magnetism

Magnetism comes from moving electric charges. A magnetic field can push on moving charges or current-carrying wires.

Key equations

\[F=qvB\sin\theta\]

Magnetic force on a moving charge.

\[F=ILB\sin\theta\]

Magnetic force on a current-carrying wire.

Worked examples

Force on a moving charge

Problem. A charge of 2 C moves at 5 m/s through a 3 T magnetic field at 90°. What force acts on it?

  1. \[F=qvB\sin\theta\]
  2. \[F=(2)(5)(3)\sin90^\circ\]
  3. \[F=30\ \text{N}\]

Answer. The magnetic force is 30 N.

Force on a wire

Problem. A wire carries 4 A. The wire length in the magnetic field is 0.5 m, and the field is 2 T. The wire is perpendicular to the field. What force acts on it?

  1. \[F=ILB\sin\theta\]
  2. \[F=(4)(0.5)(2)\sin90^\circ\]
  3. \[F=4\ \text{N}\]

Answer. The force is 4 N.

Module 13

Chemical Bonds

Chemical bonds form because atoms become more stable when electrons are shared or transferred. Physics explains bonding through electric forces, energy, and quantum mechanics.

Key equations

\[F=k\frac{q_1q_2}{r^2}\]

Coulomb’s law for electric force.

\[U=k\frac{q_1q_2}{r}\]

Electric potential energy between charges.

Worked examples

Energy between ions

Problem. Estimate the electric potential energy between Na⁺ and Cl⁻ separated by 0.28 nm.

  1. \[U=k\frac{q_1q_2}{r}\]
  2. \[q_1=+e,\quad q_2=-e,\quad e=1.60\times10^{-19}\ \text{C}\]
  3. \[r=0.28\times10^{-9}\ \text{m}\]
  4. \[U=(8.99\times10^9)\frac{(1.60\times10^{-19})(-1.60\times10^{-19})}{0.28\times10^{-9}}\]
  5. \[U\approx -8.22\times10^{-19}\ \text{J}\]

Answer. The negative sign means attraction; the ion pair is energetically favorable.

Energy per bond

Problem. A chemical bond has energy 400 kJ/mol. What is the energy per bond?

  1. \[N_A=6.022\times10^{23}\]
  2. \[400\ \text{kJ/mol}=400{,}000\ \text{J/mol}\]
  3. \[E=\frac{400{,}000}{6.022\times10^{23}}\]
  4. \[E=6.64\times10^{-19}\ \text{J}\]

Answer. Each bond has energy about 6.64 × 10⁻¹⁹ J.

Module 14

Quantum Physics

Quantum physics describes matter and energy at very small scales. Particles can behave like waves, and energy often comes in packets called quanta.

Key equations

\[E=hf\]

Photon energy depends on frequency.

\[E=\frac{hc}{\lambda}\]

Photon energy can also be calculated from wavelength.

\[\lambda=\frac{h}{p}\]

The de Broglie wavelength of matter.

Worked examples

Photon energy

Problem. Find the energy of a photon with frequency 5.0 × 10¹⁴ Hz.

  1. \[E=hf\]
  2. \[E=(6.626\times10^{-34})(5.0\times10^{14})\]
  3. \[E=3.31\times10^{-19}\ \text{J}\]

Answer. The photon energy is 3.31 × 10⁻¹⁹ J.

Electron wavelength

Problem. An electron has momentum 1.0 × 10⁻²⁴ kg·m/s. What is its wavelength?

  1. \[\lambda=\frac{h}{p}\]
  2. \[\lambda=\frac{6.626\times10^{-34}}{1.0\times10^{-24}}\]
  3. \[\lambda=6.626\times10^{-10}\ \text{m}\]
  4. \[\lambda=0.663\ \text{nm}\]

Answer. The electron wavelength is 0.663 nm, about the scale of atoms.