General Physics for Life Sciences I: Syllabus and Study Guide

General Physics for Life Sciences I

Course Overview

Major Topics and Subtopics

Nature of Physics, Models, and Vectors

Physics is the study of the fundamental laws governing the natural world. Models and vectors are essential tools for describing physical phenomena.

• Physics: The science of matter, energy, and their interactions.

• Models: Simplified representations of complex systems to predict and explain physical behavior.

• Vectors: Quantities with both magnitude and direction, such as displacement, velocity, and force.

• Example: Representing velocity as a vector allows for analysis of motion in multiple dimensions.

Motion in One and Two Dimensions

Describes how objects move along straight and curved paths, including concepts of displacement, velocity, and acceleration.

• Displacement ($\vec{d}$): Change in position of an object.

• Velocity ($\vec{v}$): Rate of change of displacement.

• Acceleration ($\vec{a}$): Rate of change of velocity.

• Equations of motion:

$v = v_0 + at$

$d = v_0 t + \frac{1}{2} a t^2$

• Example: Free fall under gravity, where $a = -9.8\,\text{m/s}^2$.

Newton's Laws of Motion

Fundamental principles describing the relationship between forces and motion.

• First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net force.

• Second Law: The net force on an object is equal to its mass times its acceleration.

$\vec{F}_{\text{net}} = m \vec{a}$

• Third Law: For every action, there is an equal and opposite reaction.

• Example: Pushing a cart causes it to accelerate; the cart pushes back with equal force.

Work, Energy, and Power

Explores how energy is transferred and transformed in physical systems.

• Work ($W$): Product of force and displacement in the direction of force.

$W = \vec{F} \cdot \vec{d}$

• Kinetic Energy ($KE$): Energy due to motion.

$KE = \frac{1}{2} m v^2$

• Potential Energy ($PE$): Energy stored due to position.

$PE_{\text{gravity}} = mgh$

• Conservation of Energy: Total energy in a closed system remains constant.

• Power ($P$): Rate at which work is done.

$P = \frac{W}{t}$

• Example: Lifting a box requires work; the faster you lift, the greater the power.

Momentum and Collisions

Momentum is a measure of motion, and collisions involve the transfer of momentum between objects.

• Momentum ($\vec{p}$): Product of mass and velocity.

$\vec{p} = m \vec{v}$

• Impulse ($\vec{J}$): Change in momentum.

$\vec{J} = \Delta \vec{p} = \vec{F} \Delta t$

• Conservation of Momentum: Total momentum before and after a collision is constant in a closed system.

• Types of Collisions: Elastic (kinetic energy conserved), Inelastic (kinetic energy not conserved).

• Example: Two billiard balls colliding and bouncing apart.

Rotational Motion and Angular Momentum

Describes motion around a fixed axis and the rotational analogs of force and momentum.

• Angular Displacement ($\theta$): Angle through which an object rotates.

• Angular Velocity ($\omega$): Rate of change of angular displacement.

• Angular Acceleration ($\alpha$): Rate of change of angular velocity.

• Torque ($\tau$): Rotational equivalent of force.

$\tau = r F \sin \theta$

• Angular Momentum ($L$): Product of moment of inertia and angular velocity.

$L = I \omega$

• Conservation of Angular Momentum: Total angular momentum remains constant in the absence of external torques.

• Example: A spinning ice skater pulling in arms to spin faster.

Temperature, Heat, and Thermodynamics

Examines the concepts of temperature, heat transfer, and the laws governing energy transformations.

• Temperature: Measure of average kinetic energy of particles.

• Heat ($Q$): Energy transferred due to temperature difference.

• First Law of Thermodynamics: Energy cannot be created or destroyed, only transformed.

$\Delta U = Q - W$

• Second Law of Thermodynamics: Entropy of an isolated system always increases.

• Entropy ($S$): Measure of disorder or randomness.

• Example: Heat flows from hot to cold objects, never spontaneously from cold to hot.

Kinetic Theory and Ideal Gas Law

Describes the behavior of gases in terms of particle motion and energy.

• Kinetic Theory: Gases consist of particles in constant, random motion.

• Ideal Gas Law: Relates pressure, volume, temperature, and number of moles.

$PV = nRT$

• Phase Transitions: Changes between solid, liquid, and gas states.

• Example: Boiling water transitions from liquid to gas.