Chapter 1: Units, Physical Quantities & Vectors

Introduction

This chapter introduces the foundational language of physics, focusing on the use of standard units, the importance of significant figures for precision, and the mathematical representation of vectors for quantities with both magnitude and direction.

• Density: The mass per unit volume of a substance. Common units include g/cm3 and kg/m3. Conversion between units is often required in problem-solving.

• Significant Figures: Digits in a measurement that reflect its precision. Used to ensure accuracy in calculations involving measured quantities.

• Vector Components: The projections of a vector along coordinate axes (typically x and y). Useful for breaking down vectors into manageable parts for calculation.

• Vector Sum (Resultant): The single vector representing the combined effect of two or more vectors. Calculated using vector addition.

Key Formulas

• Density:

• Vector Components:

• Magnitude:

Example Application

• Density Conversion: To convert 19.3 g/cm3 to kg/m3:

Chapter 2: Motion Along a Straight Line

Introduction

This chapter covers one-dimensional kinematics, describing how an object's position changes over time, and introduces velocity and acceleration.

• Average Velocity:

• Instantaneous Velocity: The velocity at a specific instant, found as the derivative of position with respect to time:

• Constant Acceleration: When velocity changes by equal amounts in equal time intervals.

• Free-Fall: Motion under gravity alone, with (downward).

Key Equations

• Position:

• Velocity:

• Velocity-Squared:

Example Application

• Free-Fall Impact Speed: For a rock thrown upward at 22.0 m/s from a 30.0-m building, use energy or kinematics to find speed just before impact.

Chapter 3: Motion in Two or Three Dimensions

Introduction

This chapter extends kinematics to two and three dimensions, including projectile and circular motion, and introduces the concept of trajectory.

• Projectile Motion: Motion under gravity with both horizontal and vertical components.

• Radial Acceleration: Acceleration directed toward the center of a circular path:

• Linear Speed: The distance traveled per unit time by a point on a rotating object.

• Trajectory: The path followed by a projectile.

Key Equations

• Projectile Range:

• Position Vector:

Example Application

• Radial Acceleration at Equator: For Earth's radius , ,

Chapter 4: Newton's Laws of Motion

Introduction

This chapter introduces Newton's three laws, which describe the relationship between force and motion, and distinguishes between mass and weight.

• Newton's Second Law:

• Weight vs. Mass: Weight is the gravitational force (); mass is the amount of matter.

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

• Resultant Force: The vector sum of all external forces.

Example Application

• Resultant Force: For two forces at an angle, use the law of cosines:

Chapter 5: Applying Newton's Laws

Introduction

This chapter applies Newton's laws to systems involving multiple objects, pulleys, inclines, and friction.

• Tension: The pulling force transmitted by a string, rope, or cable.

• Static Friction: The frictional force preventing motion,

• Kinetic Friction: The frictional force during motion,

Example Application

• Friction Force: For a box with , , and applied force :

If , friction matches ; if , use .

Chapter 6: Work & Kinetic Energy

Introduction

This chapter introduces work, kinetic energy, and the work-energy theorem, relating force and motion to energy transfer.

• Work:

• Kinetic Energy:

• Work-Energy Theorem:

• Power:

Example Application

• Spring Compression: Use energy conservation:

Chapter 7: Potential Energy & Conservation

Introduction

This chapter discusses potential energy (gravitational and elastic) and the conservation of mechanical energy.

• Gravitational Potential Energy:

• Elastic Potential Energy:

• Conservation of Mechanical Energy: (if only conservative forces act)

Example Application

• Spring Compression from Drop: Set and solve for .

Chapter 8: Momentum, Impulse, and Collisions

Introduction

This chapter explores momentum, impulse, and the conservation of momentum in collisions.

• Momentum:

• Impulse:

• Elastic Collision: Both momentum and kinetic energy are conserved.

• Thrust:

Example Application

• Rocket Thrust: For , ,

Chapter 9: Rotation of Rigid Bodies

Introduction

This chapter introduces rotational kinematics and dynamics, including angular velocity, angular acceleration, and moment of inertia.

• Angular Acceleration:

• Moment of Inertia: (sum over all mass elements)

Key Equations

• Rotational Kinematics:

• Angular Velocity:

Example Application

• Moment of Inertia of a Rod: About center: ; about end:

Chapter 10: Dynamics of Rotational Motion

Introduction

This chapter applies dynamics to rotation, introducing torque, angular momentum, and rolling motion.

• Torque:

• Angular Momentum:

• Rolling Without Slipping:

Example Application

• Torque Calculation: For force at angle and lever arm :

Chapter 11: Equilibrium & Elasticity

Introduction

This chapter covers static equilibrium (net force and net torque are zero) and the elastic properties of materials.

• Center of Gravity: The point where the total weight acts.

• Young's Modulus:

• Bulk Modulus:

Example Application

• Young's Modulus Calculation: For a rope stretched by ,

Chapter 12: Fluid Mechanics

Introduction

This chapter discusses the properties of fluids at rest and in motion, including pressure, buoyancy, and flow continuity.

• Gauge Pressure:

• Archimedes' Principle: Buoyant force equals the weight of displaced fluid:

• Equation of Continuity: (mass flow rate is constant)

Example Application

• Pressure at Depth:

Chapter 13: Gravitation

Introduction

This chapter explores Newton's law of universal gravitation, gravitational potential energy, and orbital motion.

• Newton's Law of Gravitation:

• Escape Speed:

• Orbital Period (Kepler's Third Law):

Example Application

• Gravity on Venus: (use Venus's mass and radius)

Chapter 14: Periodic Motion

Introduction

This chapter covers oscillatory systems, focusing on simple harmonic motion (SHM) such as springs and pendulums.

• Frequency:

• Angular Frequency:

• SHM Equation:

• Pendulum Period (small angle):

Example Application

• Spring Constant from Period:

Chapter 15: Mechanical Waves

Introduction

This chapter introduces mechanical waves, including their properties, wave speed, and standing waves.

• Wavelength:

• Wave Speed:

• Standing Wave: Formed by the interference of two waves traveling in opposite directions.

• Fundamental Mode: The lowest frequency standing wave.

Example Application

• Rope Wave Equation: ; amplitude , wave number , angular frequency

Additional info: The above notes expand on the provided terms and problem types, offering definitions, key equations, and example applications for each chapter. These summaries are suitable for exam preparation and foundational understanding in a college-level physics course.