Chapters 1–3: Representing Motion, Motion in One Dimension, Vectors and Motion in Two Dimensions

Significant Figures and Unit Conversion

Accurate measurement and calculation in physics require proper use of significant figures and unit conversion.

• Significant Figures: Digits in a measurement that are known with certainty plus one estimated digit.

• Unit Conversion: Use conversion factors to change units (e.g., meters to centimeters).

• Example: Convert 2.5 km to meters: m.

Displacement, Distance, Speed, and Velocity

Understanding the relationship between position, movement, and time is fundamental.

• Displacement (\( \Delta x \)): Change in position; vector quantity.

• Distance (d): Total path length; scalar quantity.

• Speed: Scalar;

• Velocity: Vector;

• Acceleration (a): Rate of change of velocity;

Kinematics Equations

Kinematics describes motion without regard to its causes.

• (for constant acceleration)

• Example: Calculating maximum height, travel time, velocity, distance, and displacement for thrown or dropped objects.

Motion Graphs

Graphs are used to visualize motion.

• x vs. t graph: Position as a function of time.

• v vs. t graph: Velocity as a function of time.

• Relationship: Slope of x vs. t gives velocity; slope of v vs. t gives acceleration.

• Direction of acceleration: Positive or negative slope indicates direction.

Vectors and Components

Vectors are quantities with both magnitude and direction.

• Breaking vectors: Use trigonometry to find x- and y-components.

• Reconstructing: ,

Projectile Motion

Projectile motion involves two-dimensional movement under gravity.

• Horizontal velocity (v_x): Constant.

• Vertical velocity (v_y): Changes due to gravity.

• Acceleration (a_y): (downward).

• Net force: Gravity acts downward.

Chapters 4–6: Forces & Newton's Laws, Applying Newton's Laws, Circular Motion, Orbits & Gravity

Newton's Laws of Motion

Newton's three laws describe the relationship between forces and motion.

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

• Second Law:

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

Types of Forces

Various forces act on objects in different situations.

• Tension: Force transmitted through a string or rope.

• Weight:

• Spring Force:

• Normal Force: Perpendicular contact force.

• Apparent Weight: Perceived weight due to acceleration.

• Friction: Static (), Kinetic ()

• Universal Gravity:

Force Diagrams

Force diagrams (free-body diagrams) help visualize all forces acting on an object.

• Draw arrows for each force.

• Label forces (e.g., , , , ).

Applying Newton's Second Law

Use to solve for acceleration or net force.

• Uniform motion: Net force is zero.

• Acceleration: Net force is nonzero.

• Inclined plane: Resolve forces parallel and perpendicular to the surface.

• Pulled at an angle: Find normal force and friction using vector components.

Circular Motion

Objects in circular motion experience centripetal acceleration and force.

• Centripetal acceleration:

• Centripetal force:

• At the top/dip/level: Analyze forces (gravity, normal, tension) depending on position.

Chapters 7–9: Rotational Motion, Equilibrium & Elasticity, Momentum

Angular Speed and Linear Speed

Relate rotational and linear motion.

• Degree to radians:

• RPM: Revolutions per minute; convert to rad/s.

Rotational Inertia

Rotational inertia depends on mass distribution and axis of rotation.

• Choice of axis: Changes value.

Torque

Torque causes rotational motion.

• Action point: Where force is applied.

• Direction: Clockwise or counterclockwise.

Balancing Torques

For equilibrium, sum of torques must be zero.

• Example: Multiple forces on a beam.

Impulse

Impulse is the change in momentum.

• Example: Pulling a spring over time.

Momentum and Conservation

Momentum is conserved in isolated systems.

• Linear momentum:

• Angular momentum:

• Conservation: in collisions.

Chapters 10–13: Energy & Work, Using Energy, Thermal Properties, Fluids

Work, Kinetic Energy, Potential Energy

Energy can be transferred and transformed.

• Work:

• Kinetic Energy (KE):

• Gravitational Potential Energy (U_g):

• Spring Potential Energy (U_s):

• Conservation of Energy: (if no losses)

• Energy chart: Track energy transformations.

• Loss to thermal: Energy dissipated as heat.

Energy Transformation

Energy changes form during motion.

• Object falls:

• Object goes up hill:

• Friction: thermal energy

Power

Power is the rate of doing work.

• (for constant velocity)

Bernoulli's Principle

Bernoulli's principle relates pressure, velocity, and height in fluids.

• Applications: Airplane lift, fluid flow in pipes.

Efficiency Calculation

Efficiency measures how much input energy is converted to useful output.

Heat Transfer Methods

Heat can be transferred by conduction, convection, and radiation.

• Conduction: Direct transfer through contact.

• Convection: Transfer via fluid movement.

• Radiation: Transfer via electromagnetic waves.

Pressure in Liquids

Pressure increases with depth in a liquid.

• Example: Pressure at the bottom of a swimming pool.

Buoyancy Calculation

Buoyant force acts upward on objects in fluids.

• Example: Floating and sinking objects.