Chapter 3: Kinematics in Two Dimensions; Vectors

Vectors and Scalars

Understanding the distinction between vectors and scalars is fundamental in physics. Vectors have both magnitude and direction, while scalars possess only magnitude.

• Examples of vectors: displacement, velocity, acceleration, force

• Examples of scalars: mass, temperature, energy

Addition and Subtraction of Vectors

Vectors can be added graphically using the tip-to-tail method or analytically using components.

• Graphical Addition: Place the tail of one vector at the tip of another; the resultant vector is drawn from the tail of the first to the tip of the last.

• Subtraction: Subtracting a vector is equivalent to adding its negative.

• Multiplication by a Scalar: Changes the magnitude but not the direction (unless the scalar is negative).

Adding Vectors by Components

Vectors can be broken into x and y components for easier calculation.

• Resultant:

Projectile Motion

Projectile motion involves two-dimensional motion under constant acceleration due to gravity.

• Horizontal motion:

• Vertical motion:

• Parabolic trajectory: The path is a parabola.

Relative Velocity

Relative velocity describes how the velocity of an object appears from different reference frames.

Chapter 6: Work and Energy

Work Done by a Force

Work is the product of force and displacement in the direction of the force.

• Constant Force: Force does not change during displacement.

• Varying Force:

Kinetic Energy and the Work-Energy Principle

Kinetic energy is the energy of motion. The work-energy principle states that the net work done on an object equals its change in kinetic energy.

Potential Energy

Potential energy is stored energy due to position or configuration.

• Gravitational potential energy:

• Elastic potential energy:

Conservative and Nonconservative Forces

• Conservative forces: Work done is path-independent (e.g., gravity, spring force).

• Nonconservative forces: Work done depends on the path (e.g., friction).

Mechanical Energy and Its Conservation

• Mechanical energy:

• Conservation: In absence of nonconservative forces,

Energy Conservation with Dissipative Forces

• When nonconservative forces (like friction) are present, mechanical energy is not conserved, but total energy is.

Chapter 7: Linear Momentum

Momentum and Relation to Force

Momentum is the product of mass and velocity. Force is the rate of change of momentum.

Conservation of Momentum

• In a closed system, total momentum before and after an event is constant.

Collisions and Impulse

• Impulse:

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

• Inelastic collisions: Only momentum is conserved.

Center of Mass

Chapter 8: Rotational Motion

Angular Quantities

• Angular displacement:

• Angular velocity:

• Angular acceleration:

Rotational Dynamics: Torque and Rotational Inertia

• Torque:

• Rotational inertia:

• Newton's second law for rotation:

Rolling Motion Without Slipping

• Condition:

Chapter 11: Oscillation and Waves

Simple Harmonic Motion (SHM)

• Equation:

• Period:

• Energy in SHM:

Damped and Forced Oscillations

• Damped: Amplitude decreases over time due to energy loss.

• Forced: External force drives the system, possibly causing resonance.

Waves: Types and Properties

• Transverse waves: Oscillations perpendicular to direction of propagation.

• Longitudinal waves: Oscillations parallel to direction of propagation.

• Wave speed:

Reflection, Transmission, and Interference

• Reflection: Wave bounces off a boundary.

• Transmission: Wave passes through a boundary.

• Interference: Principle of superposition:

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

Additional info:

• Sections referenced: Ch3, Ch6, Ch7 (7.1–7.6 and 7.7), Ch8 (8.1–8.6), Ch11 (11.1–11.22) are included in this guide.