Physics 1: Core Concepts, Formulas, and Problem-Solving Strategies

Unit Conversion Factors

Introduction

Unit conversion is essential in physics to ensure consistency and accuracy in calculations. The following are common conversion factors for various physical quantities.

• Length: 1 m = 100 cm = 1000 mm = 106 μm = 109 nm

• Area: 1 m2 = 104 cm2

• Volume: 1 m3 = 106 cm3 = 1000 L

• Time: 1 min = 60 s; 1 h = 3600 s

• Speed: 1 m/s = 3.6 km/h

• Acceleration: 1 m/s2 = 3.281 ft/s2

• Mass: 1 kg = 1000 g = 2.205 lb

• Force: 1 N = 0.225 lb = 105 dyn

• Pressure: 1 Pa = 1 N/m2 = 1.45 × 10-4 psi

• Energy: 1 J = 0.239 cal = 0.738 ft·lb

• Power: 1 W = 1 J/s = 1/746 hp

Quantity	SI Unit	Common Conversion
Length	meter (m)	1 m = 100 cm = 39.37 in
Mass	kilogram (kg)	1 kg = 2.205 lb
Force	newton (N)	1 N = 0.225 lb
Energy	joule (J)	1 J = 0.239 cal
Power	watt (W)	1 W = 1 J/s

Vectors and Kinematics

Vector Addition and Properties

Vectors are quantities with both magnitude and direction. They are fundamental in describing motion and forces in physics.

• Vector Addition: The sum of two vectors A and B is C = A + B.

• Magnitude of a Vector: For C = (Cx, Cy), $|\vec{C}| = \sqrt{C_x^2 + C_y^2}$

• Dot Product: $\vec{A} \cdot \vec{B} = |A||B|\cos\theta$

• Angle Between Vectors: $\cos\theta = \frac{\vec{A} \cdot \vec{B}}{|A||B|}$

Motion in One and Two Dimensions

Kinematics describes the motion of objects without considering the causes. It involves displacement, velocity, and acceleration.

• Displacement: $\Delta x = x_f - x_i$

• Average Velocity: $v_{avg} = \frac{\Delta x}{\Delta t}$

• Constant Acceleration Equations:

  • $v = v_0 + at$

  • $x = x_0 + v_0 t + \frac{1}{2} a t^2$

  • $v^2 = v_0^2 + 2a(x - x_0)$

• Projectile Motion: Motion in two dimensions under constant acceleration (gravity).

  • Horizontal: $x = v_{0x} t$

  • Vertical: $y = v_{0y} t - \frac{1}{2} g t^2$

Newton's Laws of Motion

Fundamental Principles

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

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

• Second Law: $\sum \vec{F} = m \vec{a}$

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

Applying Newton's Laws

• Free Body Diagram: A diagram showing all forces acting on an object.

• Friction:

  • Static: $f_s \leq \mu_s N$

  • Kinetic: $f_k = \mu_k N$

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

• Normal Force: The perpendicular contact force exerted by a surface.

Work, Energy, and Power

Work and Kinetic Energy

Work is done when a force causes displacement. Kinetic energy is the energy of motion.

• Work: $W = \vec{F} \cdot \vec{d} = Fd\cos\theta$

• Kinetic Energy: $KE = \frac{1}{2}mv^2$

• Work-Energy Theorem: $W_{net} = \Delta KE$

Potential Energy and Conservation of Energy

• Gravitational Potential Energy: $U = mgh$

• Conservation of Mechanical Energy: $E_{mech, i} = E_{mech, f}$ (if no non-conservative forces)

Problem-Solving Strategies

Dimensional Analysis

Checking the dimensions of physical quantities helps verify equations and solutions.

• Acceleration: $[a] = LT^{-2}$

• Velocity: $[v] = LT^{-1}$

• Force: $[F] = MLT^{-2}$

Example Applications

• Elevator Problem: When the cable breaks, the mass of the person does not change; only the forces acting on them do.

• Braking Car: Use kinematic equations to find time and acceleration when a car comes to rest under constant deceleration.

• Work Done by Friction: The net work done on a car slowing down is negative, as friction opposes motion.

• Projectile Drop: The time to reach the ground depends only on vertical motion; horizontal distance is found using $x = v_{x} t$.

Summary Table: Key Equations

Concept	Equation
Displacement	$\Delta x = x_f - x_i$
Velocity	$v = \frac{\Delta x}{\Delta t}$
Acceleration	$a = \frac{\Delta v}{\Delta t}$
Newton's 2nd Law	$\sum \vec{F} = m \vec{a}$
Kinetic Energy	$KE = \frac{1}{2}mv^2$
Work	$W = Fd\cos\theta$
Work-Energy Theorem	$W_{net} = \Delta KE$
Potential Energy	$U = mgh$
Dot Product	$\vec{A} \cdot \vec{B} = |A||B|\cos\theta$

Additional info:

• Some context and explanations have been expanded for clarity and completeness.

• Tables have been recreated and summarized for the most relevant unit conversions and equations.