Physics 1: Mechanics – Key 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 used in mechanics and related topics.

• Length: 1 m = 100 cm = 1000 mm = 39.37 in = 3.281 ft

• Area: 1 m2 = 104 cm2 = 1550 in2

• Volume: 1 m3 = 106 cm3 = 1000 L

• Time: 1 min = 60 s; 1 h = 3600 s

• Speed: 1 m/s = 3.6 km/h = 2.237 mi/h

• Acceleration: 1 m/s2 = 3.281 ft/s2

• Mass: 1 kg = 2.205 lb = 1000 g

• 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 = 0.7376 ft·lb/s

Example: To convert 5 m/s to km/h: 5 m/s × 3.6 = 18 km/h.

Vectors and Kinematics

Vector Operations

• Vector Addition: $\vec{C} = \vec{A} + \vec{B}$

• Magnitude of a Vector: $|\vec{A}| = \sqrt{A_x^2 + A_y^2}$

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

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

Example: If $\vec{A} = (3, 4)$ and $\vec{B} = (1, 2)$, then $\vec{C} = (4, 6)$ and $|\vec{C}| = \sqrt{4^2 + 6^2} = 7.21$.

Motion in One and Two Dimensions

• 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: Horizontal and vertical motions are independent.

  • Horizontal: $x = v_{0x} t$

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

Example: A car decelerates from 13 m/s to 0 in 36 m. Find the time and acceleration using the above equations.

Newton's Laws of Motion

Fundamental Laws

• First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net 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 Diagrams: Visual representations of all forces acting on an object.

• Friction:

  • Kinetic: $f_k = \mu_k N$

  • Static: $f_s \leq \mu_s N$

• Tension and Normal Forces: Tension acts along ropes; normal force is perpendicular to surfaces.

• Uniform Circular Motion: $a_c = \frac{v^2}{r}$

Example: Calculating the tension in a rope connecting two blocks, or the normal force on a block on a surface.

Work, Energy, and Power

Work and Kinetic Energy

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

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

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

Example: If a car's speed is halved, its kinetic energy becomes one-fourth of the original value.

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

General Steps

1. Identify knowns and unknowns.

2. Draw diagrams (e.g., free body diagrams for forces).

3. Choose appropriate equations.

4. Solve algebraically before substituting numbers.

5. Check units and reasonableness of answers.

Sample Table: Common Unit Conversions

Quantity	SI Unit	Other Units	Conversion Factor
Length	meter (m)	inch (in), foot (ft)	1 m = 39.37 in = 3.281 ft
Mass	kilogram (kg)	pound (lb)	1 kg = 2.205 lb
Force	newton (N)	pound-force (lbf)	1 N = 0.225 lbf
Energy	joule (J)	calorie (cal), ft·lb	1 J = 0.239 cal = 0.738 ft·lb
Power	watt (W)	horsepower (hp)	1 W = 0.00134 hp

Key Definitions

• Acceleration: The rate of change of velocity with respect to time. SI unit: m/s2.

• Force: An interaction that changes the motion of an object. SI unit: newton (N).

• Work: The product of force and displacement in the direction of the force.

• Kinetic Energy: The energy of motion, proportional to mass and the square of velocity.

• Potential Energy: Stored energy due to position or configuration.

Additional info:

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

• Sample problems and strategies are based on standard introductory physics curricula.