PH101 Final Test Formula Sheet – Core Physics Equations and Constants

Core Physics Equations and Constants

Introduction

This formula sheet summarizes essential equations and constants for introductory college physics, covering topics such as kinematics, dynamics, energy, momentum, rotational motion, and basic constants. These formulas are foundational for solving a wide range of physics problems.

Kinematics in One and Two Dimensions

• Position as a function of time: $x = x_0 + v_0 t + \frac{1}{2} a t^2$

• Velocity as a function of time: $v = v_0 + a t$

• Velocity squared: $v^2 = v_0^2 + 2a(x - x_0)$

• Average velocity: $\bar{v} = \frac{v_0 + v}{2}$

• Displacement (constant velocity): $x = x_0 + v t$

Projectile Motion

• Horizontal displacement: $x = v_{0x} t$

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

• Horizontal velocity: $v_x = v_{0x}$

• Vertical velocity: $v_y = v_{0y} - g t$

Newton's Laws and Forces

• Newton's Second Law: $F = m a$

• Weight: $w = m g$

• Friction force: $f = \mu N$

• Gravitational force: $F_g = G \frac{m_1 m_2}{r^2}$

Work, Energy, and Power

• Kinetic energy: $K = \frac{1}{2} m v^2$

• Potential energy (gravity): $U_g = m g h$

• Work: $W = F d \cos \theta$

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

• Power: $P = \frac{W}{t}$

Momentum and Collisions

• Momentum: $p = m v$

• Impulse: $J = F \Delta t$

• Conservation of momentum: $m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$

Rotational Motion

• Angular displacement: $\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2$

• Angular velocity: $\omega = \omega_0 + \alpha t$

• Angular acceleration: $\alpha = \frac{\omega - \omega_0}{t}$

• Moment of inertia (point mass): $I = m r^2$

• Rotational kinetic energy: $K_{rot} = \frac{1}{2} I \omega^2$

• Torque: $\tau = r F \sin \theta$

• Newton's Second Law for rotation: $\tau = I \alpha$

Gravitation and Circular Motion

• Gravitational force: $F_g = G \frac{m_1 m_2}{r^2}$

• Centripetal acceleration: $a_c = \frac{v^2}{r}$

• Centripetal force: $F_c = m a_c = m \frac{v^2}{r}$

Other Helpful Equations and Constants

Equation/Constant	Description
$a = \frac{v_f - v_i}{t}$	Average acceleration
$\sin \theta = \frac{opposite}{hypotenuse}$	Trigonometric identity
$v_{avg} = \frac{\Delta x}{\Delta t}$	Average velocity
$g = 9.8\ \mathrm{m/s^2}$	Acceleration due to gravity
$G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2/kg^2}$	Universal gravitational constant
$1\ \mathrm{revolution} = 2\pi\ \mathrm{radians}$	Angle conversion
$1\ \mathrm{revolution\ per\ minute} = \frac{2\pi}{60}\ \mathrm{radians\ per\ second}$	Angular speed conversion

Additional info:

• These formulas are applicable to a wide range of introductory physics problems, including those involving linear and rotational motion, energy, and forces.

• Students should be familiar with the use and manipulation of these equations for problem-solving and conceptual understanding.