Essential Dynamics Formulas Cheat Sheet
Master the fundamental principles of dynamics by having all key formulas for motion, forces, and energy readily accessible for quick reference and problem-solving.
Core Principles
- Kinematics: Describes motion without considering its causes (forces). Key variables are displacement, velocity, acceleration, and time.
- Kinetics: Relates motion to its causes, primarily forces and mass. Newton's Laws are central here.
- Work and Energy: Deals with energy transformations and conservation, offering an alternative approach to kinetics problems.
- Momentum and Impulse: Focuses on the effects of forces over time, particularly useful in collision problems.
Formulas
- Constant Acceleration Kinematics (1D): $v_f = v_i + at$
- Constant Acceleration Kinematics (1D): $\Delta x = v_i t + \frac{1}{2}at^2$
- Constant Acceleration Kinematics (1D): $v_f^2 = v_i^2 + 2a\Delta x$
- Constant Acceleration Kinematics (2D/3D): $\vec{r}_f = \vec{r}_i + \vec{v}_i t + \frac{1}{2}\vec{a}t^2$
- Constant Acceleration Kinematics (2D/3D): $\vec{v}_f = \vec{v}_i + \vec{a}t$
- Newton's Second Law: $\sum \vec{F} = m\vec{a}$
- Weight: $W = mg$
- Work Done by Constant Force: $W = \vec{F} \cdot \vec{d} = Fd\cos\theta$
- Work-Energy Theorem: $W_{net} = \Delta K = K_f - K_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$
- Kinetic Energy: $K = \frac{1}{2}mv^2$
- Potential Energy (Gravitational): $U_g = mgh$
- Conservation of Mechanical Energy: $E_i = E_f \implies K_i + U_i = K_f + U_f$
- Power (Average): $P_{avg} = \frac{W}{\Delta t}$
- Power (Instantaneous): $P = \vec{F} \cdot \vec{v}$
- Linear Momentum: $\vec{p} = m\vec{v}$
- Impulse: $\vec{J} = \int_{t_i}^{t_f} \vec{F}(t) dt = \Delta \vec{p} = \vec{p}_f - \vec{p}_i$
- Impulse-Momentum Theorem: $\vec{J} = \vec{F}_{avg} \Delta t = \Delta \vec{p}$
- Conservation of Linear Momentum: $\sum \vec{p}_i = \sum \vec{p}_f$ (for isolated systems)
- Centripetal Acceleration: $a_c = \frac{v^2}{r}$
- Centripetal Force: $F_c = ma_c = \frac{mv^2}{r}$
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