Dynamics

Overview

Engineering reference data for Dynamics in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Symbol	Description	Unit
$x$	Input value	—
$y$	Output value	—
$k$	Conversion factor	—

Acceleration

Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction.

$a = \frac{\Delta v}{\Delta t}$

Angular Motion

For rotating bodies, angular acceleration ($\alpha$) is the rate of change of angular velocity ($\omega$). Power ($P$) and torque ($\tau$) are related through angular velocity.

$P = \tau \cdot \omega$ $\alpha = \frac{\Delta \omega}{\Delta t}$

Centripetal and Centrifugal Acceleration

For an object moving in a circular path with radius $r$ and tangential velocity $v$, the centripetal acceleration directed towards the center of the circle is:

$a_c = \frac{v^2}{r}$

Centrifugal force is the apparent outward force felt in a rotating reference frame, with magnitude:

$F_{cf} = m \cdot a_c = \frac{m v^2}{r}$

Kinetic Energy

The kinetic energy ($KE$) of an object depends on its mass ($m$) and velocity ($v$). For rotational motion, it also depends on the moment of inertia ($I$) and angular velocity ($\omega$).

Translational: $KE_{trans} = \frac{1}{2} m v^2$

Rotational: $KE_{rot} = \frac{1}{2} I \omega^2$

Impact Force

The average impact force ($F$) experienced by an object during a collision can be estimated from its change in momentum ($\Delta p$) and the duration of the impact ($\Delta t$).

$F = \frac{\Delta p}{\Delta t} = \frac{m \Delta v}{\Delta t}$

Related Topics

The field of dynamics includes many specialized applications. Some key topics from the original page include:

• Projectile Motion: Motion under gravity in two dimensions.
• Harmonic Oscillator: Systems undergoing periodic motion, like springs and pendulums.
• Gravitational Force: The force of attraction between masses, described by Newton's Law of Universal Gravitation.
• Machines & Levers: Analysis of forces, effort, and movement ratios in simple machines.

References

• Original Source